Exploring household food security through institutional factors: A statistical and mathematical analysis

Abstract

Achieving household food security is the tumbling issue of the century. This article explores the factors affecting household food security and solutions by utilizing a synergy of statistical and mathematical models. The methodology section is divided into two portions namely sociological and mathematical methods. Sociologically, 379 household heads were interviewed through structured questions and further analyzed in terms of descriptive and binary logistic regression. The study found that 4 independent variables (poverty, poor governance, militancy, and social stratification) showed a significant association (P = 0.000) to explain variations in the dependent variable (household FS). The Omnibus test value (χ²= 102.386; P = 0.000) demonstrated that the test for the entire model against constant was statistically significant. Therefore, the set of predictor variables could better distinguish the variation in household FS. The Nagelkerke’s R Square (R² = .333) helps to interpret that the prediction variable and the group variables had a strong relationship. Moreover, 23% to 33% variation in FS was explained by the grouping variables (Cox and Snell R² = 0.237 and Nagelkerke’s R² = 0.333). The significant value of Wald test results for each variable confirmed that the grouping variables (poor governance P = 0.004, militancy P = 0.000, social stratification P = 0.021 and poverty P = 0.000) significantly predicted FS at the household level. Mathematically, all the statistics were validated further through the application of spherical fuzzy mathematics (TOPIS and MADM) to explore what factors are affecting household FS. Thus, the study found that F₃ (poverty) > F₂ (militancy) > F₄ (social stratification) > F1 (poor governance) respectively. Thus, it could be concluded from these findings that the prevalence of poverty dysfunctional all the channels of household FS at the macro and micro levels. Therefore, a sound and workable model to eradicate poverty in the study area by ensuring social safety nets for the locals was put forward some of the policy implications for the government are the order of the day.

Keywords

Food security militancy poor governance social stratification poverty logistic regression TOPIS MADM spherical fuzzy set

1 Introduction

Food security (FS) exists “when all people at all times have physical, economic, and social access to sufficient, safe, and nutritious food, essential for meeting their dietary needs and food preferences for an active and healthy life” [38]. It could be deduced from this definition that FS is a global phenomenon, which encompasses accessibility, affordability, utilization, and stability [53]. All these attributes are interconnected with each other and deficiency in any one of them leads to food insecurity (FI) [39]. FI is the antithesis of FS, which is dichotomous and can be either chronic or transient. For a household to qualify as having chronic food insecurity (CFI), it must have adequate assets or income to satisfy its food demands. Transient food insecurity (TFI), on the other hand, is associated with the current economic system’s production turbulence as having limited capabilities or as the abrupt result of any fault lines that have arisen. This predicament is usually caused by typical distribution and consumption procedures involving items and services. Such anomalies always offer a dismal portrait of a poor nutritional status, frequently as a result of recurrent or periodic abnormalities indicating a deteriorating economic system. When “people are forced to endure starvation and famine,” this circumstance occurs. If a country is unable to produce adequate food for the appropriate sections of the population in sufficient numbers, it may find itself in this predicament [2].

1.1 Background of the study

Albeit, social and economic development, the global burden of malnutrition is still too high, with current figures indicating that 800 million people are undernourished, 780 million of them inhabit in Low-to-Middle Income Countries, mostly in Sub-Saharan Africa and South Asia. In 2015, inadequate food intake and poor dietary quality were directly or indirectly responsible for causing ill health, with six of the top 11 global risk factors being associated with dietary imbalances [48]. In 2017, dietary risk factors were responsible for 11 million deaths and 255 million Disability-Adjusted Life Years (DALYs) [15]. Likewise, recent reports suggested that in 2019, 144 million children under the age of 5 were stunted (short for their age), 47 million were wasted (underweight for their height), and 38 million were overweight (abnormal or excessive bodyweight) [71]. Worldwide, 38.9% of the adult population is either overweight or obese, and the prevalence of obesity among adults is rising [20]. Despite the fact that women have a higher prevalence of obesity (15.1%) than males (11%), millions of women around the world are still underweight and an estimated one-third of women of reproductive age have anemia [20].

Globally, the Global Hunger Index has decreased from 35.2% in 1992 to 21.8% in 2017, whereas the hunger index in South Asia has decreased from 46.3% in 1992 to 30.9% in 2017, which is regarded as severe [73]. Although Pakistan’s hunger index has decreased from 42.7% to 32.6%, it still ranks 106th, one point above Afghanistan. Consequently, maintaining FS should be a Pakistani priority worthy of consideration [39]. Based on a National Nutritional Survey which was conducted in 2018, it was found that 36.9 percent of the total population of Pakistan is inclined towards FI due to the persistent nature of poverty and vulnerabilities, especially women’s access to adequate and healthy food. The survey further showed that 40.2% of under-five-year-old children were stunted, followed by 48.4% of children who depended exclusively on breastfeeding, 17.7% were wasted, and 29% of children were underweight. In addition, more than half (53.7%) of Pakistani children are anemic and 5.7% are in severe condition. Women between the ages of 15 and 49 had a double burden of malnutrition, with 14.4% suffering from malnutrition. Anemic women made up approximately 41.7 percent of reproductive-age women, with differences in proportions between urban and rural areas; urban women made up 40.2% of anemic women, while rural women made up 44.3% [52]. The following Fig. 1 further highlights those districts that come under the domain of crisis. In Baluchistan province 15 districts come under the domain of crisis as of April 2022- Jun 2022 respectively. In Khyber Pakhtunkhwa province 8 districts namely Muhamand, Bajaur, Khyber, Kurrum, Orakzai, North and South Waziristan, and Torghar come under the crisis period.

Fig. 1

Integrated Food Security Phase Classification (2023).

1.2 Sociological review

Keeping in view the institutional and multidimensional nature of FS various factors correspond to FI at the household level in general while in the study area in particular. However, the present study will only clarify the four major factors namely poverty, militancy, social stratification, and poor governance resulting in FI at the household level in the Torghar area of Northern KP Pakistan. Each of the factors is clarified below.

1.2.1 Poverty

Ending poverty in all forms by 2030 is the first goal of the United Nations Sustainable Development Goals (SDGs). The World Bank defines poverty as a multidimensional concept related to low income and consumption, low levels of education and health conditions, and limited nutritional intake and access to basic needs infrastructure [26, 27]. Over the last two decades, poverty has declined from 61.6% in 1998–99 to 21.5% in 2018–19 in Pakistan. Whereas poverty has decreased from 47.4% to 10.7% in urban areas and from 67.5% to 27.6% in rural areas, during the same time period. However, the pace at which poverty has been declining is not consistent [69]. With regards to persistent poverty is defined as a person living in a household experiencing poverty (a net household income below 60% of the median in that year) for at least 3 of the past 4 years [68]. Likewise, a person whose income falls below a pre-defined poverty line is usually counted as poor. In European studies, poverty lines tend to be defined relative to average or median income (for example, 50–60% of median income), whereas in US studies poverty lines are often defined as an absolute value (the official US poverty line is based on the cost of a defined basket of food) [12]. In addition, per Asian Development Bank (2018) reported that, in Pakistan, 21.9% proportion of the population lives below the National Poverty Line. Likewise, the poverty headcount ratio was 64.3% in 2001, which declined to 50.4% in 2005, and 29.5% in 2013. Likewise, Pakistan’s poverty rate for 2018 was 77.60%, a 1.2% increase from 2015 respectively [43].

The problem of FI, according to the researchers, is not related to the increased production and productivity of farmers but rather to poverty. Amartya Sen, a Nobel Prize in Economics from India in 1998, stated that FI is caused by problems in food distribution [29]. FI has a long history of association with poverty, as regions with persistent poverty have higher levels of malnutrition [65]. Poverty has varied effects on humans, including poor nutrition, disease susceptibility, poor levels of production, and hindered mental and physical growth. In addition, persons in poverty lack access to necessities such as nourishing food, a stable climate, proper housing, and sufficient health care [57]. Various researchers namely Mahadevan and Suardi [45], Gundersen et al. [31] and Selicati and Cardinale [63] have resulted in a significant correlation between poverty and FI. Likewise, many factors associated with FI, such as illness, nutritional deficiencies, joblessness, a lower standard of education, a rising cost of living, a lack of access to land, a lack of alternative professions, corruption, and single-parent households, are the primary causes of greater FI in the developing countries. All the causes and impacts of FI listed above contribute to poverty [10]. Likewise, the two go hand in hand in a very fundamental way: poverty and hunger. Because of the instability and unfavourable conditions that poverty creates, malnutrition may become even more of a problem. Inadequate, and nutritional, food is often unavailable due to financial restrictions [57].

1.2.2 Militancy

FI and militancy are also directly linked with each other. Conflict-affected settings as evidence suggest that there is an endogenous relationship between conflict and severe food crisis [22, 37]. Not only do 60% of the world’s hungry people live in countries experiencing conflict [25] but also prevalence of undernourishment in conflict-affected low and middle-income countries are between 1.4 and 4.4% points higher on average as compared to countries in the same income category that are not affected by conflict [32]. Directly, conflict may increase food expenditure [72], reduce the diversification of the household diet [64], and decrease household FS [16] through conflict-associated acts, such as occupation of farmlands, destruction of livestock, and theft of crops. Indirectly, the conflict impacts FI through various channels, such as disrupting agricultural production [60] and affecting farmers’ investment decisions [4]. Furthermore, the relationship between conflict and FI is marred by conflict-affected households often also experiencing non-conflict shocks namely economic dysfunctionalism [42]. In these settings, households may be adopting coping strategies that may include consuming less healthy food with higher calories or a less diverse diet, to survive the conflict [4]. These coping strategies, as suggested by studies, may lead to a lower level of household dietary diversity to increase caloric intake and mitigate overall FI.

In a nutshell, conflicts worsen all the institutional affairs of inhabitants at the macro and micro levels. A related discussion has focused on international arms imports [39]. Several contend that arms imports create a budget trade-off in terms of reduced education, nutrition, and health spending, thus reducing social welfare [49]. Others point to destabilizing consequences of arms imports, arguing that they set off regional arms races that lead to international war and increase the violence of internal conflicts [41], for example, they argue that Cold War regional arms races destabilized Somalia, precipitating a civil war that created widespread famine. Wolpin [74] contends that arms imports promote other socially harmful economic policies, such as encouragement of foreign investment and the export of cash crops, fostering internal repression, and cementing international alliances with foreign powers (including foreign investors and banks that create distorted growth and reduce social welfare [74]. Several studies have found that arms imports reduce economic growth and political rights as well as increase infant mortality [40].

1.2.3 Social stratification

Social class determines food preferences and access to nutritious food. Numerous historical and sociological studies have long emphasized the intricate relationship between FS and social class, which encompasses ethnic origin, gender, and age, among other variables [11]. FI is damaging to working-class individuals [30]. Social class, like social and cultural preferences for food, influences, and shapes food practices and preferences. It is a class that shapes food behaviours by making resources available for not only purchasing, preparing, and eating, but also for tastes in particular ways and situations, as [35, 38] witnessed.

Many research studies have been conducted, and women have been severely harmed as a result of decision-making power on farms and agricultural assets, as demonstrated by the works of Dewing et al. [21] and Mfundo [50]. Despite the fact that numerous studies have demonstrated that women are a source of food for their families and have played a positive role in the process of household FS, as well as having a positive impact on children’s nutritional status, women are often overlooked in terms of their hygienic practices [8 , 36]. FI is also influenced by the head (gender) of the home, as demonstrated by husband deaths, family separations, husband migration, and their wives’ physical access to agricultural land as well as their wives’ agricultural output [3]. According to studies by the United Nations Economic and Social Council (2007) and the World Food Program (2009), there was also a significant degree of gender inequality among both sexes as a result of gender-based malnutrition [25]. As a result of economic development, many of women in India continue to be deprived of adequate nutritional security [25].

1.2.4 Poor governance

Since the last few decades, Pakistani governments have struggled with poor governance, which has been exacerbated by a high level of corruption in virtually every sector, impeding social and economic development. One of the corruption aspects is smuggling, where Pakistan’s government loses 2 billion dollars a year in wheat grains, which are, smuggled to Afghanistan, and other food commodities due to sugar millers and political mafias of flour were just ruined and the price hiked in the 2008 food crisis in Pakistan [17]. Likewise, about 1800 tons of flour are trafficked to Afghanistan each month over the northern areas of tribal regions [66]. Due to lack of strong law enforcement agencies at the border of Pakistan with other countries, especially Afghanistan, with tribal areas, could lead to more smuggling processes. As a result, 5% of Pakistan’s wheat, 10% of its rice, and 11% of its sugar production are smuggled to other countries via informal means without paying taxes to the relevant bodies [33].

As per the report, Pakistan is ranked 139th out of 180 countries, which are hopelessly corrupt based on the 2009 report the Corruption Perception Index. As such, the report of 2009 stated that the same year, a Benazir Tractor Scheme program was also initiated by the government of Pakistan, by selecting small farmers throughout Pakistan randomly, but not giving their concerns to their concerned farmers, regardless of whether they were given to their landlords or parliamentarians (48 family members), which robbed the poor people in a miserable situation [46]. On the other hand, Pakistan’s military exploited all the situations, particularly where the masses indulged in inflation, and the government of Pakistan in 2010 diverted 30% of the social sector budget into security expenditures, where policymakers were hindered and not ensured by the help of their masses [37].

1.3 Synthesis of mathematical structure

Food security is a multifaceted problem that is of crucial importance all over the world, and the sustained attainment of this goal is dependent on the lives of millions of people. In light of this, it is very necessary to investigate novel approaches that might deepen our comprehension of this intricate problem. This paper digs into a mathematical study that utilizes the capability of the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) technique to handle challenges associated with Multi-Attribute Decision-Making (MADM) [9 , 77]. All of this is accomplished inside the complex framework of spherical fuzzy structures. The ability of the TOPSIS approach to promote logical decision-making in the face of various criteria is what drives its employment in the field of FS analysis. This is what motivates the utilization of the method. As a robust method for MADM, TOPSIS allows the systematic assessment of alternatives and the selection of the best-suited solutions based on a variety of characteristics. When applied to the issue of FS, which is a multifaceted problem determined by a wide variety of linked elements, such as availability, accessibility, use, and stability, this strategy becomes especially relevant.

The incorporation of spherical fuzzy structures into the TOPSIS approach is what distinguishes this evaluation from others of its kind. The usual idea of fuzzy sets is expanded upon by spherical fuzzy sets, which include both membership grades and uncertainty the spherical fuzzy structure is given in Fig. 2. As a result, spherical fuzzy sets provide a more thorough representation of information that is imprecise and uncertain. In the context of FS, where data might be characterized by ambiguity, vagueness, and subjectivity, the incorporation of spherical fuzzy structures enhances the decision-making process by collecting and handling a wider spectrum of real-world complications. This allows for a more comprehensive understanding of the situation at hand. Within the framework of an investigation into FS, the mathematical review takes a methodical and methodical approach to navigating the use of the TOPSIS technique. The procedures involved in building the choice matrix, normalizing the matrix, identifying the weighted normalized matrix, calculating the ideal and anti-ideal solutions, and eventually getting the relative closeness coefficient for ranking alternatives are all outlined in this section. The evaluation takes into consideration the possibility of uncertainty and imprecision by using these processes in combination with spherical fuzzy structures. This helps to ensure a more realistic portrayal of the underlying complexities that are present within food security assessments. In conclusion, the consolidation of this mathematical analysis represents a major step forward in the investigation of FS issues. In the face of several obstacles posed by MADM, the combination of the TOPSIS approach with spherical fuzzy structures offers a potentially fruitful path toward the development of robust decision-making. As the state of global FS continues to shift in response to a wide range of socioeconomic and environmental variables, novel research approaches like these play an essential part in advancing our understanding of the problem and paving the way for better informed policy actions.

Fig. 2

Updation of spherical fuzzy set.

1.4 Motivation and justification for exploring FS using the TOPSIS method within the framework of spherical fuzzy structures to address MADM issues

The extant literature endeavours to investigate FS in the context of the United Nations’ Sustainable Development Goals for 2030, specifically Goals 1 and 2.1. The primary objective of this research is to obtain a sociological perspective on the data through the utilization of descriptive and inferential statistical tools, along with mathematical validation, in order to achieve corroboration. The statistical findings were subsequently utilized in the realm of mathematical modelling, which is a subfield within the discipline of mathematics in sociology. Additionally, a multi-criteria decision-making (MCDM) model that utilizes spherical fuzzy sets to analyze the factors influencing the FS was also included in the study. The process of evaluating and selecting the optimal choice based on assessment criteria and alternatives was conducted using MCDM. The independent variables that affect FS were assessed and a real-world case study was utilized to demonstrate the practicality of the proposed methodology. MCDM has been employed across different fields to determine the most optimal solutions [1 , 76]. However, it is the 2^nd attempt to probe MCDM in conjunction with spherical fuzzy sets to develop a decision support system based on fuzzy sets while firstly described by Khan et al. [38]. However, fuzzy sets have limits. A downside is their inability to describe a neutral state without desire or aversion. To incorporate ambiguities or inaccurate information about membership degrees, Atanassov [7] invented Intuitionistic Fuzzy Sets (IFS). Atanassov’s IFSs enhance Zadeh’s fuzzy sets by formulating IFS with two parameters, membership degree and non-membership degree. The important requirement is that for any element membership and non-membership the degree must be between 0 and 1. Over the last several decades, researchers have effectively used IFS for medical diagnosis, cluster analysis, decision-making [61] and pattern recognition [18]. After that, IFS membership and non-membership degrees were expressed using interval values instead of numerals.

Real-world choice situations commonly include attributes with cumulative membership degrees greater than 1, making IFS difficult to use. Yager [75] presented Pythagorean fuzzy sets (PyFS), an extension of IFS that keeps the total of squared membership degrees within 1. However, researchers have effectively used IFS for MCDM [56], but IFS and PyFS fail to compute neutral membership degrees independently in cases that need them. To handle these difficult scenarios, [19] created Picture Fuzzy Sets (PFS) with three indices: membership degree, neutral-membership degree, and non-membership degree, subject to a sum constraint of 1. IFS and PyFS are less adept at regulating fuzziness and ambiguity than PFS. Several researchers have successfully used PFS in strategic decision-making, attribute choice, and pattern discovery in recent years [34].

PFS cannot handle real-life problems when the sum of constraints > 1. In this circumstance, PFS cannot succeed. We use an alternative with 1/4 support, 3/4 opposition, and 2/4 membership. This is not submitted for PFS since their total exceeds 1. Spherical fuzzy sets (SFSs) [6] are suggested as a generalization of PFS under these settings. SFS membership degrees meet the requirement sum of squares of the constraints lies between 0 and 1. Researchers have effectively used SFSs for MCDM such as [5, 58]. We used SFSs which is the extension of fuzzy set, IFS, PyFS, and PFS in this manuscript for MCDM problems.

FS is a worldwide phenomenon that encompasses a multidisciplinary and institutional approach. As, a single topic or body of knowledge cannot eradicate this problem, namely FI, from the planet. In light of the aforementioned social and mathematical literature, the present work emphasizes a synthesis of both fields relevant to FS. It is the second attempt to gain statistical insight into the factors influencing household FS, which was then validated through mathematical modelling and corroborated by an addition to the existing body of knowledge, i.e., sociology of agriculture through the lens of mathematical sociology. Theoretically and practically, the prevalence of poverty, militancy, social stratification, and poor governance influence household FS at the macro and micro levels. Therefore, a binary logistic regression model was used to dictate the influence of these parameters. Whereas as MCDM model further validates anyone of the mentioned variables.

1.5 Objectives

1. To determine the influence of factors namely militancy, social stratification, poor governance, and poverty affecting household FS through the application of binary logistic regression analysis.

2. To validate the statistical results in terms of mathematical modelling.

3. To explore which factors are likely to deteriorate the household FS through a spherical fuzzy decision-making approach.

4. To suggest policy recommendations and future suggestions in light of the present study.

1.6 Organization of the rest of the paper

The rest of the paper is organized as follows. In section 2, we discussed sociological methods and a mathematical TOPSIS method with its flow chart. Section 3 consists of results and discussion of the sociological and mathematical methods with their graphical representations. A sensitivity analysis is also performed in this section. Furthermore, we also compared our results with other MCDM techniques. In section 4, we conclude the whole study.

2 Methods

This section consists of two methods, namely sociological and mathematical, which are discussed below.

2.1 Sociological methods

A cross-sectional and perceptional-based study was conducted with the help of a pre-structured interview schedule from 379 household heads randomly as per Sekeran [62] criteria in District Torghar Northern KP Pakistan. Further, the selected sample size was proportionally allocated to each stratum i.e., tehsils as per the Bowley [14] formula (See Table 1). District Torghar has a 0.217 Human Development Index (HDI) means a low level of HDI as per a 2017 report. There are no urban inhabitants in the study area and all the inhabitants were rural in nature [55].

Table 1
Data collection by author’s

Name of tehsils Household Sample

head (N) size (n)

Judba 14972 214

Khander 11492 165

Grand Total 26464 379

Name of tehsils	Household	Sample
Judba	14972	214
Khander	11492	165
Grand Total	26464	379

Furthermore, the primary data were analyzed through the application of statistical tests, i.e., descriptive and binary logistic regression analysis. For measuring FS, the Likert scale procedure was adopted sociologically to determine the attitudes of sampled respondents over the study dynamics. Four independent variables namely poverty, militancy, social stratification, and poor governance were extracted from various research, and household FS is a dependent variable for the current study. Before, the indexation method all variables statement is nexus into a single variable, a reliability test statistic was used to show whether the attributes are internally consistent or not. Therefore, using Cronbach’s alpha coefficient of more than 0.6 was indexed, while the rest of the variables were not selected due to alpha value. For binary logistic regression analysis all independent variables with Cronbach’s Alpha value are portrayed as i.e., poverty (.64), militancy (.66), social stratification (.63), and poor governance (.65), and dependent variable i.e., household FS (.72) were indexed through SPSS (Statistical program for quantitative data analysis, 26 version) respectively.

2.2 Mathematical methods

2.2.1 MADM problems by using the TOPSIS method for SFNs

In this section, a method for solving the MADM problems by utilizing the TOPSIS method for the spherical fuzzy information is established.

Step 1. Suppose that any finite collection F ={ F₁, F₂, … , F_m } of m alternatives and any finite collection G ={ g₁, g₂, … , g_n } of n attributes. Let J_a = [J_ajk] = [ 〈P_ajk, I_ajk, N_ajk〉] _m×n is a decision matrix as represented in Table 2.

Table 2
Decision matrix

J _a g ₁ g ₂ … g _n

F ₁ 〈P_a11, I_a11, N_a11〉〈P_a12, I_a12, N_a12〉 … 〈P_a1n, I_a1n, N_a1n〉

F ₂ 〈P_a21, I_a21, N_a21〉〈P_a22, I_a22, N_a22〉 … 〈P_a2n, I_a2n, N_a2n〉

· · · · ·

· · · · ·

· · · · ·

F _m 〈 P_am1, I_am1, N_am1〉〈P_am2, I_am2, N_am2〉 … 〈P_amn, I_amn, N_amn 〉

J _a	g ₁	g ₂	…	g _n
F ₁	〈P_a11, I_a11, N_a11〉	〈P_a12, I_a12, N_a12〉	…	〈P_a1n, I_a1n, N_a1n〉
F ₂	〈P_a21, I_a21, N_a21〉	〈P_a22, I_a22, N_a22〉	…	〈P_a2n, I_a2n, N_a2n〉
·	·	·	·	·
·	·	·	·	·
·	·	·	·	·
F _m	〈 P_am1, I_am1, N_am1〉	〈P_am2, I_am2, N_am2〉	…	〈P_amn, I_amn, N_amn 〉

Where j is the alternative index and k is the criterion index.

Step 2. Normalized the given Decision Matrix. In extensively, there are attributes that have two types (1) benefit criteria and (2) cost criteria.

If the given criteria is a cost type then we use given below equation to modify the cost criteria into benefit criteria, J_a^c ={ 〈N_ajk, I_ajk, P_ajk〉 }, where J_a^c is the complement of J_a. If the given criteria are benefit type, then there is no need to be normalized.

Step 3. We use the given below equations to calculate the positive ideal solution (PIS) J⁺ and negative ideal solution (NIS) J^-. $\begin{matrix} J^{+} = {{J_{1}}^{+}, {J_{2}}^{+}, \dots {J_{n}}^{+}} = {(P_{1}^{+}, I_{1}^{+}, N_{1}^{+}), (P_{2}^{+}, I_{2}^{+}, N_{2}^{+}), \dots, (P_{n}^{+}, I_{n}^{+}, N_{n}^{+})} \\ = {max_{j} P_{ajk}, min_{j} I_{ajk}, min_{j} N_{ajk} | k = 1, 2, \dots n} \end{matrix}$ (1) $\begin{matrix} J^{-} = {{J_{1}}^{-}, {J_{2}}^{-}, \dots {J_{n}}^{-}} = {(P_{1}^{-}, I_{1}^{-}, N_{1}^{-}), (P_{2}^{-}, I_{2}^{-}, N_{2}^{-}), \dots, (P_{n}^{-}, I_{n}^{-}, N_{n}^{-})} \\ = {min_{j} P_{ajk}, min_{j} I_{ajk}, max_{j} N_{ajk} | k = 1, 2, \dots n} \end{matrix}$ (2)

Step 4. In this step, we calculate the Normalized Hamming Distance (NHD) and Normalized Euclidean Distance (NED) from PIS to each alternative F_j (j = 1, 2, …, m) i.e., d_NHD (F_j, J⁺) and d_NED (F_j, J⁺) as follows:

$d_{NHD} (F_{j}, J^{+}) = \frac{1}{n} \sum_{k = 1}^{n} [w_{k} (| P_{ajk} - P_{k}^{+} | + | I_{ajk} - I_{k}^{+} | + | N_{ajk} - N_{k}^{+} |)]$ (3)

$d_{NED} (F_{j}, J^{+}) = {[\frac{1}{n} \sum_{k = 1}^{n} [w_{k} ({| P_{ajk} - P_{k}^{+} |}^{2} + {| I_{ajk} - I_{k}^{+} |}^{2} + {| N_{ajk} - N_{k}^{+} |}^{2})]]}^{1 / 2}$ (4)

Similarly find the distances between NIS to each alternative F_j (j = 1, 2, … , m) i.e., d_NHD (F_j, J^-) and d_NED (F_j, J^-). Here w_k is the weight vectors of criteria.

Step 5. In this step, we use the given below Equations (5) and (6) to find the closeness relation of each alternative F_j (j = 1, 2, …, m).

$l_{NHD} (F_{j}) = (\frac{d_{NHD} (F_{j}, J^{-})}{d_{NHD} (F_{j}, J^{-}) + d_{NHD} (F_{j}, J^{+})} | j = 1, 2, \dots, m)$ (5)

$l_{NED} (F_{j}) = (\frac{d_{NED} (F_{j}, J^{-})}{d_{NED} (F_{j}, J^{-}) + d_{NED} (F_{j}, J^{+})} | j = 1, 2, \dots, m)$ (6)

Step 6. Rank all the alternatives F_j (j = 1, 2, … , m) and select the best one(s) F_j (j = 1, 2, ldots, m). If any alternative has the highest l_NHD (F_j) value, then it is the finest alternative for the decision maker, and similarly for l_NED (F_j) value. The algorithms steps are given in Fig. 3.

Fig. 3

Flowchart of Proposed MCDM Method.

3 Results and discussions

This section further consists of statistical and mathematical findings with their concerned interpretation. First statistical results were interpreted and then those results were further validated by the MCDM approach to highlight the best and suitable factor that corresponds to household FS.

3.1 Sociological results and discussions

In the binary logistic regression model, four independent variables (poverty, poor governance, militancy, and social stratification) showed a significant association (P = 0.000)to explain variations in the dependent variable (household FS). The Omnibus test value (χ² = 102.386; P = 0.000) demonstrated that the test for the entire model against constant was statistically significant. Therefore, the set of predictor variables could better distinguish the variation in household FS. The Nagelkerke’s R Square (R² = .333) helps to interpret that the prediction variable and the group variables had a strong relationship. Moreover, 23% to 33% variation in FS was explained by the grouping variables (Cox and Snell R² = 0.237 and Nagelkerke’s R² = 0.333). The significant value of Wald test results for each variable confirmed that the grouping variables (poor governance P = 0.004, militancy P = 0.000, social stratification P = 0.021 and poverty P = 0.000) significantly predicted FS at the household level.

The EXP-β value helped to explain and determine the extent of variations in FS under the influence of grouping variables. The model explains that the negative role of poor governance increased the probability of household FI (Exp β = - .912) as shown in Table 3. Based on these findings, it is possible to conclude that poor governance in terms of institutional dysfunction and prevalence of corruption at macro and micro levels in Pakistan deteriorates the household FS situation in the study area. The smuggling of food commodities through the northern borders of Khyber Pakhtunkhwa province and Baluchistan resulted in major inflation which directly influenced the inhabitants of Pakistan. These results were also narrated by Siddiqui [66] and Hussain and Routray [33] further validated that on average 1800 tones flour are smuggled to Afghanistan every month which faced severe consequences for Pakistani citizens. It could be inferred from these results that due to dysfunctional enforcement and customs agencies, the food commodities in terms of wheat (5%), rice (10%) and sugar production (11%) were smuggled to Afghanistan which deteriorated the existing equilibrium of food supply chain in Pakistan. This situation is doubled now due to the poor governance and lack of accountability in the current political system.

Table 3
Influence of poverty, poor governance, social stratification, and militancy on household FS

Independent variables Un-standardized coefficient EXP β Wald test value Sig Omnibus test Model summary

β Std. error Chi-Square Sig Cox & snell R.Sqaure Nagelkerke’s R.Sqaure

Poor Governance –.912 .319 .402 8.144 0.004 102.38 .000 .237 .333

Militancy 1.158 .209 3.182 30.545 0.000

Social stratification –.429 .185 .651 5.358 0.021

Poverty 1.494 .249 4.455 35.953 0.000

Constant –2.667 .707 .069 14.218 0.000

Independent variables	Un-standardized coefficient	EXP β	Wald test value	Sig	Omnibus test	Model summary
Poor Governance	–.912	.319	.402	8.144	0.004	102.38	.000	.237	.333
Militancy	1.158	.209	3.182	30.545	0.000
Social stratification	–.429	.185	.651	5.358	0.021
Poverty	1.494	.249	4.455	35.953	0.000
Constant	–2.667	.707	.069	14.218	0.000

Source: Authors’ Calculation.

The table further explored that a unit control in militancy has increased the likelihood of household FS by 3 times as witnessed Exp (β = 3.182. It could be inferred from these results that controlling the insurgency and militancy ensures the household FS in the study area. It is crystal clear militancy and FS are corresponding and directly linked in nature. A peaceful environment gives hope to the locals to invest in business affairs. On the other hand, militancy disrupted the overall dynamics of life in general while FS in particular. These results were also in line with Khan and Shah [37] conclusion that militancy in Torghar northern area of Pakistan compelled locals to internal migration due to fear of life and starvation. As militancy breeds FI by disrupting the farming and arms import and export spike despite of availability of food. Likewise, Pakistan’s military exploited all the situations, particularly where the masses indulged in inflation, and the government of Pakistan in 2010 diverted 30% of the social sector budget into security expenditures, where policymakers were hindered and not ensured by the help of their masses [37].

Consistent with the above, the table further probed that the severity of social stratification negatively affects household FS as witnessed from EXP (β) = .651. It could be inferred from these results that controlling social stratification increased the probability of household FS by 65% respectively. These results were supported by the findings of Bourdieu [13] and Khan et al. [38] disclosed that social class determines food preferences and access to nutritious food. Numerous historical and sociological studies have long emphasized the intricate relationship between FS and social class, which encompasses ethnic origin, gender, and age, among other variables. FI is damaging to working-class individuals as well, which needs to be further explored through various research.

Lastly, the table explored that a unit control in poverty has increased the likelihood of household FS by 4 times as dictated by the Exp β = 4.45 value. It could be deduced from these findings that, FI and the prevalence of poverty are intermingled and positively correlated with each other. These results were also supported by Mahadevan and Suardi [45] and Mahadevan and Hoang [44] concluded that poverty has varied effects on humans, including poor nutrition, FI, disease susceptibility, poor levels of production, and hindered mental and physical growth. In addition, persons in poverty lack access to necessities such as nourishing food, a stable climate, proper housing, and sufficient health care [57]. Likewise, many factors associated with FI, such as illness, nutritional deficiencies, joblessness, a lower standard of education, a rising cost of living, a lack of access to land, a lack of alternative professions, corruption, and single-parent households, are the primary causes of greater FI than predicted. All of the causes and impacts of FI listed above contribute to poverty [10]. Equally, the two go hand in hand in a very fundamental way: poverty and hunger. Because of the instability and unfavourable conditions that poverty creates, malnutrition may become even more of a problem. Inadequate, and nutritional, food is often unavailable due to financial restrictions [57].

The regression equation based on its calculated coefficients for the model is as: $Y = a + b_{1} X_{1} + b_{2} X_{2} + b_{3} X_{3} + b_{4} X_{4} .$ (7)

Household FS = – 2.667 + –.912 (poor governance) + 1.158 (Militancy) + –.429 (social stratification) + 1.494 (Poverty).

3.2 Mathematical results and discussion

In this subsection, the proposed ranking method is applied to deal with the household food security evaluation problem. Consider a committee of decision-makers to perform the evaluation and select the most suitable household food security, among the four household food security alternatives as F₁= Social Stratification, F₂= Poor Governance, F₃= Prevalence of Poverty, and F₄= Militancy. The decision maker evaluates household food security according to eight different attributes in each category. All the results before regression analysis are presented in Tables 4–7.

Table 4
Frequency and percentage distribution of sampled respondents regarding Poor Governance, Smuggling, and Corruption

S. No Criterion Agree (%) Neutral (%) Disagree (%)

1 Smuggling of food commodities adversely affects the food supply in the area 282(74.4) 81(21.4) 16(4.1)

2 Political instability provokes food insecurity 274(72.3) 71(18.7) 34(9.0)

3 Poor governance and corruption resultantly lead to hunger 261(68.9) 94(24.8) 24(6.3)

4 Smuggling of food resources to neighboring countries imbalance the social fabrics 254(67.0) 88(23.2) 37(9.8)

5 Weak official border control management adversely affects the consistency food provision to the locals. 192(50.7) 93(13.7) 94(24.0)

6 Do you believe that food shortage corresponds to hoarding and may result in food insecurity? 258(68.1) 45(11.9) 76(20.1)

7 Poor harvests, exacerbated by hoarding, caused shortages and contributed to a “serious price crisis.” 224(59.1) 64(16.9) 91(24.0)

8 Food insecurity in Pakistan is a consequence of bad management of the pre and post-harvest of wheat in the agricultural economy 206(54.4) 73(29.3) 100(26.4)

S. No	Criterion	Agree (%)	Neutral (%)	Disagree (%)
1	Smuggling of food commodities adversely affects the food supply in the area	282(74.4)	81(21.4)	16(4.1)
2	Political instability provokes food insecurity	274(72.3)	71(18.7)	34(9.0)
3	Poor governance and corruption resultantly lead to hunger	261(68.9)	94(24.8)	24(6.3)
4	Smuggling of food resources to neighboring countries imbalance the social fabrics	254(67.0)	88(23.2)	37(9.8)
5	Weak official border control management adversely affects the consistency food provision to the locals.	192(50.7)	93(13.7)	94(24.0)
6	Do you believe that food shortage corresponds to hoarding and may result in food insecurity?	258(68.1)	45(11.9)	76(20.1)
7	Poor harvests, exacerbated by hoarding, caused shortages and contributed to a “serious price crisis.”	224(59.1)	64(16.9)	91(24.0)
8	Food insecurity in Pakistan is a consequence of bad management of the pre and post-harvest of wheat in the agricultural economy	206(54.4)	73(29.3)	100(26.4)

Table 5

Frequency and Percentage distribution regarding Militancy and Food Security

S. No	Criterion	Agree (%)	Neutral (%)	Disagree (%)
1	Military insecurity and food insecurity reinforce each other.	170(44.9)	154(40.6)	35(9.2)
2	Military politics impose decisions from the top with no inclusion of the lowest segments of society.	151(39.8)	66(17.4)	139(36.7)
3	A huge military budget restricts the sinking of budget in public sector development.	170(44.9)	154(40.6)	162(42.7)
4	The displacement of the population due to military action in your areas has disrupted the smooth food availability chain.	293(77.3)	38(10.0)	163(34.0)
5	The food crisis has a direct outcome of armed recruitment gangs of the local youth.	144(38.0)	138(36.4)	48(12.7)
6	Insured and uninterrupted support both in cash and kind from militant organizations had upticked the trend of youth recruitment in the organization.	173(45.6)	157(41.4)	97(25.6)
7	Low and limited openings of jobs further deteriorated the youth’s hopes and diverted them to opt for these organizations.	164(43.3)	73(19.3)	49(12.9)
8	Insurgency not only affects the smooth access to food but also endangers the functioning social relationships at both the community and family levels.	245(64.6)	62(16.4)	55(14.5)

Table 6

Frequency and percentage distribution of sampled respondents regarding Poverty and Unemployment

S. No	Criterion	Agree (%)	Neutral (%)	Disagree (%)
1	Inadequate access to food is a fundamental outcome of poverty	230(60.7)	44(11.6)	105(27.7)
2	Poverty leads to corruption which further insecure the individual in access to food	221(58.3)	112(29.6)	46(12.1)
3	Loss of job threatens consistent food security	196(51.7)	29(7.7)	154(40.6)
4	An increase in the price of food items corresponds to a surge in poverty	287(75.7)	25(6.6)	67(17.7)
5	Food and money both exist in the market but are paradoxical in nature	164(43.3)	64(16.9)	151(39.8)
6	Are you agreeing that food is a commodity? This means food is not free from the influence of cash	273(72.0)	106(27.9)	0(0.0)
7	People are left to die not because of lack of food, but because of lack of money to buy food	309(81.5)	18(4.7)	52(13.7)
8	The more money someone possesses enhances the choice of food selection	210(55.4)	60(15.8)	109(28.8)

Table 7

Frequency and percentage distribution of social stratification

S.No	Criterion	Agree (%)	Neutral (%)	Disagree (%)
1	Men are preferred over food provision in comparison to female	227(59.9)	13(3.4)	139(36.7)
2	Social stratification directly affects the nature and frequency of food on sustainable ground	253(66.8)	81(21.6)	44(11.6)
3	Food insecurity and hunger is social injustice and reciprocal in response	234(61.7)	55(14.5)	90(23.7)
4	Various social classes exhibit distinct differences in food behaviour.	250(66.0)	55(14.5)	90(23.7)
5	People not being able to afford and access food because of social stratification	192(50.7)	155(40.9)	32(8.4)
6	Women are more contributing to agriculture than male	157(41.4)	36(9.5)	186(49.1)
7	Men often exploit women in the division of labour	163(43.0)	51(13.5)	164(43.3)
8	Division of labour does favour men as a resultant factor of cultural inclination	184(48.5)	89(23.5)	106(28.0)

Step 1: According to the suitability ratings of four alternatives, F₁, F₂, F₃, F₄ under eight attributes in the form of spherical fuzzy set can be obtained as shown in Table 8.

Table 8

Rating based descriptive statistics from 4–7 tables

J_a	g ₁	g ₂	g ₃	g ₄	g ₅	g ₆	g ₇	g ₈
F ₁	(.599,.034,.367)	(.668,.216,.116)	(.617,.145,.238)	(.617,.145,.238)	(.507,.409,.084)	(.414,.095,.491)	(.432,.135,.433)	(.485,.235,.280)
F ₂	(.607,.116,.277)	(.583,.296,.121)	(.517,.077,.406)	(.757,.066,.177)	(.533,.169,.398)	(.720,.280, 0)	(.815,.047,.138)	(.554,.158,.288)
F ₃	(.744,.215,.041)	(.723,.187,.090)	(.689,.248,.063)	(.670,.232,.098)	(.507,.245,.248)	(.681,.119,.200)	(.591,.169,.240)	(.544,.192,.264)
F ₄	(.449,.406,.145)	(.398,.235,.367)	(.449,.142,.409)	(.773,.100,.127)	(.380,.364,.256)	(.456,.288,.256)	(.433,.438,.129)	(.646,.209,.145)

Step 2: Since all are benefit-type criteria. So, we do not need to normalize the decision matrices. Thus, the normalized decision matrix is the same as shown in Table 8.

Step 3: Now, we find the PIS and NIS by using Equations (1) and (2) respectively. $J^{+} = {\begin{matrix} (. 744, . 034, . 041), (. 723, . 187, . 090), (. 689, . 077, . 063), (. 773, . 066, . 098), \\ (. 533, . 169, . 084), (. 720, . 095, . 0), (. 815, . 047, . 129), (. 646, . 158, . 145) \end{matrix}}$ and $J^{-} = {\begin{matrix} (. 499, . 034, . 367), (. 398, . 187, . 367), (. 449, . 077, . 409), (. 617, . 066, . 238), \\ (. 380, . 169, . 398), (. 414, . 095, . 491), (. 432, . 047, . 433), (. 485, . 158, . 288) \end{matrix}}$

Step 4: Now we find the normalized Hamming and Euclidean distance between PIS to each alternative F_j (j = 1, 2, …, m) by using Equations (3) and (4) as represented in Tables 9, 10.

Table 9

Normalized Hamming distance b/w PIS and alternatives

Normalized hamming distance	Value
d_NHD (F₁, J⁺)	0.43025
d_NHD (F₂, J⁺)	0.262
d_NHD (F₃, J⁺)	0.22775
d_NHD (F₄, J⁺)	0.529

and similarly

Table 10

Normalized Euclidean distance b/w PIS and alternatives

Normalized euclidean distance	Value
d_NED (F₁, J⁺)	0.335688
d_NED (F₂, J⁺)	0.231705
d_NED (F₃, J⁺)	0.184416
d_NED (F₄, J⁺)	0.382578

Now we find the normalized Hamming and Euclidean distance between NIS to each alternative F_j (j = 1, 2, …, m) as represented in Tables 11, 12.

Table 11

Normalized Hamming distance b/w NIS and alternatives

Normalized hamming distance	Value
d_NHD (F₁, J^-)	0.255
d_NHD (F₂, J^-)	0.378
d_NHD (F₃, J^-)	0.50575
d_NHD (F₄, J^-)	0.35825

and likewise

Table 12

Normalized Euclidean distance b/w NIS and alternatives

Normalized euclidean distance	Value
d_NED (F₁, J^-)	0.227386
d_NED (F₂, J^-)	0.317252
d_NED (F₃, J^-)	0.344332
d_NED (F₄, J^-)	0.29127

Step 5: Now we find the closeness relation by using Equations (5) and (6) of each alternative F_j (j = 1, 2, …, m) as represented in Tables 13, 14.

Table 13

Closeness relation using NHD

Closeness relation	The score
l_NHD (F₁)	0.372127
l_NHD (F₂)	0.590625
l_NHD (F₃)	0.689502
l_NHD (F₄)	0.403776

and

Table 14

Closeness relation using NED

Closeness relation	The score
l_NED (F₁)	0.40383
l_NED (F₂)	0.577918
l_NED (F₃)	0.651221
l_NED (F₄)	0.432249

Step 6: Now for ranking all the alternatives in descending order, the tabular representation is given below in Table 15,

Table 15

Ranking orders of alternatives

Calculation results of each household FS
Using Normalized Hamming Distances
l_NHD (F₃) > l_NHD (F₂) > l_NHD (F₄) > l_NHD (F₁)
Ranking F₃ > F₂ > F₄ > F₁
Using Normalized Euclidean Distances
l_NED (F₃) > l_NED (F₂) > l_NED (F₄) > l_NED (F₁)
Ranking F₃ > F₂ > F₄ > F₁

Thus, in conclusion, F₃ (Poverty) is the major factor affecting household FS is our finest alternative with rank 1. While the F₂ (Poor Governance) is on rank 2, F₄ (Militancy) is on rank 3 and F₁ (Social Stratification) is on 4th rank.

3.3 Sensitivity analysis

A comprehensive evaluation of the reliability of our results obtained through a combination of statistical data collection and the TOPSIS method under a spherical fuzzy data employing normalized Hamming distance and normalized Euclidean distance constitutes the sensitivity analysis in our research paper, with particular emphasis on household food security. We employ distinct criteria for each alternative to evaluate the stability and dependability of our findings. We attempt to assess the robustness of the identified major factors and their effects on food security by systematically adjusting these parameters. Also, we make sure the significant factors affecting household FS, as identified, are consistent across various distance metrics in our findings. Its graphical representation is displayed in Fig. 4.

Fig. 4

Ranking of Both NHD and NED.

To determine the sensitivity of the proposed methodology for selecting a complex combat system, it is imperative to conduct a sensitivity analysis using one of the available methods [70]. The paper executed an analysis to examine the variations in the weight coefficients of the criteria. This was done by creating 15 different scenarios of weight changes, as illustrated in Fig. 5. In the first case, all criteria have the same weight, but in the other cases, their weights can differ, but their sum is one.

Fig. 5

Scenarios of changing the weight vectors of the criteria.

By implementing the suggested methodology and utilizing the established scenarios, the rankings of the various alternatives in all scenarios are achieved by using normalized Hamming distance (see Fig. 6) and by using normalized Euclidean distance (see Fig. 7).

Fig. 6

Alternative ranks obtained after changing criteria WVs.

Fig. 7

Alternative ranks obtained after changing criteria WVs.

Based on the acquired findings and Figs. 6 and 7, it can be inferred that alternative F₃ effectively addresses the research problem, whereas alternative F₁ does not. Furthermore, there is a discernible shift in the rankings between scenarios S₅ and S₁₃. However, this change is insignificant and anticipated, considering the alterations in the weighting coefficients of the criteria. Considering all the information provided, it can be determined that the suggested approach is reliable.

The Spearman’s correlation coefficient (SRcc) of the ranks was calculated using Equation (8), and the resulting values are displayed in Fig. 8. This analysis compares the final ranking of the alternatives (Table 15) with the rankings obtained when the weight coefficients of the criteria were changed (Figs. 6 and 7). Here is the equation of SRcc as [67]:

$SRcc = 1 - \frac{6 \sum_{j = 1}^{m} D_{j}^{2}}{m (m^{2} - 1)}, - 1 \leq SRCC \leq 1 .$ (8)

Fig. 8

The values of the Spearman’s coefficient.

Here D_j represents the difference between the ranks of each observation and m is the number of alternatives.

Spearman’s rank correlation coefficient consistently indicates a strong positive correlation in all scenarios, suggesting a consistent correlation between ranks without any significant changes.

3.4 Comparison with other MCDM EDAS technique

The decision makers are interested in the reliability of the outcome of the MCDM-based analysis. The outcomes of the MCDM (Multiple Criteria Decision Making) process are contingent upon the fundamental assumptions, model characteristics, and prevailing conditions. These conditions include the size and nature of the criteria and alternative set, as well as possible deviations in the parameters. These factors collectively influence the results obtained from the MCDM analysis [54]. Hence, it is essential to verify the validity of the outcome. The existing literature, as exemplified by references [28, 54], has shown the comparison between the outcomes obtained from a particular MCDM model and those derived from applying other models. The current study compares the ranking achieved by our proposed TOPSIS model under NHD and NED with that obtained from other contemporary and widely used models, such as EDAS model. We defined the score values and ranking to assess the coherence of the rankings derived from different models as represented in Table 16. It is observed that TOPSIS continues to rank of best alternative F₃ in comparison to other models. This leads us to believe that TOPSIS produces very trustworthy outcomes.

Table 16
Comparison with other MCDM EDAS technique

Methods Score values Ranking

F ₁ F ₂ F ₃ F ₄

TOPSIS using NHD 0.3721 0.5906 0.6895 0.4037 F₃ > F₂ > F₄ > F₁

TOPSIS using NED 0.4038 0.5779 0.6512 0.4322 F₃ > F₂ > F₄ > F₁

EDAS 0.0391 0.1121 0.1247 0 F₃ > F₂ > F₁ > F₄

Methods	Score values	Ranking
TOPSIS using NHD	0.3721	0.5906	0.6895	0.4037	F₃ > F₂ > F₄ > F₁
TOPSIS using NED	0.4038	0.5779	0.6512	0.4322	F₃ > F₂ > F₄ > F₁
EDAS	0.0391	0.1121	0.1247	0	F₃ > F₂ > F₁ > F₄

4 Conclusions

Sociologically the study concluded that institutional dysfunctional prevalence in Pakistan in general while in Torghar particular directly linked to FI in the study area. Poor governance led to corruption and smuggling of food commodities along with food hoarding resultantly evoked FI and starvation at the macro and micro levels. In addition, militancy further deteriorated the existing peaceful environment for farmers and traders to supply food resources on time to the locals. This compels the locals to internally migrate due to fear of life and hunger. Moreover, the existing social stratification and prevalence of poverty further worsen the overall structure of the locals. In a nutshell, the study concluded that people were not dying because of food but because of access to buying food. Mathematically, the study concluded that all the factors namely militancy, poor governance, social stratification and poverty from greater to some extent worsen the household FS at the macro and micro levels. Thus, at a macro level, the prevalence of poverty (F3) and militancy (F4) were more deteriorating factors of FI than social stratification (F1) and poor governance (F2) respectively. Thus, the government should mitigate to eliminate and eradicate the duress of poverty and ensure household FS to the locals through sustainable safety net programs is the order of the day. In addition, the government should come forward to cope with the institutional lacunas of FI and meet the yardstick of SDGs 1 and 2 till 2030. Otherwise, if not cope with the situation, then the government of Pakistan will face severe consequences from the United Nations and security councils. Implementing the suggested solutions may encounter difficulties associated with the availability of resources, including financial and infrastructural support. It is crucial to consider and overcome these limitations in order to make the suggested interventions practically applicable. In future research, we may also conduct sensitivity analyses to evaluate the influence of different parameters in the spherical TOPSIS method and incorporate dynamic modeling techniques to capture the dynamic aspects of food security. The purpose of these directions is to strengthen the resilience, relevance, and ethical considerations of research in the field of food security.

Footnotes

Funding

The current work was assisted financially to the Dean of Science and Research at King Khalid University via the Large Group Project under grant number RGP. 2/462/44.

Acknowledgment

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Large Groups Project under grant number (project number RGP.2/ 462/44. Academic year 1444H).

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Exploring household food security through institutional factors: A statistical and mathematical analysis

Abstract

Keywords

1 Introduction

1.1 Background of the study

1.2.1 Poverty

1.2.2 Militancy

1.2.3 Social stratification

1.2.4 Poor governance

1.3 Synthesis of mathematical structure

1.5 Objectives

1.6 Organization of the rest of the paper

2 Methods

2.1 Sociological methods

Table 1 Data collection by author’s Name of tehsils Household Sample head (N) size (n) Judba 14972 214 Khander 11492 165 Grand Total 26464 379

2.2.1 MADM problems by using the TOPSIS method for SFNs

3.1 Sociological results and discussions

Table 16 Comparison with other MCDM EDAS technique Methods Score values Ranking F 1 F 2 F 3 F 4 TOPSIS using NHD 0.3721 0.5906 0.6895 0.4037 F3 > F2 > F4 > F1 TOPSIS using NED 0.4038 0.5779 0.6512 0.4322 F3 > F2 > F4 > F1 EDAS 0.0391 0.1121 0.1247 0 F3 > F2 > F1 > F4

Footnotes

Funding

Acknowledgment

References

Table 1
Data collection by author’s

Name of tehsils Household Sample

head (N) size (n)

Judba 14972 214

Khander 11492 165

Grand Total 26464 379