Solving barrier ranking in clean energy adoption: An MCDM approach with q-rung orthopair fuzzy preferences

Abstract

With a growing focus from the United Nations to eradicate the ill effects of climate change, countries around the world are transforming to green and sustainable habits/practices. Adoption of clean energy for demand satisfaction is a prime focus of many countries as it reduces carbon trace and promotes global development. In developing countries like India, there is an urge for sustainable global development. Literature shows that direct and complete adoption of clean energy incurs some barriers, which impede the sustainable development of the nation. Grading such barriers supports policymakers to effectively plan strategies, which motivates authors to put forward a novel decision model with integrated approaches. First, qualitative rating data on barriers and circular economy (CE) factors are collected from experts via questionnaires, which are transformed into q-rung orthopair fuzzy information (qRFI). Second, the weights of experts and CE factors are determined by the proposed variance measure and CRITIC. Third, barriers are graded by the proposed ranking algorithm that considers modified WAPAS formulation. Finally, these approaches are integrated into a model that is testified for practicality by using a case example from India. Sensitivity and comparative analyses are performed to realize the merits and limitations of the model for extant works.

Keywords

Clean energy sustainability barriers evidence measure CoCoSo method q-Rung orthopair fuzzy circular economy

1. Introduction

Clean energy is becoming the buzzword across the globe as countries are actively working on strategies to reduce/eradicate carbon traces to tackle the adverse effects of climate change [1]. India, on one hand, is actively planning strategies for economic development by initiating schemes and projects for growth in the health sector, transportation sector, education sector, product development sector, and so on. While on other hand, India is ambitiously working towards sustainable and green development by committing to reduce 45% carbon footprint by 2030 as per the report from climateactiontracker.org dated: 5.12.2022. To counterbalance economic and environmental development, India considers the active adoption of sustainable and green habits [2]. One core area of focus is on clean/renewable energy adoption instead of fossil fuel-triggered energy, which could drive different sectors’ energy need to be fulfilled in a green and sustainable manner [3]. To support the claim, India has launched several projects for clean energy production and utilization and claimed that it would satisfy 50% of the energy demand through clean energy adoption by 2030. Some projects from India include Raasi Green Energy, ReNew Solar, Nagarjunasagar Hydro Project, Sivasamudram Hydro Project, and alike [4, 5], which are an indication of India’s striving focus to transform to clean energy usage for the betterment of ecosystem.

But, it must be noted that the direct adoption of clean energy in various sectors of business is not straightforward and incurs challenges/barriers [6]. There are many challenges from social, economic, environmental, and technology categories that affect the adoption of clean/renewable energies. As a result, grading such barriers would help experts and policymakers to plan their strategies promptly for a well-informed decision. Multi-criteria decision-making (MCDM) is an attractive approach for grading barriers that affect the adoption of clean energy and thereby slow the pace of sustainability and green practices. In the process of MCDM, a set of candidate alternatives are present that are rated by different experts on various criteria to form decision matrices, which are provided to the framework for rational decision-making along with weight vectors of criteria.

Predominantly, barriers’ ranking is achieved via MCDM. Some examples include sustainability operation barriers [7, 8, 9], technology barriers [10, 11], health barriers [12, 13], and alike. These articles from the literature infer the importance of MCDM in barrier ranking and are motivated by the claim, in this paper, authors develop a novel integrated framework for grading barriers that typically hinder the adoption of clean/renewable energy within the Indian perspective. Circular economy (CE) is an emerging concept within Industry 4.0. The prime idea is to take the process of production to disposal in a loop so that the disposal rate reduces drastically eventually leading to zero disposal. Conceptually, the aim is to extend the waste from one process as raw material for other processes, leading to a chain of actions that would help the planet in achieving sustainability and reduction of ill effects of climate change [8]. The CE follows the principle of 4Rs viz., reuse, recycle, refurbish, and repair so that extra depletion of resources is mitigated. In a linear economy, we adopt the take-make-dispose strategy, whereas in CE we adopt, the take-make-use-reuse concept. CE factors are interesting and actively contribute to the welfare of the ecosystem [8], which motivated authors to utilize the factors as criteria for rating different barriers that hinder clean energy adoption.

In the next section, the authors review extant models for ranking barriers that affect renewable energy adoption. From the review, some research gaps can be inferred such as: (i) uncertainty is not well modeled with reduced capability to handle subjective randomness and flexibility in preference elicitation; (ii) reliability values of experts are either not considered or assigned directly causing subjectivity and inaccuracies in the process; (iii) interactions among criteria/factors are not effectively captured; and (iv) ranking of barriers by considering criteria type and choice vectors of barriers from experts is not explored adequately. With the view of addressing these gaps, motivation is gained by authors and in this research, an integrated framework is developed, which poses the following contributions:

•
Qualitative rating information from experts is converted to q-rung orthopair fuzzy information (qRFI) to enable effective modeling of uncertainty from three zones viz., membership, indeterminacy, and non-membership. Also, the qRFI reduces subjective randomness and offers flexibility to experts to express their views in a broader space. Readers may refer to Section 3 for clarity.
•
The weights/reliability of experts is determined by the variance approach that effectively captures the variability in the distribution and maps the hesitation of experts during the decision process for rational decision-making.
•
Methodically, criteria weights are determined by the CRITIC approach that allows effective capturing of interactions among CE criteria/factors.

Finally, the barriers are graded using a new ranking algorithm that considers the WAPAS (“weighted aggregated sum product assessment”) formulation with some modifications in terms of consideration of criteria type and choice vectors from experts on each barrier.

Further, the article is organized in the following fashion. Section 2 provides a review of earlier studies in the barrier ranking category and qROFS-based decision model category. The core implementation is discussed in Section 3 with a stepwise procedure. A case example to demonstrate the usefulness of the model is provided in Section 4. Section 5 deals with the comparative investigation to realize the benefits and limitations of the proposed model. Finally, concluding remarks and directions for future research are provided in Section 6.
2. Literature review

2.1 Models for grading clean energy adoption barriers

As discussed in the previous section, barriers/challenges exist in practical scenario and the grading of such barriers assist in planning proper strategies to promote better adoption of clean energy for sustainable development. Driven by the claim, researchers present decision models for barriers’ grading/prioritization. Ghimre and Kim [14] extended AHP (“analytical hierarchy process”) for barrier assessment with respect to renewable energy adoption in Nepal. Gomez-Navarro and Ribo-Perez [15] developed ANP (“analytical network process”) model for evaluating obstacles that affect clean energy based electricity generation in Colombia. Shah et al. [16] put forward a Delphi based AHP for barrier assessment with respect to clean energy adoption in Pakistan. Similarly, Asante et al. [17] evaluated renewable energy barriers by adopting MULTIMOORA (“multiple objective optimization on the basis of ratio analysis plus full multiplicative form”) and EDAS (“evaluation based on distance from average solution”) methods. Elavarasan et al. [18] came up with SWOT (“strengths weakness opportunity and threat”) analysis for grading barriers that impede renewable energy adoption in countries such as India, Sweden, China, Iceland, and United States. Sengar et al. [19] put forward the AHP method for rationally ranking barriers/obstacles that affect the energy generation process from bio-residues of pine needles. Solangi et al. [20] developed an AHP-TOPSIS (“technique for order of preference by similarity to ideal solution”) combination for barrier assessment in clean energy adoption within Pakistan. Sadat et al. [21] prepared a combined AHP-TOPSIS framework for grading barriers/obstacles that hind solar energy adoption in Iran.

Recently, Pathak et al. [22] ranked different barriers that impede the adoption of clean energy in India by using AHP approach. Asante et al. [23] extended AHP-TOPSIS combination for barrier assessment pertaining to clean energy adoption in Ghana. Irfan et al. [24] presented an integrated AHP-TOPSIS based decision model for assessing barriers that impede biomass energy adoption along with their remedies by considering grey data. Liang et al. [25] utilized the AHP method for ranking the barriers that could affect the solar energy development and the economy. Shahzad et al. [26] utilized Pythagorean fuzzy based AHP method for barrier evaluation in the context of renewable ebergy adoption from the entrepreneurial perspective. Mekonnen et al. [27] put forward the interpretive structural modeling for assessing barriers in the adoption of solar energy in the Ethiopian outlook. Shah & Longheng [28] put forward fuzzy-grey Delphi-AHP approaches for grading barriers in the context of renewable energy production and utilization. Dhingra et al. [29] extended AHP approach for ranking barriers associated with the offshore wind energy production and utilization process by considering the fuzzy data.

From the review provided above, it is clear that (i) AHP is frequently used by the extant models for ranking barriers; (ii) also, fuzzy set is commonly used as preference information; and (iii) pairwise comparison is generally adopted to assess barriers in the context of clean energy adoption.

2.2 Models for MCDM with qRFI

The family of orthopair fuzzy sets gained its inception from Atanassov [30], where intuitionistic fuzzy set with membership and non-membership grades was put forward with a condition that their sum is less than or equal to unity. To expand the expression window Yager [31] came up with Pythagorean fuzzy set that has the capacity to consider broader preferences with the condition that square of sum of membership and non-membership must be less than or equal to unity. Further, Yager [32] developed a generalized fuzzy set called q-rung orthopair fuzzy set (qROFS) that could expand and shrink window size based on a factor called $q$ and the sum of the $q^{th}$ power of membership and non-membership must be less than or equal to unity.

Driven by the generalized nature of qROFS, many researchers proposed novel decision models with qROFS for solving diverse MCDM problems [33]. With the view of extending in this line, in this section, we present recent studies with qROFS. Peng et al. [34] put forward new operational laws, score function, and extended approximation method for decision-making with respect to investment application under qROFS context. Farid and Riaz [35]developed new Einstein operators with interactive capabilities for data fusion under qROFS context with improved operational laws and utilized the operator for group decision-making. Krishankumar et al. [4] developed gini index based TODIM (“interactive multi-criteria decision-making”) for evaluating renewable energy sources for India by considering qROFS data. Zeng et al. [36] enhanced the theoretical base of qROFS by presenting logarithmic distance measure along with some properties for MCDM. Alkan and Kahraman [37] presented TOPSIS model with qROFS data for evaluating government strategies towards COVID-19. Krishankumar et al. [38] extended variance measure and VIKOR (“Visekriterijumska optimizacija i kompromisno resenje”) for green supplier selection by considering qROFS preferences. Albahri et al. [39] presented zero-inconsistency model with score measure under qROFS context for solving a distribution problem. Recently, Khan et al. [40] assessed strategies for green supply chains by extending CODAS (“combinative distance based assessment”) to the variant of qROFS preference. Limboo and Datta [41] proposed probability assignment model with qROFS data and utilized it for medical diagnosis. Yang et al. [42] evaluated green distribution manufacturer of transformers by considering cloud-based qROFS data with decision methods. Deveci et al. [43] extended ordinal priority approach to qROFS for selection of personalized mobility options in metaverse. Alamoodi et al. [44] extended WZIC (“weighted zero-inconsistency”) method and DOSM (“decision by opinion score method”) to qROFS for evaluation of hospitals for remote patients. Krishankumar et al. [38] developed an integrated model with qROFS preference, interaction criteria method, and distance from ideal point method for evaluation internet-of-things service provider to monitor pollution within smart city. Deveci et al. [45] extended CoCoSo (“combined compromise solution”) method under qROFS context for selecting sites to floating offshore wind farms. Zolfani et al. [46] put forward a VIKOR based framework for assessing countries from the Southern and Eastern Europe for global supply chain applications. Xiao et al. [47] selected appropriate manufacturer from the set of candidates by developing a model with qROFS data, score function, and best-worst method. Krishankumar et al. [48] came up with an integrated decision approach and SWOT analysis for technology provider selection for sustainable transport application. Akram et al. [49] proposed new aggregation operators with Einstein formulation and discussed properties with qROFS data and applied the same for business location and supplier selection.

From the review made above, it can be inferred that (i) qROFS is a flexible structure for preference elicitation; (ii) qROFS can handle uncertainty from three degrees viz., membership, non-membership, and hesitancy; (iii) integrated approaches with qROFS data is popular and efficient for MCDM owing its features to handle uncertainty.

2.3 Insights

Based on the review in terms of application and method discussed above, it is evident that (i) barrier evaluation for clean energy is a crucial and interesting problem in the MCDM context; (ii) determination of weights of experts and criteria methodically can reduce biases and inaccuracies by mitigating human intervention; (iii) flexibility of qROFS to handle subjective randomness and ease of preference elicitation makes it a viable choice for the problem being considered; (iv) consideration of hesitation of experts and interactions of criteria are crucial for the barrier assessment; and (v) personalized grading of barriers is unexplored in the barrier evaluation context.

Clearly, from these claims, authors can infer that the challenges identified in the present study are inline with the insights and there is an urge to circumvent the issues through integrated approaches, which is put forward in the forthcoming section.

3. Methodology

3.1 Preliminaries

Let us discuss some basic concepts of IFS and qRFI here.

Definition 1 [30]: Set GY is fixed, $\textit{GN}\subset\textit{GY}$ is also fixed. Then, $\overline{\textit{GN}}$ is an IFS in GY such that,

$\displaystyle\overline{\textit{GN}}=\left\{{\textit{gy},\mu_{\overline{\textit% {GN}}}\left({\textit{gy}}\right),\upsilon_{\overline{\textit{GN}}}\left({% \textit{gy}}\right)|\textit{gy}\epsilon\textit{GY}}\right\}$ (1)

where $\mu_{\overline{\textit{GN}}}\left({\textit{gy}}\right)$ , $\upsilon_{\overline{\textit{GN}}}\left({\textit{gy}}\right)$ , and $\pi_{\overline{\textit{GN}}}\left({\textit{gy}}\right)=1-\left({\mu_{\overline% {\textit{GN}}}\left({\textit{gy}}\right)+\upsilon_{\overline{\textit{GN}}}% \left({\textit{gy}}\right)}\right)$ , $\mu_{\overline{GN}}\left({\textit{gy}}\right),\upsilon_{\overline{\textit{GN}}% }\left({\textit{gy}}\right)$ are the truth, falsity, and indeterminacy grades, $\mu_{\overline{\textit{GN}}}\left({\textit{gy}}\right)$ , $\upsilon_{\overline{\textit{GN}}}\left({\textit{gy}}\right)$ , and $\pi_{\overline{\textit{GN}}}\left({\textit{gy}}\right)$ are values in 0 to 1 range and $\mu_{\overline{\textit{GN}}}\left({\textit{gy}}\right)+\upsilon_{\overline{% \textit{GN}}}\left({\textit{gy}}\right)\leqslant 1$ .

Definition 2 [32]:GY is as before and $\textit{gy}\in\textit{GY}$ . Then the q-ROFS RF on GY is considered as,

$\displaystyle\textit{RF}=\left\{{\textit{gy},\mu_{\textit{RF}}\left({\textit{% gy}}\right),\upsilon_{\textit{RF}}\left({\textit{gy}}\right)|\textit{gy}% \epsilon\textit{GY}}\right\}$ (2)

where $\mu_{\textit{RF}}\left({\textit{gy}}\right),\upsilon_{\textit{RF}}\left({% \textit{gy}}\right)$ are in l0,1] referred as grades of truth and falsity. Besides, $0\leqslant\left({\mu_{\textit{RF}}\left({\textit{gy}}\right)}\right)^{q}+\left% ({\upsilon_{\textit{RG}}\left({\textit{gy}}\right)}\right)^{q}\leqslant 1$ with $q\geqslant 1$ . For IFS [30] $q=$ 1, and For PFS (Yager, 2014) $q=$ 2.

Note 1: From now, $\textit{RF}=\left({\mu_{\alpha},\upsilon_{\alpha}}\right)\forall\alpha=1,2,% \ldots,\tau$ is termed as a q-rung orthopair fuzzy information (qRFI). Collectively, they form qROFS.

Definition 3 [32]: $\textit{RF}_{1}$ and $\textit{RF}_{2}$ are two qRFI. Arithmetic operations with qRFI are given by,

$\displaystyle\eta\textit{RF}_{2}=\left({\left({1-\left({1-\mu_{2}^{q}}\right)^% {\eta}}\right)^{1/q},\upsilon_{2}^{\eta}}\right),\quad\eta>0$ (3)

$\displaystyle\textit{RF}_{1}^{\eta}=\left({\mu_{1}^{\eta},\left({1-\left({1-% \upsilon_{1}^{q}}\right)^{\eta}}\right)^{1/q}}\right),\quad\eta>0$ (4)

$\displaystyle\textit{RF}_{1}\oplus\textit{RF}_{2}=\left({\left({1-\left({1-\mu% _{1}^{q}}\right)\left({1-\mu_{2}^{q}}\right)}\right)^{1/q},\upsilon_{1}% \upsilon_{2}}\right)$ (5)

$\displaystyle\textit{RF}_{1}\oplus\textit{RF}_{2}=\left({\mu_{1}\mu_{2},\left(% {1-\left({1-\upsilon_{1}^{q}}\right)\left({1-\upsilon_{2}^{q}}\right)}\right)^% {1/q}}\right)$ (6)

$\displaystyle A\left({\textit{RF}_{2}}\right)=\mu_{2}^{q}+\upsilon_{2}^{q}$ (7)

$\displaystyle S\left({\textit{RF}_{2}}\right)=\mu_{2}^{q}-\upsilon_{2}^{q}$ (8)

Equations (3)–(8) presents the scalar multiplication, power operator, sum, product, accuracy and score functions.

3.2 Experts/criteria weights

This section presents methodical procedures for determining weights of experts and criteria. Experts and criteria are crucial components of MCDM. Experts rate both alternatives and criteria, while a criteria act as an entity over which the alternatives are rated. In general, experts have different level of expertise, attitude, and/or hesitation that sets diverse importance to each expert in the panel. Similarly, criteria have trade-offs and in practical MCDM problems, their importance in not uniform. As a result, determination of such weights is crucial.

Commonly, there are two categories viz., unknown weight information and partial weight information. In the first type, the information about the parameters is unknown, while in the second type some information about the parameter is available. In the second type, such information is formulated as constraints and the optimization model is solved [50]. Kao [51] and Koksalmis and Kabak [52] argued on the need for method-wise weight calculation. They claim that weight calculation reduces subjectivity and biases, which motivate authors to propose methodical procedures.

Popular weight calculation methods in the first category are analytical hierarchy process [53], entropy methods [54], ratio analysis method [55], and alike. But, such methods cannot capture hesitation of experts during preference articulation nor consider interactions of entities during weight assessment. As it can be noted, these factors are essential for rational calculation of weights and to handle the issue, we present the systematic procedure below by formulating variance based CRITIC method.

Step 1:
Form $p$ matrices of $t\times v$ with qualitative rating data that are transformed to qRFI for processing purpose using tabular values. $p$ experts rate $t$ barriers based on $v$ CE criteria.
Step 2:
Determine the variability measure of the preference vectors from each expert, which is further normalized to determine the net hesitation expressed by the experts during the preference articulation process. Equation (9) is adopted for this purpose.

$\displaystyle h_{l}=\frac{\mathop{\sum}\nolimits_{j=1}^{v}\left({\mathop{\sum}% \nolimits_{i=1}^{t}\frac{\left({A\left({\textit{RF}_{ij}}\right)-\overline{A% \left({\textit{RF}_{j}}\right)}}\right)^{2}}{t-1}}\right)}{\mathop{\sum}% \nolimits_{l=1}^{p}\left({\mathop{\sum}\nolimits_{j=1}^{v}\left({\mathop{\sum}% \nolimits_{i=1}^{t}\frac{\left({A\left({\textit{RF}_{ij}}\right)-\overline{A% \left({\textit{RF}_{i}}\right)}}\right)^{2}}{t-1}}\right)}\right)}$ (9)

where $A\left(.\right)$ Is the accuracy measure calculated from Eq. (7), $\overline{A\left({\textit{RF}_{i}}\right)}$ is the average accuracy measure.
Step 3:
Determine the reliability vector of experts by applying Eq. (10) by considering values from Step 2.

$\displaystyle\lambda_{l}=\frac{1-h_{l}}{\mathop{\sum}\nolimits_{l=1}^{p}1-h_{l}}$ (10)

where $\lambda_{l}$ is the weight (reliability) value of expert $l$ .
Step 4:
$p$ experts share their views/opinions on each criterion to form a $p\times v$ matrix for criteria weight calculation.
Step 5:
Determine accuracy by using Eq. (7) based on the data from Step 4. Calculate interaction measure among criteria by using Eq. (11).

$\displaystyle\rho_{\textit{xy}}=\frac{\mathop{\sum}\nolimits_{l=1}^{p}\left({% \left({wA\left({\textit{RF}_{lj}}\right)-\overline{wA\left({\textit{RF}_{j}}% \right)}}\right)_{x}.\left({wA\left({\textit{RF}_{\textit{lj}}}\right)-w% \overline{A\left({\textit{RF}_{j}}\right)}}\right)_{y}}\right)}{\sqrt{\mathop{% \sum}\nolimits_{{\begin{array}[]{{20}c}{l=1}\hfill\\ {\left(x\right)}\hfill\\ \end{array}}}^{p}\left({wA\left({\textit{RF}_{\textit{lj}}}\right)-w\overline{% A\left({\textit{RF}_{j}}\right)}}\right)^{2}.\mathop{\sum}\nolimits_{{\begin{% array}[]{{20}c}{l=1}\hfill\\ {\left(y\right)}\hfill\\ \end{array}}}^{p}\left({wA\left({\textit{RF}_{\textit{lj}}}\right)-w\overline{% A\left({\textit{RF}_{j}}\right)}}\right)^{2}}}$ (11)

where $wA\left(.\right)$ is the weighted accuracy calculated by taking product of $\lambda_{l}$ and $A\left(.\right)$ and $\overline{wA\left({\textit{RF}_{j}}\right)}$ is the weighted accuracy mean.
Step 6:
Determine the weights of criteria by calculating the information significance value of criteria and normalizing the value by using Eq. (12).

$\displaystyle c_{j}=\frac{\sigma_{j}^{2}.\mathop{\sum}\nolimits_{y}\rho_{% \textit{xy}}}{\mathop{\sum}\nolimits_{j}\left({\sigma_{j}^{2}.\mathop{\sum}% \nolimits_{y}\rho_{\textit{xy}}}\right)}$ (12)

where $\sigma_{j}^{2}$ is the variance measure of criterion $j$

From Eq. (12) weights of criteria are determined that are in the 0 to 1 range and sums to unity. It can be inferred that hesitation of experts during preference articulation and interactions of criteria are captured by the proposed approach and provides rational weight values.
3.3 Ranking algorithm

This section offers an algorithm for ranking barriers that hinder the adoption of clean energy by considering weights of experts and criteria from the previous section along with the preference data from experts on each barrier based on CE criteria and choice vector from experts on barriers. Ranking, as it can be seen, is a popular and crucial step in the MCDM. In this step, the candidate options (barriers in this case) are ordered in a fashion so as to help experts and policymakers plan their actions. Typically, ranking is supported via a mathematical background so that the experts/policymakers can revert back to the approach to determine the rational reasons behind a particular selection.

WASPAS [56] is a popular and elegant approach for ranking alternatives (barriers here). Traditional WASPAS method cannot consider criteria type and choice vectors in its formulation. But, studies infer that these features are essential for obtaining rational ordering of candidate alternatives [57, 58, 59]. Driven by the claim, in this section, a new algorithm is put forward for rational ranking of barriers.

Steps for the proposed algorithm are described below:

Step 1:
$p$ matrices of $t\times v$ considered in the previous section is considered here for rank determination. Data are collected from $p$ experts in the form of rating information on $t$ barriers rated based on $v$ criteria.
Step 2:
Equation (13) is used to aggregate data from Step 1 after considering weights from earlier section.

$\displaystyle\textit{ARF}_{ij}=\left({\mathop{\prod}\limits_{l=}^{p}\mu_{ij}^{% \lambda_{l}},\mathop{\prod}\limits_{l=}^{p}\upsilon_{ij}^{\lambda_{l}}}\right)$ (13)

where $\lambda_{l}$ is the weight of expert calculated from previous section.
Step 3:
Apply Eq. (14) normalize the data from Step 2. Use Eq. (7) to determine the accuracy of qRFI obtained obtained from Eq. (14).

$\displaystyle\textit{NARF}_{ij}=\left\{{{\begin{array}[]{*{20}c}{\left({\mu_{% ij}^{4}+\upsilon_{ij}^{4}}\right)\textit{when j is benefit}}\hfill\\ {1-\left({\mu_{ij}^{4}+\upsilon_{ij}^{4}}\right)\textit{when j is cost}}\hfill% \\ \end{array}}}\right.$ (14)
Step 4:
Calculate weighted sum and weighted product vectors of barriers by considering data from Step 3 and choice vectors from experts. Equation (15) is applied to determine the weighted normalized accuracy values. Later Eqs (16)–(17) are applied to determine sum and product vectors.

$\displaystyle\textit{WNA}_{ij}=\eta_{i}.\textit{NARF}_{ij}$ (15)

where $\eta_{i}$ is the choice of barrier $i$ from the expert committee.

A choice vector is obtained from the committee on the overall preference or grade of each barrier’s importance and this is embedded with the normalized accuracy measure to obtain a weighted matrix of $t\times v$ order.

$\displaystyle U_{i}=\mathop{\sum}\limits_{j=1}^{v}c_{j}.\textit{WNA}_{ij}$ (16)

$\displaystyle D_{i}=\mathop{\prod}\limits_{j=1}^{v}\textit{WNA}_{ij}^{c_{j}}$ (17)

where $c_{j}$ is criteria weight obtained from previous section.
Step 5:
Determine final rank values of barriers by applying Eq. (18). Vectors from Step 4 are linearly combined for calculating the values.

$\displaystyle\textit{OF}_{i}=\kappa U_{i}+\left({1-\kappa}\right)D_{i}$ (18)

where $\kappa$ is the strategy values in the 0 to 1 range.

Barrier with higher $F_{i}$ value is preferred more and so on the ordering is done. Thereby experts gain clarity on the importance of barriers, which eventually aids in rational strategy planning and adoption to circumvent the top hindering barriers.

Figure 1.
qROFS based integrated model for barrier grading in clean energy sector.

The working procedure of the proposed framework is provided in Fig. 1. Data is collected from experts via questionnaire in the form of qualitative terms by following the Likert scales. Later, these values are transformed to qROFN values based on the tabular content. Weights of both experts and criteria are determined methodically by considering hesitation of experts and interactions of criteria. Weights of experts are utilized by the criteria weight estimation procedure and these vectors are in-turn used for personalized ranking of barriers. Choice vector, decision matrices, and weight vectors of criteria and experts are considered by the developed ranking algorithm for determining the rank values of barriers. Specifically, the ranking algorithm considers criteria type and choice vectors for rank estimation. In the next section, the practical use of the framework is described in detail by considering a case example for demonstration.
4. Example

This section focuses on providing a case example to showcase the practicality of the developed framework by considering a case of ranking barriers that hinder clean energy adoption within India. As discussed earlier, it is clear that India is shifting its focus towards active use of clean energy to combat the demand and sustainability hand-in-hand. Many initiatives and schemes are put forward for reducing carbon trace within the country and efforts are made to transform the lifestyle of people more green and sustainable.

Though the efforts are being made, direct adoption and transformation at the ground level is not straightforward and literatures present diverse barriers and challenges that arise during such adoption. Since energy is the prime demand for developing countries like India, adoption of clean energy would create a win-win notion for both economic and environmental development. But, there are diverse challenges/barriers that hinder the adoption of clean energy and it is essential for policymakers and experts to obtain an ordering of these barriers so as to plan the sequence of actions to mitigate such barriers. As a result, in this section, we put forward a stepwise procedure for ranking the barriers based on CE criteria, which are considered to be effective in rating barriers from the sustainability and green aspects.

In the present example, we consider three experts who are well qualified and have close to eight years of expertise in clean energy and sustainability aspects. A panel is constituted with a senior professor from the department of sustainability, an operational manager from the clean energy division of a company, and a professional from energy economics sector. These experts surf the literatures to identify potential barriers that hinder clean energy adoption and based on voting principle, they shortlist 13 barriers from an initial set of 17 barriers. These barriers spread across five major zones viz., technical, environment, socio-economic, administrative, and political. Further, nine CE criteria are considered by the panel for rating these barriers to arrive at a rational ranking order. Barriers considered in this study are: social acceptance issue, decision process transparency issue, lack of institutional capacity, lack of adequate clean energy policy, corruption & nepotism, unstable governance, entrepreneur & innovation shortage, research facility shortage, social awareness, market size issue, cooperation issue, waste disposal, and, land use. CE criteria considered in this study are: green design, research circularity, job chance, green production profit, green purchase, green logistics, cost, pollution emission, and resource wastage. The last three are cost type criteria and the others are of benefit type criteria.

Let $Q$ be the set of barriers, DM is the panel, and $F$ is the CE criteria. Steps for grading/ranking of barriers are:

Step 1:
Construct three matrices of $13\times 9$ order with qualitative scales, which are converted to qROFN by using the tabular values from Krishankumar and Ecer [60].

Table 1
qROFS based integrated model for barrier grading in clean energy sector

$Q$ $F_{1}$ $F_{2}$ $F_{3}$ $F_{4}$ $F_{5}$ $F_{6}$ $F_{7}$ $F_{8}$ $F_{9}$

$\textit{DM}_{1}$

$Q_{1}$ H ML M VL VL L H ML M

$Q_{2}$ MH VH H MH M H MH VH VL

$Q_{3}$ L MH ML ML VH ML M AH ML

$Q_{4}$ L MH L ML MH AH MH MH MH

$Q_{5}$ VL ML M L M H H ML VH

$Q_{6}$ MH MH M H VL VH M MH L

$Q_{7}$ ML ML VL MH VH ML M L ML

$Q_{8}$ VH VH ML L M ML ML ML VL

$Q_{9}$ MH L VH H VH VH L MH MH

$Q_{10}$ ML ML ML VH H AH MH L M

$Q_{11}$ H L VH M L VH VH VH L

$Q_{12}$ VH H ML L H M H M M

$Q_{13}$ MH VL H ML M ML ML L ML

$\textit{DM}_{2}$

$Q_{1}$ H H M AH VH VL MH H ML

$Q_{2}$ ML L H AH VH L ML ML M

$Q_{3}$ ML L H VH H L MH VL VH

$Q_{4}$ ML ML M L AH H H VH H

$Q_{5}$ ML ML M H AH VH ML M AH

$Q_{6}$ M VL VL ML M H H H H

$Q_{7}$ H AH MH L AH VL M VH MH

$Q_{8}$ H ML VH VH L VL L M H

$Q_{9}$ AH VH VH VH AH L H L VH

$Q_{10}$ H ML L VH H ML VL VL ML

$Q_{11}$ VH ML ML ML H H H ML M

$Q_{12}$ M ML VH H VH M M ML H

$Q_{13}$ H H MH AH MH H VH VH H

$\textit{DM}_{3}$

$Q_{1}$ VL M M VL M MH M L MH

$Q_{2}$ VH ML VH M M L M MH VL

$Q_{3}$ VL M AH VH VH ML H M H

$Q_{4}$ M VH VH VH VL M AH VH M

$Q_{5}$ M VH M H AH M L AH MH

$Q_{6}$ VL VH MH H ML VH VL VL H

$Q_{7}$ M M MH VL M H H L H

$Q_{8}$ H L L M ML H VH M H

$Q_{9}$ M L ML AH AH MH L M ML

$Q_{10}$ MH ML L MH M VH H M ML

$Q_{11}$ H MH VH ML VH ML VH L MH

$Q_{12}$ VH M H VH MH M VH M VH

$Q_{13}$ VL AH L M H ML M M VL

Table 1 depicts the qROFN values associated with each Likert scale. First two columns pertain to Table 1 and last two columns pertain to Table 3. Specifically, Table 2 shares the rating from each expert on different barriers that hinder clean energy adoption based on CE criteria.
Step 2:
Construct an opinion vector for criteria of $1\times 9$ order by considering data from three experts.

Table 2
Data from experts on barriers

DM $F_{1}$ $F_{2}$ $F_{3}$ $F_{4}$ $F_{5}$ $F_{6}$ $F_{7}$ $F_{8}$ $F_{9}$

$\textit{DM}_{1}$ MLP AP LP MLP VMP MP MLP MP AP

$\textit{DM}_{2}$ N MLP VMP MLP AP N MLP LP VLP

$\textit{DM}_{3}$ LP VLP MP N MP MLP VMP MLP MP

As mentioned above, Table 3 utilizes values from last two columns of Table 2 to determine the criteria weights. Opinions from each expert on the criteria are given in Table 3.
Step 3:
Weights of experts and criteria are determined by using the procedure given in Section 3.2.

Based on the data from Table 2, it is clear that the variance measure is calculated as 0.452, 0.455, and 0.689, respectively. Weights/reliability of experts are calculated as 0.36, 0.36, and 0.28, respectively. Equations (9)–(10) are used for determining the weights of experts.

Equations (11)–(12) are applied to determine the weights of criteria. Based on Eq. (11) (Fig. 2), the interaction values are determined, which are further applied to Eq. (12) to calculate the weights of criteria and it is obtained as 0.026, 0.042, 0.144, 0.063, 0.201, 0.037, 0.011, 0.143, and 0.331, respectively.
Step 4:
Data from Step 1 and weights from Step 3 are considered for grading barriers by adopting the procedure proposed in Section 3.3.

Table 3
Choice from experts on criteria

$Q$ $U_{i}$ $D_{i}$ $\textit{OF}_{i}$

$Q_{1}$ 0.171 0.157 0.164

$Q_{2}$ 0.089 0.092 0.045

$Q_{3}$ 0.236 0.239 0.237

$Q_{4}$ 0.281 0.273 0.277

$Q_{5}$ 0.142 0.133 0.138

$Q_{6}$ 0.219 0.220 0.220

$Q_{7}$ 0.174 0.178 0.176

$Q_{8}$ 0.295 0.289 0.292

$Q_{9}$ 0.287 0.281 0.284

$Q_{10}$ 0.252 0.248 0.251

$Q_{11}$ 0.369 0.368 0.369

$Q_{12}$ 0.233 0.226 0.229

$Q_{13}$ 0.136 0.137 0.137

Table 3 depicts the values pertaining to the rank algorithm presented in Section 3.3 and from the last column of the table, the rank values are obtained for each barrier that affects the clean energy adoption. Choice vector considered is 0.35, 0.35, 0.45, 0.55, 0.40, 0.45, 0.35, 0.60, 0.50, 0.45, 0.65, 0.40, and 0.30, respectively and from Table 4, the ordering is determined as $Q_{11}\succ Q_{8}\succ Q_{9}\succ Q_{4}\succ Q_{10}\succ Q_{3}\succ Q_{12}% \succ Q_{6}\succ Q_{7}\succ Q_{1}\succ Q_{13}\succ Q_{5}\succ Q_{2}$ . Clearly, barrier $Q_{11}$ is of high preference and there is a need to actively focus on that barrier with proper strategies to counter the ill-effects of the barrier on clean energy adoption. Following this, focus must be on barriers $Q_{8}$ , $Q_{9}$ , $Q_{4}$ , and so on. Intuitively, it can be noted that there is certain level of influence from the choice vectors that dictates the net preference of the panel with respect to a particular barrier and in some sense, the ordering overlaps the choices giving a sense of personalization in the decision process.

Figure 2.
Criteria interrelationship.

Figure 3.
Sensitivity analysis of weights (a) biased criteria weights and (b) unbiased criteria weights.

5. Comparison and sensitivity

$Q$	$F_{1}$	$F_{2}$	$F_{3}$	$F_{4}$	$F_{5}$	$F_{6}$	$F_{7}$	$F_{8}$	$F_{9}$
$\textit{DM}_{1}$
$Q_{1}$	H	ML	M	VL	VL	L	H	ML	M
$Q_{2}$	MH	VH	H	MH	M	H	MH	VH	VL
$Q_{3}$	L	MH	ML	ML	VH	ML	M	AH	ML
$Q_{4}$	L	MH	L	ML	MH	AH	MH	MH	MH
$Q_{5}$	VL	ML	M	L	M	H	H	ML	VH
$Q_{6}$	MH	MH	M	H	VL	VH	M	MH	L
$Q_{7}$	ML	ML	VL	MH	VH	ML	M	L	ML
$Q_{8}$	VH	VH	ML	L	M	ML	ML	ML	VL
$Q_{9}$	MH	L	VH	H	VH	VH	L	MH	MH
$Q_{10}$	ML	ML	ML	VH	H	AH	MH	L	M
$Q_{11}$	H	L	VH	M	L	VH	VH	VH	L
$Q_{12}$	VH	H	ML	L	H	M	H	M	M
$Q_{13}$	MH	VL	H	ML	M	ML	ML	L	ML
$\textit{DM}_{2}$
$Q_{1}$	H	H	M	AH	VH	VL	MH	H	ML
$Q_{2}$	ML	L	H	AH	VH	L	ML	ML	M
$Q_{3}$	ML	L	H	VH	H	L	MH	VL	VH
$Q_{4}$	ML	ML	M	L	AH	H	H	VH	H
$Q_{5}$	ML	ML	M	H	AH	VH	ML	M	AH
$Q_{6}$	M	VL	VL	ML	M	H	H	H	H
$Q_{7}$	H	AH	MH	L	AH	VL	M	VH	MH
$Q_{8}$	H	ML	VH	VH	L	VL	L	M	H
$Q_{9}$	AH	VH	VH	VH	AH	L	H	L	VH
$Q_{10}$	H	ML	L	VH	H	ML	VL	VL	ML
$Q_{11}$	VH	ML	ML	ML	H	H	H	ML	M
$Q_{12}$	M	ML	VH	H	VH	M	M	ML	H
$Q_{13}$	H	H	MH	AH	MH	H	VH	VH	H
$\textit{DM}_{3}$
$Q_{1}$	VL	M	M	VL	M	MH	M	L	MH
$Q_{2}$	VH	ML	VH	M	M	L	M	MH	VL
$Q_{3}$	VL	M	AH	VH	VH	ML	H	M	H
$Q_{4}$	M	VH	VH	VH	VL	M	AH	VH	M
$Q_{5}$	M	VH	M	H	AH	M	L	AH	MH
$Q_{6}$	VL	VH	MH	H	ML	VH	VL	VL	H
$Q_{7}$	M	M	MH	VL	M	H	H	L	H
$Q_{8}$	H	L	L	M	ML	H	VH	M	H
$Q_{9}$	M	L	ML	AH	AH	MH	L	M	ML
$Q_{10}$	MH	ML	L	MH	M	VH	H	M	ML
$Q_{11}$	H	MH	VH	ML	VH	ML	VH	L	MH
$Q_{12}$	VH	M	H	VH	MH	M	VH	M	VH
$Q_{13}$	VL	AH	L	M	H	ML	M	M	VL

DM	$F_{1}$	$F_{2}$	$F_{3}$	$F_{4}$	$F_{5}$	$F_{6}$	$F_{7}$	$F_{8}$	$F_{9}$
$\textit{DM}_{1}$	MLP	AP	LP	MLP	VMP	MP	MLP	MP	AP
$\textit{DM}_{2}$	N	MLP	VMP	MLP	AP	N	MLP	LP	VLP
$\textit{DM}_{3}$	LP	VLP	MP	N	MP	MLP	VMP	MLP	MP

$Q$	$U_{i}$	$D_{i}$	$\textit{OF}_{i}$
$Q_{1}$	0.171	0.157	0.164
$Q_{2}$	0.089	0.092	0.045
$Q_{3}$	0.236	0.239	0.237
$Q_{4}$	0.281	0.273	0.277
$Q_{5}$	0.142	0.133	0.138
$Q_{6}$	0.219	0.220	0.220
$Q_{7}$	0.174	0.178	0.176
$Q_{8}$	0.295	0.289	0.292
$Q_{9}$	0.287	0.281	0.284
$Q_{10}$	0.252	0.248	0.251
$Q_{11}$	0.369	0.368	0.369
$Q_{12}$	0.233	0.226	0.229
$Q_{13}$	0.136	0.137	0.137

This section describes the efficacy of the proposed model via comparison with state-of-the-art models from literatures. The impact of change of criteria weights and strategy values are realized by the intra-inter sensitivity analysis of criteria weight vector and strategy values. Equal and unequal criteria weights are considered along with the alteration of strategy values with unit step size. Figure 3 shows the rank values of barriers at each strategy value over a specific weight vector. Typically, the values infer that there is change in rank values along with ordering when criteria weights are altered, which shows that criteria weights are essential in determining the rank order. Further, from the unequal weight set, it can be seen that though strategy values are altered, the ordering is intact indicating that the proposed model is robust in nature. Whereas, in the equal weight set, as strategy values change, the ordering also changes. As a result, it can be observed that methodical determination of weights is crucial and it helps in retaining the ordering of barriers even after alterations of strategy values, thereby realizing the robustness of the proposed model.

Both application and method driven comparisons are conducted by considering respective extant models from the literature. Extant hydrogen storage method selection models such as Shah et al. [16], Sengar et al. [19], Solangi et al. [20], Asante et al. [23], and Irfan et al. [24] are compared with the proposed framework in terms of the application perspective.

Table 4
Ranking algorithm parameters

Context	Proposed	Shah et al. [16]	Sengar et al. [19]	Solangi et al. [20]	Asante et al. [23]	Irfan et al. [24]
Data	qROFS	Fuzzy	Fuzzy	Fuzzy	Fuzzy	Grey
Experts’ reliability	Determined	No	No	No	No	No
Hesitation of experts	Considered	No	No	No	No	No
Interactions of criteria	Considered	No	No	No	No	No
Reliability consideration	Both in criteria weight and ranking	No	No	No	No	No
Variability in preference distribution	Considered	No	No	No	No	No
Consideration of criteria type	Yes	No	No	Yes	Yes	Yes
Choice vector	Considered	No	No	No	No	No

Table 4 gives feature summary and to expand, here some innovative features of the proposed model are pointed:

•

qROFS is adopted as the preference information that can effectively consider uncertainty from three degrees such as membership, indeterminacy, and non-membership. Also, subjective randomness can be effectively mitigated and flexible preference elicitation is possible via this structure.

•

Weights of both criteria and experts are methodically determined, which eventually reduces bias and subjectivity. Hesitation involved within experts can be captured during the assessment of reliability of experts, which other models subtle explore.

•

Besides, interactions of criteria and variability in the distribution of preferences from experts are captured during criteria weight estimation.

•

It can also be noted that the weights/reliability of criteria are utilized both for criteria weight calculation and ranking of barriers, which is not available in extant models.

•

Choice vectors along with criteria type are considered by the ranking algorithm during grading of barriers and extant models sometime consider criteria type, but do not focus on choice vectors during rank estimation. A sense of personalization is possible during rank estimation in the proposed model.

Figure 4.

Test for uniqueness of ordering (Y axis 1 is Proposed vs. Proposed; 2 is Proposed vs. Farid and Riaz [35]; 3 is Proposed vs. Alkan & Kahraman [37]; 3 is Proposed vs. Zolfani et al. [46]; 4 is Proposed vs. Khan et al. [40]; and 5 is Proposed vs. Akram et al. [49]).

From the perception of method, qROFS based decision models such as Farid and Riaz [35] model, Alkan and Kahraman [37] model, Zolfani et al. [46] model, Khan et al. [40] model, and Akram et al. [49] model are compared with the proposed model to understand the uniqueness of the proposed work. In this context, data is fed to all models and the rank vectors of barriers are determined, which are then given as input to the Spearman correlation for determining the coefficient values. Proposed versus extant models yield values as 1.0, 0.40, 0.50, 0.50, 0.50, 0.40, respectively. From Fig. 4, it is clear that the developed model yields an unique rank order compared to its counterparts and intuitively, this is due to the consideration of choice vector from experts, which is unaviailable in the extant model formulations.

Figure 5.

Test for broadness of rank values.

Besides, an experiment with simulated decision matrices is performed to understand the efficacy of the proposed model in terms of broadness of rank values and the discriminative nature of the model. For this, 350 matrices are considered that are given as input to the model with unequal weight vector and equal weight vector. Unequal weight vector is the one that we obtain from Section 3.2 and equal weight vector is $\frac{1}{b}$ where $b$ is the number of criteria. Specifically, all the 350 matrices are simulated each of order $13\times 9$ and for the unequal weight set, we can obtain it from the previous section. Similarly, equal weight set is 0.111 for each criterion. Based on these values, the simulation experiment is conducted. Each matrix is given as input to the developed model and rank values are obtained. Eventually, 350 rank vectors each of $1\times 13$ order are obtained for both the weight sets and the variance measure is used to determine the variability of each vector. It is clear that 350 variance values are obtained for each weight set and they are plotted in Fig. 5. From the figure, it is evident that the proposed model with unequal weight vector yields a broader rank value set compared to the equal weight variant and the discrimination ability of the former is better than the latter. Hence, it is observed that the determination of methodical weights of criteria is crucial for determining rational rank values and the association of choice vector to the formulation, further enhances the rank determination process and provides sensible rank values to the experts for effective backup management and task planning.

6. Conclusion

This paper puts forward a novel integrated framework are grading barriers that hinder the clean energy adoption. This is a value addition to the clean energy sector as it aids in preparing appropriate strategies to counter the high priority barriers so that the sector does not suffer much loss and downfalls. Proposed model methodically determines criteria/experts’ weights by reducing subjective features along with effective consideration of hesitation of experts and interrelationship among criteria. Besides, the subjective randomness is reduced and flexibility is improved via qROFS, which is a generalized form of orthopair sets. Grading of barriers is also done by considering the criteria type and the choice vector from experts, which is lacking in extant barrier ranking models.

Apart from the value additions, the proposed model is robust to alterations of strategy values and produces unique ordering of barriers by intuitively considering choice vectors, which acts as a net opinion of experts on each barrier that provides an overall choice on the barriers and offers a sense of personalization to experts. Also, it is inferred that the methodical calculation of weights followed by embedding of choice vectors in the formulation for determining rank values of barriers produces broad rank values that could eventually aid in efficient backup management at critical times and easily discriminate options compared to the counterparts.

Some limitations of the model are: (i) preferences are assumed to be complete and the proposed model cannot handle unavailable or missing values; (ii) partial information on entities of the decision process cannot be handled by the present integrated model. Implications of the developed framework are: (i) it can be used as a readymade tool for gradring barriers; (ii) uncertainty is handled effectively from three degrees along with reduced human intervention and subjectivity; (iii) the framework can provide the degree of influence of each barrier in hindering the clean energy adoption, which could further strategize the plan of action for its remedies; (iv) experts and stakeholders need to be trained for effective utilization of the model; and (v) the developed framework can be tweaked to grade other crucial aspects of clean energy sector such as sites, sources, equipments/gadgets, and so on.

In the future, plans are made to tackle the limitations of the present model. Also, we plan to extend the model to new application in the energy sector and other sustainable and green aspects. Furthermore, there is plan from authors to extend the model to different fuzzy variants such as neutrosophic fuzzy set, hesitant fuzz set, and probabilistic versions. In order to realize the practical use further, authors plan for mobile apps and integration of machine learning and recommender system concepts to achieve larage scale decisions from diverse data sources.

Authors contributions

Raghunathan Krishankumar Data processing, Analysis and writing.

Dragan Pamucar Conceptualization, methodology and supervision.

Raghunathan Krishankumar and Dragan Pamucar. Supervision on statistical analysis, Revision, visualization, and editing.

Funding

This research was conducted without any financial support.

Availability of data and materials

The data used to support the findings of this study are included within this article; however, the reader may contact the corresponding author for more details on the data.

Declaration of interests

All persons who meet authorship criteria are listed as authors, and all authors certify that they have participated sufficiently in the work to take public responsibility for the content, including participation in the concept, design, analysis, writing, or revision of the manuscript. Furthermore, each author certifies that this material or similar material has not been and will not be submitted to or published in any other publication before its appearance in the Environmental Science and Pollution Research.

Ethical approval and consent to participate

Not applicable.

Consent to publish

Not applicable.

Footnotes

Conflict of interest

No conflict of interest, financial or other, exists.

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Solving barrier ranking in clean energy adoption: An MCDM approach with q-rung orthopair fuzzy preferences

Abstract

Keywords

1. Introduction

2.1 Models for grading clean energy adoption barriers

2.2 Models for MCDM with qRFI

2.3 Insights

3. Methodology

3.1 Preliminaries

Table 4 Ranking algorithm parameters

Authors contributions

Funding

Availability of data and materials

Declaration of interests

Ethical approval and consent to participate

Consent to publish

Footnotes

Conflict of interest

References

Table 4
Ranking algorithm parameters