Multi-attribute decision making method based on probabilistic linguistic term sets and its application in the evaluation of emergency logistics capacity

Abstract

The occurrence of public health emergency will cause huge economic losses and casualties, which posed a huge threat to the economic and social development. In response to the emergency, a large amount of emergency relief supplies will be transported to the affected areas. Faced with this public health emergency of international concern, the concept of emergency logistics capacity and the evaluation model based on probabilistic linguistic term sets are proposed. In this paper, the emergency logistics capability evaluation is transformed into user demand evaluation, and the importance of each index of emergency logistics capability is determined by using Quality Function Deployment (QFD) and prospect theory. Under the probabilistic language information environment, a multi-attribute decision making method is established by using TODIM method. Finally, an example is given to verify the feasibility of the proposed method.

Keywords

Emergency logistics capacity probabilistic linguistic term sets quality function deployment (QFD)

1 Introduction

Emergency logistics is a special activity that aims to provide relief materials when natural disasters and public health emergencies occur and provides emergency support after emergencies, which can maximize time benefit and disaster loss [1]. In recent years, sudden natural disasters, public health events, social security events and other emergencies occur frequently in the world, and the research on emergency logistics has attracted more and more attention from scholars. In 1984, the logistics management method is applied to the dispatching process of disaster relief materials for the first time by Ken and Cook [2]; Aikens constructed nine models for selecting the optimal location in the warehouse construction process [3]; Carter believed that emergency logistics is the act of delivering emergency supplies to the point of demand in an accurate time according to the demand. After an emergency, the government should respond actively to ensure that emergency supplies reach the disaster area in the shortest time [4]; Suleyman proposed the early description of emergency logistics management, the construction of a comprehensive and effective emergency decision support system, to help rescue workers to carry out traffic control and emergency evacuation after the occurrence of emergency events, and make emergency relief materials quickly sent to the disaster area [5]. The research on emergency logistics in China started from SARS in 2003, and the related research on the evaluation of emergency logistics capability has been gradually deepened. He analyzed the causes of emergency logistics caused by natural disasters, decision-making mistakes, complex international environment, consumer rights protection and third parties [6]; Wang et al. defined the concept of emergency logistics, comprehensively expounded it, and pointed out the problems existing in the existing research [7]; Sun et al. defined the characteristics of emergency logistics, constructed the emergency logistics guarantee system and risk assessment model, and pointed out the future development trend of emergency logistics [8]. Emergency logistics requires not only timely release of emergency response by government departments, but also cooperation with all sectors of society. However, the academic research on emergency logistics capability is not thorough enough. This is also the direction of future research.

In 1965, Zadeh proposed the fuzzy set to describe relevant information [9], and then the concept of hesitating fuzzy set was proposed [10]. Rodriguez et al. proposed the hesitating fuzzy language term set combined with the language term set [12]. Pang et al. proposed the concept of probabilistic language term set (PLTSs) to express the preference of the decision maker and to deal with the information in the decision-making process effectively. The set of probabilistic language terms represents evaluation information through linguistic values and corresponding probabilities [13]; Then, Zhang et al. redefined some operations of the probabilistic language term set, so that the probability of the prediction term was reflected in the decision result and the decision result was guaranteed to be in the form of the probabilistic language term set [14]; Through equivalent transformation function, Guo et al. proposed the operation of probabilistic language term sets based on algebraic T-conorm and T-norm [15]; The distance measure is defined by the deviation degree of the normalized probabilistic language term set, Zhang proposed the distance measure of the normalized probabilistic language preference relation. Wang et al. proposed generalized distance and Hausdorff distance by introducing the concept of probabilistic language term set [16]; Then Liu and Li proposed Maclaurin symmetric average aggregation operator [17]; Pang et al. studied the extended TOPSIS method and information aggregation operator based on the probabilistic language decision making method [18]; According to the nature of language preference relation, Wu et al. proposed the probabilistic cosine similarity measure [19]; Lin et al proposed the distance measure between two probabilistic language term sets to reasonably measure the relationship between two corresponding language term sets, including Hamming distance, Euclidean distance, Hausdorff distance and mixed distance [20]. Mo proposed a new method to solve the problem of emergency decision-making named D-PLTS, which can be directly transferred to the form of the D number, no matter whether the information is complete or not [21]. At present, probabilistic language term sets have been successfully applied in many research fields.

In recent years, decision making methods based on language information have been widely studied and some achievements have been made. Some other methods have also been conducted to solve the problem of emergency decision making, such as D number theory. D number is a new tool for expressing and processing uncertain information. Its framework is based on evidence theory and is an effective extension of evidence theory, but it has more flexible and more relaxed application conditions than evidence theory. In d-number theory, decision experts are allowed to make reasonable evaluation of candidates without considering the integrity constraints of evaluation data, that is, it can clearly express unknown and uncertain information. Experts have flexibility in evaluation. After the expert evaluation information is collected, the expert evaluation information is regarded as D number, and then the information is integrated step by step with the relevant characteristics of D number, and finally the candidate’s final evaluation score is obtained, and then the ranking is carried out according to this. For example, Mo and Deng proposed a new methodology to deal with MADA problem based on D numbers [22]. The decision-making model is scientific and effective, and the process is intuitive, clear and time complexity is low.

Probabilistic language term sets not only enable participants or groups to use multiple language terms to express their judgments, but also reflect the preference of participants or groups to different language terms. It is more flexible and advantageous to use probabilistic language term sets to describe the opinions of decision-making groups. A probabilistic language decision matrix is used to express the opinions of the participant groups, which not only takes into account the different evaluations of the participants on the scheme, but also the different preferences of the participant groups on the evaluation information.

The structure of the paper is settled in the following. Section 2 presents some relevant basics. Section 3 proposes evaluation criteria for emergency logistics capacity. Section 4 establishes the multi-objective optimization by TODIM method using QFD and prospect theory. An application study is provided in Section 5 about the evaluation of emergency logistics capacity to verify the value of the presented framework in application. At last, the conclusions and possible directions for future research are analyzed in Section 6.

2 Preliminaries

2.1 Basic theory of PLTS

Firstly, this section introduces some basic definitions and operations for PLTSs.

Definition 1. [14] Let S ={ S_t|t = - τ, . . . , -1, 0, 1, . . . , τ } be a finite set composed of an odd number of language terms, where is a specific language term, and the set meets the following four conditions:

S_i < S_j, when i < j;

Neg (S_i) = S_j, when i = - j;

max { S_i, S_j } = S_i, when i ⩾ j;

min { S_i, S_j } = S_j, when i ⩾ j.

Definition 2. [13] Let S ={ S_t|t = - τ, . . . , -1, 0, 1, . . . , τ } be a LTS, a PLTS is defined as:

$\begin{matrix} L (p) = & {L^{(k)} (p^{(k)}) | L (k)} \in S, r^{(k)} \in t, p^{(k)} \\ ⩾ 0, k = 1, 2, . . ., # L (p), \sum_{k = 1}^{# L (p)} p^{(k)} ⩽ 1 \end{matrix}$ (1)

Where # L (p) is the number of all different linguistic terms in L (p).

If $\sum_{k = 1}^{# L (p)} p^{(k)} = 1$ , then the probability information is complete; otherwise, the probability information is incomplete. Then, Pang et al. proposed a normalization method for PLTS.

Definition 3. [13] L (p) ={ L^(k) (p^(k)) |k = 1, 2, . . . , # L^(p) } be a PLTS, the normalized PLTS can be defined as:

$\begin{matrix} L (p) = {L^{(k)} (p^{(k)}) | L (k)} \in S, p^{(k)} ⩾ 0, \\ k = 1, 2, . . ., # L (p), \sum_{k = 1}^{# L (p)} p^{(k)} ⩽ 1 \\ \dot{L} (p) = {{\dot{L}}^{(k)} ({\dot{p}}^{(k)}) | k = 1, 2, . . ., # L (p)} \end{matrix}$ (2)

Where ${\dot{p}}^{(k)} = p^{(k)} / \sum_{k = 1}^{# L (p)} p^{(k)}, k = {1, 2, . . ., # L (p)}$ .

Let L₁ (p) and L₂ (p) be any two PLTS s, $L_{1} (p) = {L_{1}^{(k)} (p_{1}^{(k)}) | k = 1, 2, . . ., # L_{1}^{(p)}}$ and $L_{2} (p) = {L_{2}^{(k)} (p_{2}^{(k)}) | k = 1, 2, . . ., # L_{2}^{(p)}}$ , the standardization process of the formula is:

If $\sum_{k = 1}^{# L (p)} p^{(k)} < 1$ , then the probability information is incomplete. Equation (1) is used to calculate $\dot{L} (p)$ .

If # L₁ (p) ≠ # L₂ (p), then add corresponding elements to the probabilistic language term sets with fewer elements.

Definition 4. [13] Let L₁ (p) and L₂ (p) be any two PLTS s, $L_{1} (p) = {L_{1}^{(k)} (p_{1}^{(k)}) | k = 1, 2, . . ., # L_{1}^{(p)}}$ and $L_{2} (p) = {L_{2}^{(k)} (p_{2}^{(k)}) | k = 1, 2, . . ., # L_{2}^{(p)}}$ , and let # L₁ (p) and # L₂ (p) be the numbers of linguistic terms in L₁ (p) and L₂ (p) respectively. If # L₁ (p) > # L₂ (p), then we will add # L₁ (p) - # L₂ (p) linguistic terms to L₂ (p) so that the numbers of linguistic terms in L₁ (p) and L₂ (p) are identical. The added linguistic terms are the smallest ones in L₂ (p), and the probabilities of all the linguistic terms are zero.

Definition 5. [13] Let L (p) ={ L^(k) (p^(k)) |k = 1, 2, . . . , # L^(p) } be a PLTS, and r (k) be the subscript of linguistic term L (k). Then the score of L (p) is:

$E (L (p)) = s_{α}$ (3)

Where $α = \sum_{k = 1}^{# L (p)} (p^{(k)} r^{(k)}) / \sum_{k = 1}^{# L (p)} p^{(k)}$ , and r (k) is the subscript of linguistic term L (k) = (k = 1, 2, . . . , # L (p)).

Definition 6. [13] Let L (p) ={ L^(k) (p^(k)) |k = 1, 2, . . . , # L^(p) } be a PLTS, and r (k) be the subscript of linguistic term L (k), and E (L (p)) = s_α, where $α = \sum_{k = 1}^{# L (p)} (p^{(k)} r^{(k)}) / \sum_{k = 1}^{# L (p)} p^{(k)}$ . Then the deviation degree of L (p) is:

$Δ = (\sum_{k = 1}^{# L (p)} (p^{(k)} (r^{(k)} - \bar{α}))^{2})^{\frac{1}{2}} / \sum_{k = 1}^{# L (p)} p^{(k)}$ (4)

Given arbitrary L₁ (p) and L₂ (p) then following conclusions can be drawn:

if E (L₁ (p)) < E (L₂ (p)), then L₁ (p) < L₂ (p);

if E (L₁ (p)) > E (L₂ (p)), then L₁ (p) > L₂ (p);

if E (L₁ (p)) = E (L₂ (p)), then

if Δ (L₁ (p)) < Δ (L₂ (p)), then L₁ (p) < L₂ (p);

if Δ (L₁ (p)) > Δ (L₂ (p)), then L₁ (p) > L₂ (p);

if Δ (L₁ (p)) = Δ (L₂ (p)), then L₁ (p) = L₂ (p).

Definition 7. [14] Let , and be three arbitrary PLTSs,

$L_{1} (p) \oplus L_{2} (p) = {L_{3}^{(k_{3})} (p^{(k_{3})}) | k_{3} = 1, 2, . . ., # L_{3} (p)}$

λL₁ (p) ={ λL₁ (k₁) |k₁ = 1, 2, . . . , # L₁ (p) }

Where $L_{3}^{(k_{3})} = L_{1}^{(k_{1})} \oplus_{2}^{(k_{2})}$ , $p_{3}^{(k_{3})} = p_{1}^{(k_{1})} \cdot p_{2}^{(k_{2})} (k_{1} = 1, 2, . . ., # L_{1} (p); k_{2} = 1, 2, . . ., # L_{2} (p))$ .

Definition 8. [23] Let , be two arbitrary PLTSs and # L₁ (p) = # L₂ (p), then the distance between L₁ (p) and L₂ (p) can be calculated by: $\begin{matrix} d (L_{1} (p), L_{2} (p)) = | p_{1}^{(k_{1})} \frac{I (r_{1}^{(k)})}{τ} - p_{2}^{(k_{2})} \frac{I (r_{2}^{(k)})}{τ} | \end{matrix}$

The normalize Euclidean distance between L₁ (p) and L₂ (p) can be calculated by:

$\begin{matrix} d (L_{1} (p), L_{2} (p)) \\ = \sqrt{\sum_{k = 1}^{# L_{1} (p)} (p_{1}^{(k)} r_{1}^{(k)} - p_{2}^{(k)} r_{2}^{(k)})^{2} / # L_{1} (p)} \end{matrix}$ (5) where $r_{1}^{(k)}$ and $r_{2}^{(k)}$ are the subscripts for $L_{1}^{(k)}$ and $L_{2}^{(k)}$ , respectively.

Remark 1. If # L₁ (p) < # L₂ (p), then add corresponding elements for # L₁ (p) until # L₁ (p) = # L₂ (p).

Definition 9. [24] Let $L_{i} (p) = {L_{i}^{(k_{i})} (p_{i}^{(k_{i})}) | k_{i} = 1, 2, . . ., # L_{i} (p)} (i = 1, 2, . . ., n)$ be n PLTSs, w = (w₁, w₂, . . . , w_n) ^T is the weight vector of L_i (p) (i = 1, 2, . . . , n), w_i ⩾ 0 (i = 1, 2, . . . , n) and $\sum_{i = 1}^{n} w_{i} = 1$ . Probabilistic language weighted average operator (PLWA) is:

$\begin{matrix} PLWA (L_{1} (p), L_{2} (p), . . ., L_{n} (p)) = \oplus_{i = 1}^{n} w_{i} L_{i} \\ = w_{1} L_{1} (p) \oplus w_{2} L_{2} (p) \oplus . . . \oplus w_{n} L_{n} (p) \\ = ⋃_{L_{1}^{(k_{1})} \in L_{1} (p)} {w_{1} L_{1}^{(k_{1})}} \oplus ⋃_{L_{2}^{(k_{2})} \in L_{2} (p)} \\ {w_{2} L_{2}^{(k_{2})}} \oplus . . . \oplus ⋃_{L_{n}^{(k_{n})} \in L_{n} (p)} {w_{n} L_{n}^{(k_{n})}} \end{matrix}$ (6)

2.2 Prospect theory

Tversky and Kahneman believed that managers had bounded rationality rather than complete rationality, and they showed irrational behavior in the face of risks. Based on this, they put forward the prospect theory. The value function is expressed as follows:

$v (x) = {\begin{matrix} {(x)}^{α}, x ⩾ 0 \\ - λ {(- x)}^{β}, x < 0 \end{matrix}$ (7)

The decision maker measures gains and losses against reference points. Reference points are generally determined according to one’s own risk preference and psychological state. The reference point can be specified by the following methods: (1) the zero point, (2) the mean value, (3) the medium value, (4) the worst value and (5) the best value. We formally consider rational expectations as a reference point [25]. Prospect values under probabilistic linguistic environment are as follows:

$π (k) = {\begin{matrix} \frac{k^{γ}}{{(k^{γ} + {(1 - k)}^{γ})}^{\frac{1}{γ}}}, x ⩾ 0 \\ \frac{k^{δ}}{{(k^{δ} + {(1 - k)}^{δ})}^{\frac{1}{δ}}}, x < 0 \end{matrix}$ (8)

2.3 TODIM method

TODIM method was first proposed by Gomes et al. It is an interactive multi-attribute decision making method based on prospect theory, which can adjust the parameters in the decision process according to the decision maker’s risk preference, and the result is more consistent with the decision maker’s preference, considering the decision maker’s psychological behavior. It is an effective method to solve multi-attribute decision making problem. Generally speaking, after the initial decision matrix is normalized by TODIM method, the overall advantage degree of each scheme is obtained by calculating the advantage degree between each scheme and other schemes. The optimal scheme is selected according to the overall advantages of each scheme. The greater the overall superiority, the better the scheme.

Set A ={ A₁, A₂, . . . , A_m } represents the set of m alternatives, where A_i represents the ith alternative. C ={ c₁, c₂, . . . c_n } is the set of attributes, where C_j represents the ith attribute. The corresponding attribute weight vector is denoted as w = (w₁, w₂, . . . , w_n), and $\sum_{j = 1}^{n} w_{j} = 1, w_{j} ⩾ 0$ . Let $X_{u} = {[x_{ij}^{u}]}_{m \times n}$ be the decision matrix, where $x_{ij}^{u}$ represents the attribute value of expert e_u to scheme A_i about attribute C_j. The main operation steps of TODIM:

Step 1: Determine the evaluation value of each alternative scheme under each decision attribute and construct the initial decision matrix $X_{u} = {[x_{ij}^{u}]}_{m \times n}$ . The initial decision matrix is normalized to eliminate the dimensionality effect and then the normalized matrix $X_{u}^{*} = {[x_{ij}^{u^{*}}]}_{m \times n}$ is obtained.

Step 2: Calculate the relative weight of attribute C_j relative to attribute C_r, and its calculation formula is as follows:

$w_{jr} = \frac{w_{j}}{w_{r}}, j = 1, 2, . . . n$ (9)

Where w_r = max{ w_j|j ∈ N } w_r = max { w₁, w₂, ⋯ , w_n }.

Step 3: Calculate the superiority of scheme A_i over scheme A_k for attribute C_j by experts, and its calculation formula is:

$Φ_{j}^{u} (A_{i}, A_{k}) = {\begin{cases} (x_{i j}^{u *} - x_{k j}^{u *}) w_{j r} / (\sum_{j = 1}^{n} w_{j r}), x_{i j}^{u *} - x_{k j}^{u *} > 0 \\ 0, x_{i j}^{u *} - x_{k j}^{u *} = 0 \\ - \frac{1}{θ} \sqrt{(x_{k j}^{u *} - x_{k j}^{u *}) (\sum_{j = 1}^{n} w_{j r}) / w_{j r},} x_{k j}^{u *} - x_{k j}^{u *} < 0 \end{cases}$ (10)

Where, θ is the loss attenuation coefficient, indicating the sensitivity of decision makers to losses.

Step 4: Calculate the comprehensive advantage degree of scheme A_i relative to scheme A_k, and the calculation formula is as follows:

$δ (A_{i}, A_{k}) = \sum_{j = 1}^{n} Φ_{j} (A_{i}, A_{k})$ (11)

Step 5: Calculate the overall superiority of scheme A_i relative to all other schemes, and the calculation formula is as follows:

$δ (A_{i}) = \frac{\sum_{k = 1}^{m} δ (A_{i}, A_{k}) - min_{i} {\sum_{k = 1}^{m} δ (A_{i}, A_{k})}}{max_{i} {\sum_{k = 1}^{m} δ (A_{i}, A_{k})} - min_{i} {\sum_{k = 1}^{m} δ (A_{i}, A_{k})}}$ (12)

Step 6: Rank the schemes according to the overall superiority degree of the schemes. The larger δ (A_i) is, the better the scheme A_i is.

3 Development of evaluation criteria for emergency logistics capacity

Emergency logistics capacity refers to the process of special logistics capacity for emergency activities in the event of an emergency, including the entire process of determining the purchase, sorting, transportation and delivery of materials to emergency relief points, starting from emergency needs analysis [26]. The evaluation of emergency logistics capability has strong flexibility and openness, and the evaluation system of emergency logistics capability is still in the development stage.

3.1 Emergency logistics capacity

The research on emergency logistics capability in China is still in the initial stage, and the main research focuses on the micro level, such as the definition, characteristics and index selection of emergency logistics capability. At present, there are few researches on emergency logistics capacity evaluation, and emergency logistics capacity evaluation will become an important research direction.

Li et al. constructed the Hilbert index space with support capacity as the center, put forward the comprehensive evaluation model of emergency logistics capability of railway military transportation support [27]. Yao et al. constructed a multi-level evaluation model of emergency logistics capability based on gray and fuzzy theory and applied gray scale theory and membership theory in fuzzy mathematics [28]. Sun et al. built an evaluation index system for emergency logistics using fuzzy analytic hierarchy process, including the input of emergency logistics system, operation management of emergency logistics and operation efficiency of emergency logistics [29]. Taking the emergency logistics capacity of the Beijing-Tianjin-Hebei region as the object, Ma et al. established the regional emergency logistics capacity model based on the fuzzy mattering element method, evaluated the emergency logistics capacity of the Beijing-Tianjin-Hebei region in recent years with this model. Based on this, the change chart of main index capability and the trend chart of comprehensive capability are obtained, and the conclusion of the research is summarized and verified in the end [30].

Based on the analysis and summary of related literatures on the evaluation of logistics capability at home and abroad, we divide the emergency logistics capability into 5 levels. They are defined as follows: initial stage (L₁), individual response stage (L₂), decentralized coordination stage (L₃), coordinated efficiency stage (L₄) and continuous improvement stage (L₅). In order to better describe the characteristics of each level in emergency logistics, key links of emergency logistics including coordinated operational capability (C₁) of each level, logistics operation supply (C₂), information processing (C₃), human resource management (C₄) and influence degree (C₅) are selected as the evaluation that constitute the evaluation index system. Different levels' characteristics for emergency logistics are given in Table 1.

Table 1
Different levels’ characteristics for emergency logistics

Dimensions levels C1 C2 C3 C4 C5

LI Emergency logistics command is absent or in disorder. Emergency supplies is absent or in disorder. Disorderly supervision, information feedback is inefficiency. Lack of specific policies for the human resources allocation. The masses live in disorder.

L2 Responsibilities are not well defned. There are rules to follow, standard management. Passive response to emergency information. Insufficient personnel, policies concerned are implemented in disorder. Standardization supervision, high resource utilization, service quality has been improved.

L3 Emergency relief main body dislocation, mechanism impassability. The process is managed and controlled in both directions. Multi agent participation with sound coordination, including government, the thrid party, media and the public. Transfer instructions for relief workers from top to bottom. The supervision is highly goaldirected, effective. The process is in control.

L4 The functions related to emergency manangement of multiple departments are integrated. There are specific standards for measuring the process. Quantitative analysis can be conducted. Mature and stable management model. Sound supervision system for information processing. Good coordination. Condtrollable performance. Multi agent participation, diverse personnel structure. Effective regulation of the emergency, which could be quantitatively measured and evaluated.

L5 Defects in supervision could be found out and strategies for improvement could be made to develop a continuous improvement process. New concepts and technologies in the process of emergency supply could be quantitatively analyzed and effectively applied. The supervision process is improved continuously. Disaster relief personnel are dispatched in batches and grades. Supervision effectiveness is enhanced, which could continuously improve the satisfaction of the affected people.

Dimensions levels	C1	C2	C3	C4	C5
LI	Emergency logistics command is absent or in disorder.	Emergency supplies is absent or in disorder.	Disorderly supervision, information feedback is inefficiency.	Lack of specific policies for the human resources allocation.	The masses live in disorder.
L2	Responsibilities are not well defned.	There are rules to follow, standard management.	Passive response to emergency information.	Insufficient personnel, policies concerned are implemented in disorder.	Standardization supervision, high resource utilization, service quality has been improved.
L3	Emergency relief main body dislocation, mechanism impassability.	The process is managed and controlled in both directions.	Multi agent participation with sound coordination, including government, the thrid party, media and the public.	Transfer instructions for relief workers from top to bottom.	The supervision is highly goaldirected, effective. The process is in control.
L4	The functions related to emergency manangement of multiple departments are integrated.	There are specific standards for measuring the process. Quantitative analysis can be conducted. Mature and stable management model.	Sound supervision system for information processing. Good coordination. Condtrollable performance.	Multi agent participation, diverse personnel structure.	Effective regulation of the emergency, which could be quantitatively measured and evaluated.
L5	Defects in supervision could be found out and strategies for improvement could be made to develop a continuous improvement process.	New concepts and technologies in the process of emergency supply could be quantitatively analyzed and effectively applied.	The supervision process is improved continuously.	Disaster relief personnel are dispatched in batches and grades.	Supervision effectiveness is enhanced, which could continuously improve the satisfaction of the affected people.

Coordinated operational capability (C₁): In the face of the emergency logistics demand, the government should establish the command organization and operation system in time, mainly to coordinate and dispatch emergency logistics in emergencies. The indicators are organizational mobilization ability, emergency logistics command and dispatch ability, command response time, organizational decision-making ability, etc.

Logistics operation supply (C₂): It is the basic guarantee of emergency logistics activities. The evaluation of logistics operation supply capacity is mainly based on three specific indexes: emergency material support capacity, emergency material transportation and distribution capacity, and the rationality of emergency logistics center.

Information processing (C₃): It refers to the role played by emergency logistics information in various processes in the whole emergency logistics activities. The information processing ability is evaluated from five specific indicators: the ability to monitor emergencies, the ability to predict emergencies, the ability to collect and analyze information, the ability to share information, and the ability to give information feedback.

Human resource management (C₄): As the basic guarantee of emergency logistics, human resource evaluation is the core of emergency logistics capability test. The human resource support ability is evaluated from the indicators of personnel composition, expert support ability, personnel training and drills, personnel response processing ability and rescue team construction.

Influence degree (C₅): It mainly evaluates the consequences brought by the emergency logistics activities after the emergency logistics, evaluates the overall satisfaction of the survey masses. The specific indicators mainly include the satisfaction rate of the masses and the number of complaints from the masses. After the emergency, the rescue workers to ensure the victims of the living supplies, psychological comfort. Emergency relief materials are related to the survival of the victims, should be distributed in accordance with the principle of “first urgent, then slow, focus", overall planning, reasonable arrangements, make full use of it.

4 Methodology

4.1 Description

Assume that the emergency decision-making team consists of E_p (1 ⩽ p ⩽ h) experts, the set composed of emergency areas is denoted as A ={ A₁, A₂, . . . , A_n }. There are m indicators for evaluating emergency logistics capacity, and the index set is denoted as C ={ c₁, c₂, . . . c_m }. The corresponding attribute weight vector is denoted as w = (w₁, w₂, . . . , w_n), and $\sum_{j = 1}^{n} w_{j} = 1, w_{j} ⩾ 0$ . When experts evaluate schemes, attribute values are expressed and described with probabilistic language term set. The language term set is denoted as S ={ s_α|α = - τ, . . . , 0, 1, . . . , τ }, the evaluation value of expert E_p on attribute c_j of scheme A_i is denoted as $L_{ij}^{k} {(p)}_{m \times n} (i = 1, 2, . . ., n; j = 1, 2, . . ., m; k = 1, 2, . . ., p)$ , and the standardized decision matrix is denoted as $B = {(b_{ij}^{k})}_{m \times n}$ . In this paper, the probabilistic language term set is combined with the improved QFD and TODIM method to evaluate emergency logistics capacity.

4.2 The proposed Importance calculation based on improved QFD

Quality Function Deployment (QFD) is a product design and development tool driven by user demand, which is widely used in the analysis of user demand to ensure product Quality and improve user satisfaction. Demand evaluation involves many qualitative and quantitative indicators [31]. Aimed at the uncertainty of demand evaluation environment and user preferences, using the user needs assessment in the mixed information characterization of QFD, considering the language more accord with experts in the expression of fuzzy situation habit, linguistic term set representation using probability relationship of demand and module in QFD, obtain high degree of differentiation of the needs of the expert important degree, determine the importance of requirements. In this paper, the emergency logistics capability evaluation is transformed into user demand evaluation, and the importance of each index of emergency logistics capability is determined by using QFD theory as the attribute weight. The demand analysis method at the user level is proposed to solve the impact of group consistency and balance on the demand analysis results, and the demand analysis method at the expert level is proposed to integrate the demand analysis into the group comprehensive decision-making process.

First, based on the attitude of experts, the optimization model is constructed. Prospect theory can well reflect the attitude of experts to user needs, and experts give the highest importance to the demand that is closest to the expectation, namely the demand with the largest prospect value. Build optimization goals to maximize the prospect value. $M_{1} {\begin{cases} \max f (B) = \sum_{j = 1}^{m} \sum_{i = 1}^{m} u_{i j}^{P} b_{i j} \\ s . t \sum_{j = 1}^{n} w_{j}^{2} = 1, w_{j} ⩾ 0, j = 1, 2, ... n \end{cases}$ Where $u_{ij}^{P} = {\begin{matrix} {(d (d_{ij}, d_{qj}))}^{α}, d_{ij} ⩾ d_{qj} \\ - λ {(d (d_{ij}, d_{qj}))}^{β}, d_{ij} < d_{qj} \end{matrix}$ , represents the prospect value of the association value d_ij and the ideal association value d_qj of expert e^P. According to the literature [29], α = β = 0.88λ = 2.25. Second, obtain the weight of each expert. The weight of expert E_p is:

$ɛ_{p} = \frac{u_{ij}^{p}}{\sum_{p = 1}^{h} u_{ij}^{p}}$ (13) Then, based on the difference degree, the optimization model is built. $\begin{matrix} M_{2} {\begin{matrix} max f (B) = \sum_{j = 1}^{m} \sum_{i = 1}^{m} {(1 / (m - 1) \sum_{i, q = 1, i \neq q}^{m} d^{2} (u_{ij}^{P}, u_{qj}^{P}))}^{2} b_{ij} \\ s . t \sum_{j = 1}^{n} w_{j}^{2} = 1, w_{j} ⩾ 0, j = 1, 2, . . . n \end{matrix} \end{matrix}$ Obtain the importance of development requirements from the perspective of experts. Taking expert attitude and difference degree into consideration, the combination model is obtained. $\begin{matrix} M_{3} {\begin{matrix} max f (B) = \sum_{j = 1}^{m} \sum_{i = 1}^{m} u_{ij} b_{ij} + \sum_{j = 1}^{m} \sum_{i = 1}^{m} {(1 / (m - 1) \sum_{i, q = 1, i \neq q}^{m} d {(b_{ij}, b_{qj})}^{2})}^{2} b_{ij} \\ s . t \sum_{j = 1}^{n} w_{j}^{2} = 1, w_{j} ⩾ 0, j = 1, 2, . . . n \end{matrix} \end{matrix}$ Finally, the importance of user needs from the perspective of expert E_p is obtained by solving Model M₃, $w_{j} = (w_{1}, w_{2}, . . ., w_{n})$

4.3 Evaluation procedure for the TODIM method for PLTSs

TODIM method was an effective method to solve multi-attribute decision making problems. Hu et al. proposed a new three-way decision model TODIM method, which adopts a new probability degree. Ji et al. proposed an item-based TODIM method for neutral information. Llamazares popularized the traditional TODIM method with a series of functions and proved some properties of the TODIM method. The key idea is to select the dominant value superior to other options. In general, after the normalization of the initial decision matrix, the traditional TODIM method obtains the overall advantage degree of each scheme by calculating the advantage degree between each scheme and other schemes. This method can only be used to solve the multi-attribute decision making problem where the evaluation attribute value is exact.

According to the criteria weights, calculate the relative weights of criterion c_j:

$w_{jr} = \frac{w_{j}}{w_{r}}, j = 1, 2, . . . n$ (14) where w_r = max{ w₁, w₂, . . . , w_n }.

Then calculate the dominance degree for alternative A_i over A_k in terms of criterion c_j, where θ is the losses attenuation factor, d (b_ij, b_kj) is the distance between b_ijand b_kj. The smaller the θ is, the better the loss aversion is.

$\begin{matrix} Φ_{j} (A_{i}, A_{k}) \\ = {\begin{matrix} \sqrt{d (b_{ij}, b_{kj}) w_{jr} / (\sum_{j = 1}^{n} w_{jr})}, & if & b_{ij} ≻ b_{kj} \\ 0, & if & b_{ij} = b_{kj} \\ - \frac{1}{θ} \sqrt{d (b_{ij}, b_{kj}) (\sum_{j = 1}^{n} w_{jr}) / w_{jr}}, & if & b_{ij} ≺ b_{kj} \end{matrix} \end{matrix}$ (15)θ is the attenuation factor, $0 < θ < \frac{1}{w_{jr}}$ . d (b_ij, b_kj) is the distance between b_ij and b_kj. $\begin{matrix} | \sqrt{w_{jr} d (b_{ij}, b_{kj})} | < | - \frac{1}{θ} \sqrt{\frac{1}{w_{jr}} d (b_{ij}, b_{kj})} | \end{matrix}$

The above formula indicates that the smaller θ is, the higher the risk of loss aversion of experts is.

Calculate the dominance degree for A_i over A_k in all criteria.

$Φ (A_{i}, A_{k}) = \sum_{j = 1}^{n} Φ_{j} (A_{i}, A_{k})$ (16)

Then, calculate the overall dominance degree for A_i:

$Z (A_{k}) = \frac{\sum_{k = 1}^{m} Φ (A_{i}, A_{k}) - min_{i} {\sum_{k = 1}^{m} Φ (A_{i}, A_{k})}}{max_{i} {\sum_{k = 1}^{m} Φ (A_{i}, A_{k})} - min_{i} {\sum_{k = 1}^{m} Φ (A_{i}, A_{k})}}$ (17)

In this Section, the TODIM method for PLTSs model for evaluation criteria for emergency logistics capacity will be built based on the prospect theory and QFD, as shown in Fig. 1.

Fig. 1

The flowchart of the TODIM method for PLTSs model.

5 A case study

The epidemic of COVID-19 has seriously threatened human health and brought heavy burdens and severe challenges to the world economy and society. The global epidemic continues to spread, and the situation in some countries remains grim. Relevant researches on emergency logistics have become a major demand. In this COVID-19 pandemic, emergency logistics plays a key role in public health emergencies. Suppose that an occurrence of unexpected public health events caused huge economic losses and casualties. There were four representatives of the hardest-hit. Therefore, these four typical cities selected to be evaluated. They are A₁, A₂, A₃ and A₄. We assume that the five levels (L₁, L₂, L₃, L₄, L₅) are the corresponding linguistic fuzzy terms s₀, s₁, s₂, s₃, s₄. Suppose the assessment team has four experts (X₁, X₂, X₃, X₄) in the field of emergency management. Then, emergency logistics capacity of the four cities will be evaluated based on PLTSs.

Tables 2–5 can be translated into the following decision matrix B with PLTSs: $\begin{matrix} \begin{matrix} B = [\begin{matrix} {S_{2} (0.5), S_{3} (0.5)} & {S_{2} (0.5), S_{3} (0.5)} & {S_{2} (0.22), S_{3} (0.78)} \\ {S_{2} (0.52), S_{3} (0.26), S_{4} (0.2)} & {S_{2} (0.23), S_{3} (0.54), S_{4} (0.23)} & {S_{3} (1)} \\ {S_{1} (0.22), S_{2} (0.78)} & {S_{1} (0.22), S_{2} (0.26), S_{4} (0.52)} & {S_{3} (0.78), S_{4} (0.22)} \\ {S_{3} (0.5), S_{4} (0.5)} & {S_{3} (0.78), S_{4} (0.22)} & {S_{2} (1)} \end{matrix} \\ \begin{matrix} {S_{1} (0.23), S_{2} (0.54), S_{3} (0.23)} & {S_{3} (1)} \\ {S_{4} (1)} & {S_{2} (0.22), S_{3} (0.26), S_{4} (0.52)} \\ {S_{2} (0.22), S_{3} (0.78)} & {S_{3} (1)} \\ {S_{2} (0.22), S_{3} (0.26), S_{4} (0.52)} & {S_{3} (0.5), S_{4} (0.5)} \end{matrix}] \end{matrix} \end{matrix}$

Table 2
The assessment of Expert (X₁) corresponding to different criteria

C₁ C₂ C₃ C₄ C₅

A₁ S₃ S₂ S₂ S₃ S₃

A₂ S₂ S₃ S₃ S₄ S₄

A₃ S₂ S₁ S₃ S₃ S₃

A₄ S₄ S₃ S₂ S₄ S₃

	C₁	C₂	C₃	C₄	C₅
A₁	S₃	S₂	S₂	S₃	S₃
A₂	S₂	S₃	S₃	S₄	S₄
A₃	S₂	S₁	S₃	S₃	S₃
A₄	S₄	S₃	S₂	S₄	S₃

Table 3

The assessment of Expert (X₂) corresponding to different criteria

	C₁	C₂	C₃	C₄	C₅
A₁	S₃	S₃	S₃	S₂	S₃
A₂	S₃	S₄	S₃	S₄	S₂
A₃	S₂	S₃	S₄	S₃	S₃
A₄	S₃	S₃	S₂	S₄	S₄

Table 4

The assessment of Expert (X₃) corresponding to different criteria

	C₁	C₂	C₃	C₄	C₅
A₁	S₂	S₃	S₃	S₁	S₃
A₂	S₄	S₃	S₃	S₄	S₃
A₃	S₁	S₂	S₃	S₂	S₃
A₄	S₃	S₄	S₂	S₂	S₄

Table 5

The assessment of Expert (X₄) corresponding to different criteria

	C₁	C₂	C₃	C₄	C₅
A₁	S₂	S₂	S₃	S₂	S₃
A₂	S₂	S₂	S₃	S₄	S₄
A₃	S₂	S₃	S₃	S₃	S₃
A₄	S₄	S₃	S₂	S₂	S₃

After normalization, matrix B can be transformed into normalized matrix $\dot{B}$ .

$\begin{matrix} \begin{matrix} \dot{B} = [\begin{matrix} {S_{1} (0), S_{2} (0.5), S_{3} (0.5), S_{4} (0)} & {S_{1} (0), S_{2} (0.5), S_{3} (0.5), S_{4} (0)} & {S_{1} (0), S_{2} (0.22), S_{3} (0.78) S_{4} (0)} \\ {S_{1} (0), S_{2} (0.52), S_{3} (0.26), S_{4} (0.2)} & {S_{1} (0), S_{2} (0.23), S_{3} (0.54), S_{4} (0.23)} & {S_{1} (0), S_{2} (0), S_{3} (1) S_{4} (0)} \\ {S_{1} (0.22), S_{2} (0.78), S_{3} (0), S_{4} (0)} & {S_{1} (0.22), S_{2} (0.26), S_{3} (0), S_{4} (0.52)} & {S_{1} (0), S_{2} (0), S_{3} (0.78), S_{4} (0.22)} \\ {S_{1} (0), S_{2} (0), S_{3} (0.5), S_{4} (0.5)} & {S_{1} (0), S_{2} (0), S_{3} (0.78), S_{4} (0.22)} & {S_{1} (0), S_{2} (1) S_{3} (0), S_{4} (0)} \end{matrix} \\ \begin{matrix} {S_{1} (0.23), S_{2} (0.54), S_{3} (0.23), S_{4} (0)} & {S_{1} (0), S_{1} (0), S_{3} (1), S_{4} (0)} \\ {S_{1} (0), S_{2} (0), S_{3} (0), S_{4} (1)} & {S_{1} (0), S_{2} (0.22), S_{3} (0.26), S_{4} (0.52)} \\ {S_{1} (0), S_{2} (0.22), S_{3} (0.78), S_{4} (0)} & {S_{1} (0), S_{2} (0), S_{3} (1), S_{4} (0)} \\ {S_{1} (0), S_{2} (0.22), S_{3} (0.26), S_{4} (0.52)} & {S_{1} (0), S_{2} (0), S_{3} (0.5), S_{4} (0.5)} \end{matrix}] \end{matrix} \end{matrix}$

Step 1 According to Model M₁, M₂ and Equation (14), Obtain the importance of user needs from the perspective of experts. The expert weight is obtained w = (0.142, 0.193, 0.220, 0.312, 0.133).

Step 2 Select C₄ with the highest weight as the reference criterion, calculate the relative weights w_r = (0.455, 0.618, 0.683, 1, 0.412) based on Equation (15).

Step 3 Let θ = 2.25 and calculate the dominance degree for A_i over A_k in all criteria (A_i, A_k) according to Equations (16-17). $\begin{matrix} \begin{matrix} Z_{1} = [\begin{matrix} 0 & - 0.362 & 0.371 & - 1.038 \\ - 0.423 & 0 & 0.164 & - 1.226 \\ 0.355 & - 0.512 & 0 & - 1.618 \\ 0.473 & 0.541 & 0.739 & 0 \end{matrix}] \\ Z_{2} = [\begin{matrix} 0 & - 0.348 & 0.237 & - 0.459 \\ 0.173 & 0 & 0.356 & - 0.338 \\ - 0.703 & - 0.647 & 0 & - 0.923 \\ 0.294 & 0.257 & 0.447 & 0 \end{matrix}] \end{matrix} \end{matrix}$ $\begin{matrix} \begin{matrix} Z_{3} = [\begin{matrix} 0 & 0.411 & - 0.911 & 0.412 \\ 0.288 & 0 & - 0.248 & 0.338 \\ 0.353 & 0.152 & 0 & 0.246 \\ - 0.675 & - 2.080 & - 2.808 & 0 \end{matrix}] \\ Z_{4} = [\begin{matrix} 0 & - 1.247 & - 1.183 & - 1.351 \\ 0.798 & 0 & 0.669 & 0.365 \\ 0.545 & - 1.359 & 0 & - 0.568 \\ 0.596 & - 1.091 & 0.614 & 0 \end{matrix}] \end{matrix} \end{matrix}$ $\begin{matrix} \begin{matrix} Z_{5} = [\begin{matrix} 0 & - 0.130 & 0 & - 0.130 \\ 0.109 & 0 & 0.059 & - 0.215 \\ 0 & - 0.158 & 0 & - 0.134 \\ 0.120 & 0.128 & 0.120 & 0 \end{matrix}] \end{matrix} \end{matrix}$

Step 4 Calculate the overall dominance degree, as shown in Table 6. Z(A₁) = 0, Z(A₂) = 1, Z(A₃) = 0.235, Z(A4) = 0.475. Therefore, the ranking result is A₂ > A₄ > A₃ > A₁.

Table 6

Dominance degrees for 4 cities

	A₁	A₂	A₃	A₄
A₁	0	–2.927	–1.302	–2.791
A₂	0.629	0	1.211	–0.592
A₃	–0.127	–2.877	0	–2.723
A₄	0.898	–2.064	–0.802	0

6 Conclusions

Scientific and reasonable evaluation of emergency logistics capacity is of great significance to the establishment and improvement of disaster relief material reserve system and emergency material guarantee system. This paper studies the concept of emergency logistics capability and the weight determination model based on QFD, which can better reflect the comprehensive effect of emergency logistics. On this basis, in order to fully reflect the expert preference and evaluation information, the evaluation model of the improved TODIM method is constructed by combining the probabilistic language term sets with the improved TODIM method. In terms of improving the information representation of QFD, considering the user’s preference for requirements and the vagueness and uncertainty of demand information and the difference degree of experts’ attitudes and users’ needs, it provides a more stable guarantee mechanism for the realization of users’ needs, and obtains the importance degree of demands at the expert level. The next step is to study the requirement importance determination method from the dual perspectives of user demand analysis and expert demand analysis.

Footnotes

Acknowledgments

This paper is supported by the National Social Science Foundation of China (NO: 20BTJ012), the Social Science Foundation of Hebei province of China (No. HB18GL008), Beijing Intelligent Logistics System Collaborative Innovation Center (BILSCIC-2019KF-15), and Philosophy and Social Science key cultivation project of Hebei University(2019HPY035).

References

, Wang

and Jiang

, Emergency logistics, Journal of Chongqing University (Natural Science Edition) 27(3) (2004), 164–167.

Ken

, Cook

and Stephenson.

, Lesson in logistics form Somalia, Disaster 8 (1984), 57–66.

Aikens

C.H.

, Facility location on models for distribution planning, European Joumal of Operational Research 22(2) (1985), 263–279.

Carter

W.N.

, Disaster Management: A Disaster Manager’s Handbook;. Philippines: Asian Development Bank (1992), 5–25.

Suleyman

and Willman

A.W.

, The emerging area of emergency management and engineering, IE Transportation on Engineering 45(2) (1998), 103–105.

, The cost loss of emergency logistics is everywhere, China Materials Distribution 23 (2003), 18–19.

Wang

, Research summary on China’s emergency logistics, Logistics Sci-Tech 6 (2009), 04–06.

Sun

, Emergency Logistics Status and Its Development Trend Analysis, China Safety Science Journal 20(10) (2010), 166–168.

Zadeh

L.A.

, Fuzzy sets, Information Control 8(3) (1965), 338–353.

10.

Rodriguez

R.M.

, Martinez

and Herrera

, Hesitant fuzzy linguistic term sets for decision making[J], IEEE Transactions on Fuzzy Systems 20(1) (2012), 109–119.

11.

Torra

, Hesitant fuzzy sets, International Journal of Intelligent Systems 25 (2010), 529–539.

12.

ZadehL

, The concept of a linguistic variable and its application to approximate reasoning, Information Sciences 8 (1975), 199–249.

13.

Pang

, Wang

and Xu

, Probabilistic linguistic term sets in multi-attribute group decision making, Information Sciences 369(10) (2016), 128–143.

14.

Zhang

, Xu

, Wang

and Liao

, Consistency based risk assessment with probabilistic linguistic preference relation, Applied Soft Computing 49 (2016), 817–833.

15.

Gou

and Xu

, Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic term sets, Information Sciences 372(1) (2016), 407–427.

16.

Wang

, Wang

and Zhang

, Distance-based multicriteria group decision-making approach with probabilistic linguistic term sets, Expert Systems 36 (2019)–.

17.

Liu

and Li

, Multi-attribute decision making method based on generalized maclaurin symmetric mean aggregation operators for probabilistic linguistic information, Computers & Industrial Engineering 131 (2019), 282–294.

18.

Luo

, Zhang

and Wang

, Group decision-making approach for evaluating the sustainability of constructed wetlands with probabilistic linguistic preference relations, Journal of the Operational Research Society 70(12) (2019), 2039–2055.

19.

and Liao

, A consensus-based probabilistic linguistic gained and lost dominance score method, European Journal of Operational Research 272 (2019), 1017–1027.

20.

Lin

and Xu

, Probabilistic linguistic distance measures and their applications in multi-criteria group decision making, Soft Computing Applications for Group Decision-Making and Consensus Modeling. Cham: Springer, (2018), 411–440.

21.

, An Emergency Decision-Making Method for Probabilistic Linguistic Term Sets Extended by D Number Theory, Symmetry 12 (2020), 380–.

22.

and Deng

, A New MADA Methodology Based on D Numbers, ms 20(8) (2018), 2458–2469.

23.

Lin

, Chen

, Liao

and Xu.

, ELECTRE II method to deal with probabilistic linguistic term sets and its application to edge computing, Nonlinear Dynamics 96(3) (2019), 2125–2143.

24.

Guo

and Sun

, Multi-attribute decision making method based on single-valued neutrosophic linguistic variables and prospect theory, Journal of Intelligent & Fuzzy Systems 37 (2019), 5351–5362.

25.

Liu

, Conception and Constitution Research of Emergency Logistics Capability, Journal of Catastrophology 22(2) (2007), 123–.

26.

, Study on Evaluation Model for Warrant of Emergency Logistics, Journal of Lanzhou Jiaotong University 26(6) (2007), 64–.

27.

Yao

and He

, Grey fuzzy comprehensive evaluation of emergency logistics capability,s, Commercial Time 23 (2012), 44–46.

28.

Sun

, Evaluation of Emergency Logistics Capabilities Based on GF-AHP Combined Models——Taking the Earthquake Disaster as an Example, Journal of Beijing University of Technology 9 (2014), 1354–.

29.

, Liang

, Yang

and Ge

, Evaluation of Emergency Logistics Capacity of Jing-Jin-Ji Region Based on Fuzzy Matter Element, Logistics Technology 08 (2017), 87–94.

30.

Vinodh

and Pathod

, Integration of ECQFD and LCA for design of sustainable product design, Journal of Cleaner Production 18(8) (2010), 833–842.

31.

Kahneman

and Tversky

, Prospect theory: an analysis of decision under risk, Econometrica: Journal of the Econometric Society 47(2) (1979), 140–170.

Multi-attribute decision making method based on probabilistic linguistic term sets and its application in the evaluation of emergency logistics capacity

Abstract

Keywords

1 Introduction

2 Preliminaries

2.1 Basic theory of PLTS

3.1 Emergency logistics capacity

4.1 Description

4.2 The proposed Importance calculation based on improved QFD

Table 2 The assessment of Expert (X1) corresponding to different criteria C1 C2 C3 C4 C5 A1 S3 S2 S2 S3 S3 A2 S2 S3 S3 S4 S4 A3 S2 S1 S3 S3 S3 A4 S4 S3 S2 S4 S3

Footnotes

Acknowledgments

References

Table 2
The assessment of Expert (X₁) corresponding to different criteria

C₁ C₂ C₃ C₄ C₅

A₁ S₃ S₂ S₂ S₃ S₃

A₂ S₂ S₃ S₃ S₄ S₄

A₃ S₂ S₁ S₃ S₃ S₃

A₄ S₄ S₃ S₂ S₄ S₃