A criteria weighting approach by combining fuzzy quality function deployment with relative preference relation

In past, fuzzy multi-criteria decision-making (FMCDM) models desired to find an optimal alternative from numerous feasible alternatives under fuzzy environment. However, researches seldom focused on determination of criteria weights, although they were also important components for FMCDM. In fact, criteria weights can be computed through extending quality function deployment (QFD) under fuzzy environment, i.e. fuzzy quality function deployment (FQFD). By FQFD, customer demanded qualities expressing the opinions of customers and service development capabilities presenting the opinions of experts can be integrated into criteria weights for FMCDM. However, deriving criteria weights in FQFD may be complex and different to multiply two fuzzy numbers in real world. To resolve the tie, we will combine FQFD with relative preference relation on FMCDM problems. With the relative preference relation on fuzzy numbers, it is not necessary multiplying two fuzzy numbers to derive criteria weights in FQFD. Alternatively, adjusted criteria weights will substitute for original criteria weights through relative preference relation. Obviously, adjusted criteria weights are clearly determined and then utilized in FMCDM models.     

Fuzzy AHP to determine the relative weights of evaluation criteria and Fuzzy TOPSIS to rank the alternatives

The aim of this study is to propose a Fuzzy multi-criteria decision-making approach (FMCDM) to evaluate the alternative options in respect to the user's preference orders. Two FMCDM methods are proposed for solving the MCDM problem: Fuzzy Analytic Hierarchy Process (FAHP) is applied to determine the relative weights of the evaluation criteria and the extension of the Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) is applied to rank the alternatives. Empirical results show that the proposed methods are viable approaches in solving the problem. When the performance ratings are vague and imprecise, this Fuzzy MCDM is a preferred solution.     

Generalizing TOPSIS for fuzzy multiple-criteria group decision-making

In this paper, we generalize TOPSIS to fuzzy multiple-criteria group decision-making (FMCGDM) in a fuzzy environment. TOPSIS is one of the well-known methods for multiple-criteria decision-making (MCDM). Most of the steps of TOPSIS can be easily generalized to a fuzzy environment, except max and min operations in finding the ideal solution and negative ideal solution. Thus we propose two operators Up and Lo which satisfy the partial ordering relation on fuzzy numbers to the generalization of TOPSIS. In generalized TOPSIS, these two operations (Up and Lo) are employed to find ideal and negative ideal solutions under a fuzzy environment. Then the FMCGDM problem can be solved effectively and efficiently.     

Multi-criteria decision-making using interval-valued hesitant fuzzy QUALIFLEX methods based on a likelihood-based comparison approach

QUALIFLEX is a very efficient outranking method to handle multi-criteria decision-making (MCDM) involving cardinal and ordinal preference information. Based on a likelihood-based comparison approach, this paper develops two interval-valued hesitant fuzzy QUALIFLEX outranking methods to handle MCDM problems within the interval-valued hesitant fuzzy context. First, we define the likelihoods of interval-valued hesitant fuzzy preference relations that compare two interval-valued hesitant fuzzy elements (IVHFEs). Then, we propose the concepts of the concordance/discordance index, the weighted concordance/discordance index and the comprehensive concordance/discordance index. Moreover, an interval-valued hesitant fuzzy QUALIFLEX model is developed to solve MCDM problems where the evaluative ratings of the alternatives and the weights of the criteria take the form of IVHFEs. Additionally, this paper propounds another likelihood-based interval-valued hesitant fuzzy QUALIFLEX method to accommodate the IVHFEs’ evaluative ratings of alternatives and non-fuzzy criterion weights with incomplete information. Finally, a numerical example concerning the selection of green suppliers is provided to demonstrate the practicability of the proposed methods, and a comparison analysis is given to illustrate the advantages of the proposed methods.

     

The evaluation of financial performance for Taiwan container shipping companies by fuzzy TOPSIS

In this paper, financial performance of Taiwan container shipping companies are evaluated by fuzzy multi-criteria decision-making (FMCDM). In the evaluating problem, we first apply grey relation analysis to partition financial ratios into several clusters and find representative indices from the clusters. Then the representative indices are considered as evaluation criteria on financial performance assessment of Taiwan container shipping companies, and an FMCDM method called fuzzy technique for order preference by similarity to ideal solution (fuzzy TOPSIS) is utilized to evaluate financial performance. By fuzzy TOPSIS, financial performances of container shipping companies are ranked, and thus a container shipping company can realize its finance competitive strength and weakness between container shipping companies.     

Investigation of multiple heterogeneous relationships using a q-rung orthopair fuzzy multi-criteria decision algorithm

Neural Computing and Applications - Q-rung orthopair fuzzy (q-ROF) set is one of the powerful tools for handling the uncertain multi-criteria decision-making (MCDM) problems, various MCDM methods...     

Generalized score functions on interval-valued intuitionistic fuzzy sets with preference parameters for different types of decision makers and their application

In this paper, the interval-valued intuitionistic fuzzy sets (IVIFSs) are studied from the viewpoint of the decision makers’ preference. Firstly, two series of principles are proposed to guide the ranking of interval-valued intuitionistic fuzzy numbers (IVIFNs), and two kinds of illustrative generalized score functions on IVIFSs are proposed according to the newly proposed principles. Secondly, two kinds of generalized score functions on IVIFSs are proposed based on decision-makers’ preference. The two generalized score functions are both of two parameters, which represent the decision makers’ attitudinal characters on the classical score values and the classical accuracy values on IVIFNs, respectively. Thirdly, two kinds of generalized score functions on IVIFSs, which are suitable for ranking IVIFNs when there is no information about the importance weights of the classical score values and accuracy values on IVIFNs, are proposed based on integral. Fourthly, three kinds of multi-criteria decision-making (MCDM) methods in interval-valued intuitionistic fuzzy setting are proposed. Finally, an example shows that when a novel generalized score function on IVIFSs is proposed, its suitable application environments should also be pointed out.     

PGA/MOEAD: a preference-guided evolutionary algorithm for multi-objective decision-making problems with interval-valued fuzzy preferences

In this research, we propose a preference-guided optimisation algorithm for multi-criteria decision-making (MCDM) problems with interval-valued fuzzy preferences. The interval-valued fuzzy preferences are decomposed into a series of precise and evenly distributed preference-vectors (reference directions) regarding the objectives to be optimised on the basis of uniform design strategy firstly. Then the preference information is further incorporated into the preference-vectors based on the boundary intersection approach, meanwhile, the MCDM problem with interval-valued fuzzy preferences is reformulated into a series of single-objective optimisation sub-problems (each sub-problem corresponds to a decomposed preference-vector). Finally, a preference-guided optimisation algorithm based on MOEA/D (multi-objective evolutionary algorithm based on decomposition) is proposed to solve the sub-problems in a single run. The proposed algorithm incorporates the preference-vectors within the optimisation process for guiding the search procedure towards a more promising subset of the efficient solutions matching the interval-valued fuzzy preferences. In particular, lots of test instances and an engineering application are employed to validate the performance of the proposed algorithm, and the results demonstrate the effectiveness and feasibility of the algorithm.     

A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems

The objective of this paper is divided into two folds. Firstly, a new generalized improved score function has been presented in the interval-valued intuitionistic fuzzy sets (IVIFSs) environment by incorporating the idea of weighted average of the degree of hesitation between their membership functions. Secondly, an IVIFSs based method for solving the multi-criteria decision making (MCDM) problem has been presented with completely unknown attribute weights. A ranking of the different attributes is based on the proposed generalized improved score functions and the sensitivity analysis on the ranking of the system has been done based on the decision-making parameters. An illustrative examples have been studied to show that the proposed function is more reasonable in the decision-making process than other existing functions.     

Application of TOPSIS in evaluating initial training aircraft under a fuzzy environment

This paper develops an evaluation approach based on the Technique for Order Performance by Similarity to Ideal Solution (TOPSIS), to help the Air Force Academy in Taiwan choose optimal initial training aircraft in a fuzzy environment where the vagueness and subjectivity are handled with linguistic terms parameterised by triangular fuzzy numbers. This study applies the fuzzy multi-criteria decision-making (MCDM) method to determine the importance weights of evaluation criteria and to synthesize the ratings of candidate aircraft. Aggregated the evaluators’ attitude toward preference; then TOPSIS is employed to obtain a crisp overall performance value for each alternative to make a final decision. This approach is demonstrated with a real case study involving 16 evaluation criteria, seven initial propeller-driven training aircraft assessed by 15 evaluators from the Taiwan Air Force Academy.     

The fuzzy cross-entropy for intuitionistic hesitant fuzzy sets and their application in multi-criteria decision-making

In this paper, the cross-entropy of intuitionistic hesitant fuzzy sets (IHFSs) is developed by integrating the cross-entropy of intuitionistic fuzzy sets (IFSs) and hesitant fuzzy sets (HFSs). First, several measurement formulae are discussed and their properties are studied. Then, two approaches, which are based on the developed intuitionistic hesitant fuzzy cross-entropy, are proposed for solving multi-criteria decision-making (MCDM) problems within an intuitionistic hesitant fuzzy environment. For both methods, an optimisation model is established in order to determine the weight vector for MCDM problems with incomplete information on criteria weights. Finally, an example is provided in order to illustrate the practicality and effectiveness of the proposed approaches.     

Pythagorean fuzzy average aggregation operators based on generalized and group-generalized parameter with application in MCDM problems

The concept of intuitionistic fuzzy set (IFS) theory plays an important role in dealing with real-life issues under uncertain and imprecise environment. But it has certain limitations and further extended by many researchers by taking different situations. One of the extensions of IFS theory is Pythagorean fuzzy set (PFS), in which the condition of IFS theory, ie, sum of membership degree and nonmembership degree is less than (or equal to) one is related to the square sum of its membership degree and nonmembership degree is less than (or equal to) one. In this study, the concept of the generalized parameter is incorporated into the PFS theory and presented some generalized Pythagorean fuzzy average aggregation operators. Then, the operators are extended to a group-based generalized parameter by taking the opinions of multiple senior experts/observers. Based on the defined operators, a multi-criteria decision-making (MCDM) approach is provided and illustrated with a numerical example to show the proposed approach effectively. Finally, a comparison analysis is also considered to validate the proposed approach over the existing ones.     

An extended outranking approach for multi-criteria decision-making problems with linguistic intuitionistic fuzzy numbers

Linguistic intuitionistic fuzzy numbers (LIFNs), characterized by a linguistic membership degree, linguistic non-membership degree, and linguistic indeterminacy degree, represent a helpful tool for depicting uncertain information under complex environments. This paper focuses on developing an innovative method to address multi-criteria decision-making (MCDM) problems with LIFNs in which the weight information is completely unknown. First, the distance of LIFNs is defined with the aid of linguistic scale functions (LSFs). Second, some extended outranking relationships between each pair of LIFNs are proposed based on the elicitation of the classic relation models. Moreover, a ranking method is constructed to deal with MCDM problems according to the proposed outranking relationships of LIFNs. Finally, an illustrative example concerning coal mine safety evaluation is provided to demonstrate the proposed method, and its feasibility and validity are further verified by a sensitivity analysis and comparison with other existing methods.     

A robust correlation coefficient for probabilistic dual hesitant fuzzy sets and its applications

As a generalization of the hesitant fuzzy sets (HFSs) and dual HFSs (DHFSs), probabilistic dual hesitant fuzzy sets (PDHFSs) are a strong and valuable tool to represent the imprecise information by embedding both the features of HFSs and probabilistic information instantaneously. Meanwhile, a correlation coefficient is a prominent measure to measure the relationship between two sets. Motivated by these primary characteristics, it is interesting to present some information measures to the PDHFSs and hence decision-making approach based on the correlation coefficient. In this paper, we develop a method to solve the multi-criteria decision-making (MCDM) problem under PDHFS environment. For it, firstly, we define the informational energy and the covariance between the two PDHFSs and study their properties. Secondly, we develop correlation coefficients and the weighted correlation coefficients for PDHFSs. In the formulation, DHFSs are able to represent the information in terms of their respective degrees, while the assigned probabilities give more details about the level of agreeness or disagreeness. Also, some properties of the proposed measures are also studied. Thirdly, a novel algorithm is developed based on the proposed operators to solve MCDM problems. A practical example is provided to verify the developed approach and to demonstrate its practicality and feasibility. Also, a comparative analysis with several existing studies reveals the proposed method is better during solving the decision-making problems.

     

Fuzzy MCDM approach for selecting the best environment-watershed plan

In the real word, the decision-making problems are very vague and uncertain in a number of ways. Most of the criteria have interdependent and interactive features, so they cannot be evaluated by conventional measure method. Such as the feasibility, thus, to approximate the human subjective evaluation process, it would be more suitable to apply a fuzzy method in the environment-watershed plan topic. This paper describes the design of a fuzzy decision support system in multi-criteria analysis approach for selecting the best plan alternatives or strategies in environment watershed. The fuzzy analytic hierarchy process (FAHP) method is used to determine the preference weightings of criteria for decision makers by subjective perception (natural language). A questionnaire was used to find out from three related groups comprising 15 experts, including 5 from the university of expert scholars (include Water Resources Engineering and Conservation, Landscape and Recreation, Urban Planning, Environment Engineering, Architectural Engineering, etc.), 5 from the government departments, and 5 from industry. Subjectivity and vagueness analysis is dealt with the criteria and alternatives for selection process and simulation results by using fuzzy numbers with linguistic terms. It incorporated the decision-makers’ attitude towards the preference; overall performance value of each alternative can be obtained based on the concept of fuzzy multiple-criteria decision-making (FMCDM). This research also gives an example of evaluation consisting of five alternatives, solicited from an environment-watershed plan work in Taiwan, is illustrated to demonstrate the effectiveness and usefulness of the proposed approach. The result is useful for destination planning and the sustainability of watershed tourism resources as well.     

基于TOPSIS方法改进的多属性决策模型:最小化偏好反转

针对多属性决策方法(MCDM)中出现的偏好反转问题,提出一种基于TOPSIS方法改进的MCDM模型.该模型用MAX法代替矢量法对数据进行标准化处理,并根据备选方案的相似距离衡量每个选项的优劣性.这种基于距离计算的综合属性评价方法不仅计算简单,而且可以较好地测度选项间的差异,增强决策结果的准确性.同时,将该模型计算的结果与SAW、AHP、TOPSIS、VIKOR方法进行对比分析,发现只存在原选项时,所提出的模型与SAW、AHP方法的排序结果一致,而当添加或删除某个选项时,SAW、AHP、TOPSIS、VIKOR方法均会产生不同程度的偏好反转现象,而所提出的基于TOPSIS改进的模型可以保持选项的相对顺序不变,表明所提出的模型是有效的,且在避免偏好反转问题时较SAW、AHP、TOPSIS、VIKOR方法具有一定的优越性和可靠性.     

直觉模糊POWA算子及其在多准则决策中的应用

为了解决具有优先级的直觉模糊多准则决策问题,定义了直觉模糊优先有序加权平均(IFPOWA)算子.基于优先关系.利用直觉模糊值修正得分函数给出其关联权重向量的计算方法,分析并证明了IFPOWA算子的性质;提出了基于IFPOWA算了的具有优先级的直觉模糊多准则决策方法.最后,利用实例对方法的有效性进行了分析.     

Selection of industrial robots using compromise ranking and outranking methods

Selection of a robot for a specific industrial application is one of the most challenging problems in real time manufacturing environment. It has become more and more complicated due to increase in complexity, advanced features and facilities that are continuously being incorporated into the robots by different manufacturers. At present, different types of industrial robots with diverse capabilities, features, facilities and specifications are available in the market. Manufacturing environment, product design, production system and cost involved are some of the most influencing factors that directly affect the robot selection decision. The decision maker needs to identify and select the best suited robot in order to achieve the desired output with minimum cost and specific application ability. This paper attempts to solve the robot selection problem using two most appropriate multi-criteria decision-making (MCDM) methods and compares their relative performance for a given industrial application. The first MCDM approach is ‘VIsekriterijumsko KOmpromisno Rangiranje’ (VIKOR), a compromise ranking method and the other one is ‘ELimination and Et Choice Translating REality’ (ELECTRE), an outranking method. Two real time examples are cited in order to demonstrate and validate the applicability and potentiality of both these MCDM methods. It is observed that the relative rankings of the alternative robots as obtained using these two MCDM methods match quite well with those as derived by the past researchers.     

Pythagorean fuzzy TODIM approach to multi-criteria decision making

Recently, the TODIM (an acronym in Portuguese for Interactive Multi-criteria Decision Making) approach, which can characterize the decision makers’ psychological behaviours under risk, has been introduced to handle multi-criteria decision making (MCDM) problems. Moreover, Pythagorean fuzzy set is an effective tool for depicting uncertainty of the MCDM problems. In this paper, based on the prospect theory, we first extend the TODIM approach to solve the MCDM problems with Pythagorean fuzzy information. Then, we conduct simulation tests to analyze how the risk attitudes of the decision makers exert the influence on the results of MCDM under uncertainty. Finally, a case study on selecting the governor of Asian Infrastructure Investment Bank is made to show the applicability of the proposed approach.     

Development of optimal water supply plan using integrated fuzzy Delphi and fuzzy ELECTRE III methods—Case study of the Gamasiab basin

This paper presents a novel method for the development of an optimal water supply plan showcased using data from the Gamasiab basin, located in Kermanshah province, Iran, concerning new dams that are being constructed in this semi-arid region. In this paper, a new group multi-criteria decision-making (MCDM) plan is proposed by combining two MCDM methods based on the fuzzy Delphi and fuzzy ELECTRE III methods that convert the experts' opinions to triangular fuzzy numbers based on the level of uncertainty associated with various quantitative and qualitative criteria. Considering the opinions of four non-stakeholder experts and data analysis using the fuzzy Delphi method, the criteria were evaluated. Then, by analysing the results using the fuzzy ELECTRE III method, the final ranking of scenarios is obtained. A sensitivity analysis was conducted to assess the effect of uncertainty on the performance of the decision-making system in scenarios ranking. The total expense, flood control, reservoir capacity and diversion and water transfer played a significant role in selecting the optimal scenario. Additionally, a hydrologic model was developed to evaluate the performance of the optimal scenario in terms of qualitative criteria. The data indicated that there was a good agreement between the results obtained from the hydrological model and the scenario ranking by the employed method. Altogether, a comparison of the proposed method with other MCDM methods, including fuzzy analytic hierarchy process and fuzzy technique for order preference by simulation of ideal solution, indicated that the results of the employed method matched more closely to the local experts' opinion.