Weapon selection using the AHP and TOPSIS methods under fuzzy environment

The weapon selection problem is a strategic issue and has a significant impact on the efficiency of defense systems. On the other hand, selecting the optimal weapon among many alternatives is a multi-criteria decision-making (MCDM) problem. This paper develops an evaluation model based on the analytic hierarchy process (AHP) and the technique for order performance by similarity to ideal solution (TOPSIS), to help the actors in defence industries for the selection of optimal weapon in a fuzzy environment where the vagueness and subjectivity are handled with linguistic values parameterized by triangular fuzzy numbers. The AHP is used to analyze the structure of the weapon selection problem and to determine weights of the criteria, and fuzzy TOPSIS method is used to obtain final ranking. A real world application is conducted to illustrate the utilization of the model for the weapon selection problem. The application could be interpreted as demonstrating the effectiveness and feasibility of the proposed model.     

Bidirectional project method for dual hesitant Pythagorean fuzzy multiple attribute decision-making and their application to performance assessment of new rural construction

The dual hesitant Pythagorean fuzzy set (DHPFS) consists of two parts, that is, the membership hesitancy function and the nonmembership hesitancy function, supporting a more exemplary and flexible access to assign values for each element in the domain. It is very suitable to handle the situation that there are various possible values in membership and nonmembership degrees to depict the true circumstance. The bidirectional project method of DHPFS calculates method considered not only the bidirectional projection magnitudes and the distance but also includes angle between objects evaluated. Therefore, this paper proposes a bidirectional project method of DHPFS to handle the multiple attribute decision-making (MADM) problem under the dual hesitant Pythagorean fuzzy environment. Through the measure between each alternative decision matrix and the positive and negative ideal alternative matrix, the ranking order all alternatives can be used to select the best alternative. Furthermore, a model for MADM has been given. Finally, a numerical example for performance assessment of new rural construction has been given to demonstrate the application of bidirectional project method of DHPFS, and we used the dual hesitant Pythagorean weighted Bonferroni mean to compare its reasonable and effectiveness.     

A new multiple criteria decision making method based on intuitionistic fuzzy information

The risk attitude of a decision maker is considered in the decision process. Inspired by mean-variance type utility functions in the financial risk management, a new class of decision functions are defined based on the weighted score function and the weighted accuracy function in the intuitionistic fuzzy setting. By choosing a suitable parameter value, the decision maker’s risk attitude can be flexibly reflected by our decision function. The new method can be applied for both the exactly known and partly known criteria weight situations. For the latter case, it is only necessary to solve one linear programming problem. The developed models and algorithms are then extended to multiple criteria decision making problems with the interval-valued intuitionistic fuzzy information. Numerical examples are provided to illustrate the practicality, flexibility and efficiency of our new algorithms.     

A projection-based compromising method for multiple criteria decision analysis with interval-valued intuitionistic fuzzy information

The purpose of this paper is to develop a projection-based compromising method for addressing multiple criteria decision-making problems based on interval-valued intuitionistic fuzzy sets. The concept of projections considers not only the distance but also the included angle between evaluative ratings of alternative actions with respect to a criterion. In the interval-valued intuitionistic fuzzy context, this paper determines the respective projections of the evaluative ratings of each alternative on the positive-ideal and negative-ideal solutions and explores several essential properties. Next, this paper introduces the concepts of projection-based compromising indices and comprehensive compromising indices and further investigates relevant theorems for supporting the usefulness of these indices. Additionally, this paper proposes the projection-based comparative index and the comprehensive comparative index to serve as benchmark values for the comparison purpose. The improvement percentage of the comprehensive compromising value is acquired to determine the priority order of the alternatives, including the complete ranking order and the approval status for each alternative. The feasibility and the applicability of the proposed method are validated with an application problem of watershed site selection. Finally, several comparative analyses are conducted to verify the effectiveness and advantages of the proposed method over other relevant compromising decision-making methods.     

Interval-valued fuzzy multiple criteria decision-making methods based on dual optimistic/pessimistic estimations in averaging operations

This study aimed to consider the effect of dispositional optimism and pessimism to provide simple and useful decision models and methods for multiple criteria decision analysis within an interval-valued fuzzy environment. Uncertain and imprecise assessment information is usually present in many practical decision-making situations. Interval-valued fuzzy sets are useful for modeling impressions and quantifying the ambiguous nature of subjective judgments in a convenient way. Based on measurement tool estimations defined on interval-valued fuzzy sets, dual optimistic and pessimistic point operators were utilized in this study, and this paper discusses several important properties of optimistic/pessimistic averaging operations. Two algorithmic procedures were developed to address the effects of optimism and pessimism, involving changes in overall judgments and in the separate evaluations of alternatives with respect to each criterion. Furthermore, this study explored the practical problem of medical decision making to demonstrate the feasibility and applicability of the proposed method and to make a comparison with other existing methods. Finally, computational experiments were designed using enormous amounts of simulation data, and a comparative analysis of rank orders yielded by dual optimistic and pessimistic averaging operations was conducted.     

A novel PROMETHEE-based method using a Pythagorean fuzzy combinative distance-based precedence approach to multiple criteria decision making

This paper aims at developing a novel preference ranking organization method for enrichment evaluations (PROMETHEE) using a Pythagorean fuzzy combinative distance-based precedence approach under complex uncertainty based on Pythagorean fuzzy sets. This paper introduces a new generalized distance measure for adequately expressing differences between Pythagorean fuzzy information and utilizing fundamental parameters of Pythagorean membership grades. This paper defines the useful concept of precedence indices for determining the desirability of evaluative ratings about competing alternatives on a criterion. In Pythagorean fuzzy contexts, this paper establishes a combinative distance-based precedence approach for reflecting an overall balance between the connection with approach-oriented anchor values and the remotest connection with avoidance-oriented anchor values. This paper presents six types of new preference functions and proposes the comprehensive preference index for measuring the intensity of a pairwise preference. Based on the concepts of a dominant flow, a dominated flow, and an outranking flow, this paper develops a Pythagorean fuzzy PROMETHEE-based method and validates its feasibility and applicability using a multiple criteria decision-making problem of bridge-superstructure construction methods. A sensitivity analysis is carried out to investigate the effects of various parameter settings on the partial preordering and complete preordering of alternatives. Furthermore, a comparative analysis is performed with other relevant methods to evaluate the effectiveness of the proposed methodology.     

An interval-valued intuitionistic fuzzy permutation method with likelihood-based preference functions and its application to multiple criteria decision analysis

This paper presents an interval-valued intuitionistic fuzzy permutation method with likelihood-based preference functions for managing multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets. First, certain likelihood-based preference functions are proposed using the likelihoods of interval-valued intuitionistic fuzzy preference relationships. Next, selected practical indices of concordance/discordance are established to evaluate all possible permutations of the alternatives. The optimal priority order of the alternatives is determined by comparing all comprehensive concordance/discordance values based on score functions. Furthermore, this paper considers various preference types and develops another interval-valued intuitionistic fuzzy permutation method using programming models to address multiple criteria decision-making problems with incomplete preference information. The feasibility and applicability of the proposed methods are illustrated in the problem of selecting a suitable bridge construction method. Moreover, certain comparative analyses are conducted to verify the advantages of the proposed methods compared with those of other decision-making methods. Finally, the practical effectiveness of the proposed methods is validated with a risk assessment problem in new product development.     

Intuitionistic fuzzy evidential power aggregation operator and its application in multiple criteria decision-making

The theory of intuitionistic fuzzy sets (IFS) is widely used for dealing with vagueness and the Dempster--Shafer (D-S) evidence theory has a widespread use in multiple criteria decision-making problems under uncertain situation. However, there are many methods to aggregate intuitionistic fuzzy numbers (IFNs), but the aggregation operator to fuse basic probability assignment (BPA) is rare. Power average (P-A) operator, as a powerful operator, is useful and important in information fusion. Motivated by the idea of P-A power, in this paper, a new operator based on the IFS and D-S evidence theory is proposed, which is named as intuitionistic fuzzy evidential power average (IFEPA) aggregation operator. First, an IFN is converted into a BPA, and the uncertainty is measured in D-S evidence theory. Second, the difference between BPAs is measured by Jousselme distance and a satisfying support function is proposed to get the support degree between each other effectively. Then the IFEPA operator is used for aggregating the original IFN and make a more reasonable decision. The proposed method is objective and reasonable because it is completely driven by data once some parameters are required. At the same time, it is novel and interesting. Finally, an application of developed models to the ‘One Belt, One road’ investment decision-making problems is presented to illustrate the effectiveness and feasibility of the proposed operator.     

To construct a monitoring mechanism of production loss by using Fuzzy Delphi method and fuzzy regression technique – A case study of IC package testing company

The development of information technology and internet capabilities over the years has been at an accelerated pace of global intense challenges and competitions of the technologies markets. Therefore, the issue of effectively utilizing valuable information located in databases worldwide, by monitoring the performance of their operations became an important issue in the electronic business environment. Methods to address this issue were employed to quickly identify the Key Performance Indicators (KPI’s) and operational problems and clarify any relationships between them, to allow the overall business objectives to be achieved. In this paper, the Fuzzy Delphi and ranking methods were used to extract the most concerning issues through expert questionnaires. A fuzzy regression model was then constructed and applied to clarify the relationships between the KPI’s and the key management objective, the area of production loss. Therefore, the key factors for future improvements were obtained by tracking the fuzzy regression model. Finally a case study of a semiconductor assembly and testing, through a company in Taiwan, was used to illustrate the proposed framework. The results indicated that this model could be easily implemented to analyze the influence of concerned KPIs on key management objectives.     

A simulated annealing-based permutation method and experimental analysis for multiple criteria decision analysis with interval type-2 fuzzy sets

The aim of this paper is to develop a simulated annealing-based permutation method for multiple criteria decision analysis within the environment of interval type-2 fuzzy sets. The outranking methodology constitutes one of the most fruitful approaches in multiple criteria decision making and has been applied in numerous real-world problems. The permutation method is a classical outranking model, which generalizes Jacquet–Lagreze's permutation method and is based on a pairwise criterion comparison of the alternatives. Because modeling of the uncertainty in the decision-making process becomes increasingly important, an extension to the interval type-2 fuzzy environment is a useful generalization of the permutation method and is appropriate for handling uncertain and imprecise information in practical decision-making situations. This paper produces a signed-distance-based comparison among the comprehensive rankings of alternatives for concordance and discordance analyses. An integrated nonlinear programming model is constructed for estimation of the criterion weights and the optimal ranking order of the alternatives under incomplete preference information. To enhance the implementation efficiency, a simulated annealing-based permutation method and its meta-heuristic algorithm are developed to produce a polynomial time solution for the total completion time problem. Furthermore, computational experiments with notably large amounts of simulation data are conducted to test the solution approach and validate the correctness of the approximate solution compared with the optimal all-permutation-based result.     

The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making

The technique for order preference by similarity to ideal solution (TOPSIS) method is a well-known compromising method for multiple criteria decision analysis. This paper develops an extended TOPSIS method with an inclusion comparison approach for addressing multiple criteria group decision-making problems in the framework of interval-valued intuitionistic fuzzy sets. Considering the relative agreement degrees and the importance weights of multiple decision makers, this paper presents a modified hybrid averaging method with an inclusion-based ordered weighted averaging operation for forming a collective decision environment. Based on the main structure of the TOPSIS method, this paper utilizes the concept of inclusion comparison possibilities to propose a new index for an inclusion-based closeness coefficient for ranking the alternatives. Additionally, two optimization models are established to determine the criterion weights for addressing situations in which the preference information is completely unknown or incompletely known. Finally, the feasibility and effectiveness of the proposed methods are illustrated by a medical group decision-making problem.     

基于改进熵和新得分函数的区间直觉模糊多属性决策

针对决策信息为区间直觉模糊数且属性权重完全未知的多属性决策问题, 提出基于改进的区间直觉模糊熵和新得分函数的决策方法. 首先, 利用改进的区间直觉模糊熵确定属性权重; 然后, 利用区间直觉模糊加权算术平均算子集成信息, 得到各备选方案的综合属性值, 进而指出现有得分函数存在排序失效或排序不符合实际的不足, 同时给出一个新的得分函数, 并以此对方案进行排序; 最后, 通过实例表明了所提出方法的有效性.

     

基于熵和风险态度的二型模糊多属性决策方法

针对属性权重信息完全未知的二型模糊多属性决策问题,提出了一种基于二型模糊熵和决策者风险态度的决策方法。首先,为了准确测度二型模糊集（T2FS）的不确定性,通过引入模糊因子和犹豫因子建立了二型模糊熵的公理化准则,并基于距离测度给出了对应的计算公式。其次,为了减少整体不确定信息对决策结果的影响,结合二型模糊熵构建非线性规划模型来确定属性权重。同时,将决策者的风险态度引入二型模糊信息的得分函数中并给出具体的决策步骤。最后,通过实例分析验证了该决策方法的可行性,并与现有文献对比发现该决策方法更具有灵活性。     

A multi-attribute decision-making model for the robust classification of multiple inputs and outputs datasets with uncertainty

Many multiple-criteria decision-making (MCDM) methods have been proposed for decision-making environments. However, the performance of these methods is degraded by the uncertainty and inaccuracy which characterizes most practical decision-making environments as a result of the inherent prejudices and preferences of the decision-makers or experts and an insufficient volume of multiple inputs and outputs (MIO) information. Accordingly, the present study proposes an enhanced MIO classification method to address these limitations of existing MCDM methods. The proposed MIO classification method designated as the FVM-index method integrates fuzzy set theory (FST), variable precision rough set (VPRS) theory, and a modified cluster validity index (MCVI) function, and is designed specifically to filter out the uncertainty and inaccuracy inherent in the surveyed MIO real-valued dataset; thereby improving the classification performance. The effectiveness of the proposed approach is first demonstrated by comparing the MIO classification results obtained for three relating UCI datasets: (1) the original dataset; (2) a dataset with a large amount of inaccurate instances; and (3) an FVM-index filtered dataset extracted from the original dataset using a statistical approach. Then, the validity of the proposed approach is illustrated by using an Augmented Reality product design and a hospital related datasets. The results confirm that the proposed FVM-index method provides a good classification performance even in the presence of inaccuracy and uncertainty. As a result, it provides a robust approach for the extraction of reliable decision-making rules.     

A multiple attributes decision making method using individual and collaborative attribute data in a fuzzy environment

Although multiple attribute decision making (MADM) problems with both individual attribute data of a single alternative and collaborative attribute data of pairwise alternatives exist in the real world, they have seldom been a focus of research. This paper proposes a MADM method using individual and collaborative attribute data in a fuzzy environment, in which experts use linguistic variables to express their opinions. In the method, first, the evaluation matrix of individual attributes date and the judgment matrix of collaborative attributes data are constructed. Then, the central dominance of one alternative outranking other all alternatives is defined for aggregating the collaborative data. From this, an integrated decision matrix incorporating individual and collaborative attribute data is constructed. Further, based on an extended TOPSIS, the fuzzy positive-ideal solution (FPIS) and the fuzzy negative-ideal solution (FNIS) are determined, and the relative closeness of each alternative to the FPIS and FNIS is calculated to determine the ranking order of all alternatives. Finally, two examples are used to illustrate the applicability of the proposed method.     

Some q-rung orthopair fuzzy Hamy mean operators in multiple attribute decision-making and their application to enterprise resource planning systems selection

In this paper, the Hamy mean (HM) operator, weighted HM (WHM), dual HM (DHM) operator, and dual WHM (WDHM) operator under the q-rung orthopair fuzzy sets (q-ROFSs) is studied to propose the q-rung orthopair fuzzy HM (q-ROFHM) operator, q-rung orthopair fuzzy WHM (q-ROFWHM) operator, q-rung orthopair fuzzy DHM (q-ROFDHM) operator, and q-rung orthopair fuzzy weighted DHM (q-ROFWDHM) operator and some of their desirable properties are investigated in detail. Then, we apply these operators to multiple attribute decision-making problems. Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Evaluating the quality of airport service using the fuzzy multi‐criteria decision‐making method: a case study of Taiwanese airports

In today's highly competitive air transportation environment, the quality of airport service is an important issue. In this paper, we present a fuzzy multi‐criteria decision‐making (MCDM) method for the evaluation of the quality of airport service. The data are collected from the passengers who depart from two international airports in Taiwan. The fuzzy MCDM model is defuzzied using the inverse function arithmetic representation method. The results show that the average quality of the Taoyuan International Airport service is better than that of the Kaohsiung International Airport service. This paper also analyses the quality of airport service using the fuzzy expert system to improve the performance of airport service. The analysis results show that the Kaohsiung International Airport and the Taoyuan International Airports' improvement efforts should be concentrated on seven and five specific service items, respectively. The findings of this paper are to help the decision‐makers and the managers of airports improve the quality of airport service.     

An interval type-2 fuzzy PROMETHEE method using a likelihood-based outranking comparison approach

Based on the preference ranking organization method for enrichment evaluations (PROMETHEE), the purpose of this paper is to develop a new multiple criteria decision-making method that uses the approach of likelihood-based outranking comparisons within the environment of interval type-2 fuzzy sets. Uncertain and imprecise assessment of information often occurs in multiple criteria decision analysis (MCDA). The theory of interval type-2 fuzzy sets is useful and convenient for modeling impressions and quantifying the ambiguous nature of subjective judgments. Using the approach of likelihood-based outranking comparisons, this paper presents an interval type-2 fuzzy PROMETHEE method designed to address MCDA problems based on interval type-2 trapezoidal fuzzy (IT2TrF) numbers. This paper introduces the concepts of lower and upper likelihoods for acquiring the likelihood of an IT2TrF binary relationship and defines a likelihood-based outranking index to develop certain likelihood-based preference functions that correspond to several generalized criteria. The concept of comprehensive preference measures is proposed to determine IT2TrF exiting, entering, and net flows in the valued outranking relationships. In addition, this work establishes the concepts of a comprehensive outranking index, a comprehensive outranked index, and a comprehensive dominance index to induce partial and total preorders for the purpose of acquiring partial ranking and complete ranking, respectively, of the alternative actions. The feasibility and applicability of the proposed method are illustrated with two practical applications to the problem of landfill site selection and a car evaluation problem. Finally, a comparison with other relevant methods is conducted to validate the effectiveness of the proposed method.     

Undergraduate teaching audit and evaluation using an extended MABAC method under q-rung orthopair fuzzy environment

Undergraduate teaching audit and evaluation (UTAE) is a new type of evaluation pattern, which is extremely important for a university to improve its quality assurance system and enhance teaching quality. Selecting an optimal university for benchmarking through UTAE to promote the quality of teaching can be regarded as a complex multicriteria decision making (MCDM) problem. Furthermore, in the process of UTAE, experts' evaluations over the teaching quality of universities are often imprecise and fuzzy due to the subjective nature of human thinking. In this paper, we propose a new UTAE approach based on q-rung orthopair fuzzy sets and the multiattribute border approximation area comparison (MABAC) method for evaluating and selecting the best university for benchmarking. The introduced method deals with the linguistic assessments given by experts by using q-ROFSs, assigns the weights of audit elements based on the indifference threshold-based attribute ratio analysis method, and acquires the ranking of universities with an extended MABAC method. The feasibility and effectiveness of the proposed q-rung orthopair fuzzy MABAC method is demonstrated through a realistic UTAE example. Results show that the UTAE method being proposed is valid and practical for UTAE.     

Supplier selection in the airline retail industry using a funnel methodology: Conjunctive screening method and fuzzy AHP

Since a company can only perform as well as it is allowed to by its suppliers, the importance of supplier selection in supply chain management has been increasingly recognized. Supplier selection can best be described as a highly complex process, due to the involvement of many, sometimes conflicting, qualitative and quantitative criteria. The objective is to select the most suitable supplier(s) that meet a company’s specific needs. This paper investigates supplier selection in the airline retail industry. We discuss a number of issues that make airline retail complex and distinguish it from conventional retail. The supplier selection problem is solved by means of a two-phased methodology. In the first phase, a conjunctive screening method is used, which aims to reduce the initial set of potential suppliers prior to the comprehensive final choice phase. In the second phase, a fuzzy analytic hierarchy process (AHP) is used, in which suppliers are evaluated against the main criteria and sub-criteria. By combining the decision-maker’s preferences, using the developed methodology will eventually result in a ranking of suppliers that makes it possible to select the most suitable supplier(s). The proposed methodology is applied to one of the largest airlines in Europe, the Royal Dutch Airlines (KLM), and the results are discussed extensively in this paper. We conclude by proposing avenues for future research regarding the general applicability and further extensions.