基于区间直觉模糊集的供应商选择方法

提出一种基于区间直觉模糊集和TOPSIS法的供应商选择方法。给出了区间直觉模糊集的概念,定义了区间直觉模糊集之间的距离测度,在此基础上,将区间直觉模糊集和TOPSIS法相结合,提出了一种供应商选择的新方法,算例分析说明了该方法的有效性。     

Linguistic hesitant intuitionistic fuzzy decision-making method based on VIKOR

Linguistic hesitant intuitionistic fuzzy set, which allows an element having several linguistic evaluation values and each linguistic argument having several intuitionistic fuzzy memberships, is a power tool to model uncertain information existing in multiple attribute decision-making problems. In this paper, we propose new methods by using TOPSIS and VIKOR for multiple attribute decision-making problems, in which evaluation values are in the form of linguistic hesitant intuitionistic fuzzy elements. Different situations of attribute weight information are considered. If attribute weights are partly known, a linear programming model is set up based on the idea that reasonable weights should make the relative closeness of each alternative evaluation value to the linguistic hesitant intuitionistic fuzzy positive ideal solution as large as possible. If attribute weights are unknown completely, an optimization model is set up based on the maximum deviation method. A numerical example is presented to illustrate feasibility and practical advantages of the proposed method. We compare the alternatives’ rankings derived from the linguistic hesitant intuitionistic fuzzy TOPSIS method with those derived from the hesitant fuzzy linguistic TOPSIS and the hesitant intuitionistic fuzzy TOPSIS approach to further illustrate their advantages.

     

A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method

Supplier selection, the process of finding the right suppliers who are able to provide the buyer with the right quality products and/or services at the right price, at the right time and in the right quantities, is one of the most critical activities for establishing an effective supply chain. On the other hand, it is a hard problem since supplier selection is typically a multi criteria group decision-making problem involving several conflicting criteria on which decision maker’s knowledge is usually vague and imprecise. In this study, TOPSIS method combined with intuitionistic fuzzy set is proposed to select appropriate supplier in group decision making environment. Intuitionistic fuzzy weighted averaging (IFWA) operator is utilized to aggregate individual opinions of decision makers for rating the importance of criteria and alternatives. Finally, a numerical example for supplier selection is given to illustrate application of intuitionistic fuzzy TOPSIS method.     

基于模糊结构元的模糊数直觉模糊多准则决策方法

针对准则权重信息不完全确定的模糊数直觉模糊多准则决策问题,采用模糊结构元方法进行处理.基于模糊数直觉模糊集的模糊结构元表示、模糊数比较和排序的模糊结构元方法以及直觉模糊数的记分函数和距离测度,定义了模糊数直觉模糊数的记分函数和距离测度,进而提出两种准则权重信息不完全确定而准则值为模糊数直觉模糊数的多准则决策方法:记分函数法和逼近理想解排序(TOPSIS)法.实例分析表明了这两种方法的可行性和有效性.     

An analytical solution to fuzzy TOPSIS and its application in personnel selection for knowledge-intensive enterprise

Personnel selection is a critical enterprise strategic problem in knowledge-intensive enterprise. Fuzzy number which can be described as triangular (trapezoid) fuzzy number is an adequate way to assess the evaluation and weights for the alternatives. In that case, fuzzy TOPSIS, as a classic fuzzy multiple criteria decision making (MCDM) methods, has been applied in personnel selection problems. Currently, all the researches on this topic either apply crisp relative closeness but causing information loss, or employ fuzzy relative closeness estimate but with complicated computation to rank the alternatives. In this paper, based on Karnik–Mendel (KM) algorithm, we propose an analytical solution to fuzzy TOPSIS method. Some properties are discussed, and the computation procedure for the proposed analytical solution is given as well. Compared with the existing TOPSIS method for personnel selection problem, it obtains accurate fuzzy relative closeness instead of the crisp point or approximate fuzzy relative closeness estimate. It can both avoid information loss and keep computational efficiency in some extent. Moreover, the global picture of fuzzy relative closeness provides a way to further discuss the inner properties of fuzzy TOPSIS method. Detailed comparisons with approximate fuzzy relative closeness method are provided in personnel selection application.     

Switching between type-2 fuzzy sets and intuitionistic fuzzy sets: an application in medical diagnosis

When dealing with vagueness, there are situations when there is insufficient information available, making it impossible to satisfactorily evaluate membership. The intuitionistic fuzzy set theory is more suitable than fuzzy sets to deal with such problem. In 1996, Atanassov proposed the mapping from intuitionistic fuzzy sets to fuzzy sets. Furthermore, intuitionistic fuzzy sets are isomorphic to interval valued fuzzy sets, and interval valued fuzzy sets are regarded as the special cases of type-2 fuzzy sets in recently studies. However, their discussions are not only hardly comprehending but also lacking the reliable applications. In this study, the advantage of type-2 fuzzy sets is employed, and the switching relation between type-2 fuzzy sets and intuitionistic fuzzy sets is defined axiomatically. The switching results are applied to show the usefulness of the proposed method in pattern recognition and medical diagnosis reasoning.     

直觉模糊环境下的物流配送中心选址方法研究

物流配送中心选址决策是直接关系到物流配送系统运作效率的重要问题之一。提出了一种基于直觉模糊TOPSIS法的物流配送中心选址方法,给出了直觉模糊集的概念和运算,定义了直觉模糊集之间的距离测度;在此基础上,将直觉模糊集和TOPSIS法相结合,提出了一种配送中心选址决策的新方法,最后的算例分析说明了该方法的有效性。     

A Novel Approach for Linguistic Group Decision Making Based on Generalized Interval‐Valued Intuitionistic Fuzzy Linguistic Induced Hybrid Operator and TOPSIS

In the multiple attribute linguistic group decision making analysis with interval‐valued intuitionistic fuzzy linguistic information, seeking highly efficient aggregation method and order relation play a crucial role. In this paper, we redefine an interval‐valued intuitionistic fuzzy linguistic variable that considers principal component and propose generalized interval‐valued intuitionistic fuzzy linguistic induced hybrid aggregation (GIVIFLIHA) operator with entropic order‐inducing variable and interval‐valued intuitionistic fuzzy linguistic technique for order preference by similarity to an ideal solution (TOPSIS) order relation based on interval‐valued intuitionistic fuzzy linguistic distance measure. Then, some primary properties of the GIVIFLIHA operator are discussed, and a linguistic group decision‐making approach based on GIVIFLIHA operator and interval‐valued intuitionistic fuzzy linguistic TOPSIS order relation is proposed. Finally, a numerical example concerning the investment strategy is given to illustrate the validity and applicability of the proposed method, and then the method is compared with the existing method to further illustrate its flexibility.     

Multi-criteria group decision making based on trapezoidal intuitionistic fuzzy information

With respect to multi-criteria group decision making (MCGDM) problems under trapezoidal intuitionistic fuzzy environment, a new MCGDM method is investigated. The proposed method can effectively avoid the failure caused by the use of inconsistent decision information and provides a decision-making idea for the case of “the truth be held in minority”. It consists of three interrelated modules: weight determining mechanism, group consistency analysis, and ranking and selection procedure. For the first module, distance measures, expected values and arithmetic averaging operator for trapezoidal intuitionistic fuzzy numbers are used to determine the weight values of criteria and decision makers. For the second module, a consistency analysis and correction procedure based on trapezoidal intuitionistic fuzzy weighted averaging operator and OWA operator is developed to reduce the influence of conflicting opinions prior to the ranking process. For the third module, a trapezoidal intuitionistic fuzzy TOPSIS is used for ranking and selection. Then a procedure for the proposed MCGDM method is developed. Finally, a numerical example further illustrates the practicality and efficiency of the proposed method.     

基于直觉梯形模糊TOPSIS的多属性群决策方法

提出一种改进的逼近理想解排序(TOPSIS)方法,即直觉梯形模糊TOPSIS多属性群决策方法。首先,应用直觉梯形模糊数形式表示方案属性偏好和属性权重信息且专家权重完全未知;然后,利用直觉梯形模糊数间距离测度和期望值及直觉梯形模糊加权平均算子来确定决策者权重信息和属性权重信息;进而给出直觉梯形模糊环境下方案优选的算法;最后,通过算例进一步说明了该直觉梯形模糊TOPSIS方法的有效性。     

A new preference scale mcdm method based on interval-valued intuitionistic fuzzy sets and the analytic hierarchy process

The intuitionistic fuzzy analytic hierarchy process (IF-AHP), in which intuitionistic fuzzy numbers are utilized in defining decision makers’ linguistic judgment, has been used to solve various multi-criteria decision-making problems. Previous theories have suggested that interval-valued intuitionistic fuzzy numbers (IVIFN) with hesitation degree can act as alternative fuzzy numbers that can handle vagueness and uncertainty. This paper proposes a new preference scale in the framework of the interval-valued intuitionistic fuzzy analytic hierarchy process (IVIF-AHP). The comparison matrix judgment is expressed in IVIFN with degree of hesitation. The proposed new preference scale concurrently considers the membership function, the non-membership function and the degree of hesitation of IVIFN. To define the weight entropy of the aggregated matrix of IVIFN, a modified interval-valued intuitionistic fuzzy weighted averaging is proposed, by considering the interval number of the hesitation degree. Three multi-criteria decision-making problems are used to test the proposed method. A comparison of the results is also presented to check the feasibility of the proposed method. It is shown that the ranking order of the proposed method is slightly different from that of the other two methods because of the inclusion of the hesitation degree in defining the preference scale.     

A novel group decision making method with intuitionistic fuzzy preference relations for RFID technology selection

A more scientific decision making process for radio frequency identification (RFID) technology selection is important to increase success rate of RFID technology application. RFID technology selection can be formulated as a kind of group decision making (GDM) problem with intuitionistic fuzzy preference relations (IFPRs). This paper develops a novel method for solving such problems. First, A technique for order preference by similarity to ideal solution (TOPSIS) based method is presented to rank intuitionistic fuzzy values (IFVs). To achieve higher group consensus as well as possible, we construct an intuitionistic fuzzy linear programming model to derive experts’ weights. Depending on the construction of membership and non-membership functions, the constructed intuitionistic fuzzy linear programming model is solved by three kinds of approaches: optimistic approach, pessimistic approach and mixed approach. Then to derive the ranking order of alternatives from the collective IFPR, we extend quantifier guided non-dominance degree (QGNDD) and quantifier guided dominance degree (QGDD) to intuitionistic fuzzy environment. A new two-phase ranking approach is designed to generate the ordering of alternatives based on QGNDD and QGDD. Thereby, the corresponding method is proposed for the GDM problems with IFPRs. Some generalizations on the constructed intuitionistic fuzzy linear programming model are further discussed. At length, the validity of the proposed method is illustrated with a real-world RFID technology selection example.     

基于改进TOPSIS法的体育产业可持续发展水平评价

针对体育产业可持续发展水平测度中存在的不确定性,提出了改进的区间直觉模糊TOPSIS方法。该方法考虑到现有区间直觉模糊TOPSIS方法的存在信息损失的不足,引入区间直觉模糊集的三维Hamming距离和三维Hausdorff距离进行改进。通过具体的实例说明了新方法在体育产业可持续发展水平评价中的适用性和有效性。     

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.     

A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS

An extension of TOPSIS, a multi-criteria interval-valued intuitionistic fuzzy decision making technique, to a group decision environment is investigated, where inter-dependent or interactive characteristics among criteria and preference of decision makers are taken into account. To get a broad view of the techniques used, first, some operational laws on interval-valued intuitionistic fuzzy values are introduced. Based on these operational laws, a generalized interval-valued intuitionistic fuzzy geometric aggregation operator is proposed which is used to aggregate decision makers’ opinions in group decision making process. In addition, some of its properties are discussed. Then Choquet integral-based Hamming distance between interval-valued intuitionistic fuzzy values is defined. Combining the interval-valued intuitionistic fuzzy geometric aggregation operator with Choquet integral-based Hamming distance, an extension of TOPSIS method is developed to deal with a multi-criteria interval-valued intuitionistic fuzzy group decision making problems. Finally, an illustrative example is used to illustrate the developed procedures.     

Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge

Abstract: Just like rough set theory, fuzzy set theory addresses the topic of dealing with imperfect knowledge. Recent investigations have shown how both theories can be combined into a more flexible, more expressive framework for modelling and processing incomplete information in information systems. At the same time, intuitionistic fuzzy sets have been proposed as an attractive extension of fuzzy sets, enriching the latter with extra features to represent uncertainty (on top of vagueness). Unfortunately, the various tentative definitions of the concept of an ‘intuitionistic fuzzy rough set’ that were raised in their wake are a far cry from the original objectives of rough set theory. We intend to fill an obvious gap by introducing a new definition of intuitionistic fuzzy rough sets, as the most natural generalization of Pawlak's original concept of rough sets.     

Fuzzy multicriteria decision making method based on the improved accuracy function for interval-valued intuitionistic fuzzy sets

A new accuracy function for the theory of interval-valued intuitionistic fuzzy set, which overcomes some difficulties arising in the existing methods for determining rank of interval-valued intuitionistic fuzzy numbers, is proposed by taking into account the hesitancy degree of interval-valued intuitionistic fuzzy sets. By comparing it with several proposed accuracy functions, the necessity and efficiency of our accuracy function are provided by giving related examples. A fuzzy multicriteria decision making method is established to select the best alternative in multicriteria decision making process which is taken as interval-valued intuitionistic fuzzy set of criterion values for alternatives. While aggregating the interval-valued intuitionistic fuzzy information corresponding to each alternative, we utilize the interval-valued intuitionistic fuzzy weighted aggregation operators. Then the accuracy degree of the aggregated interval-valued intuitionistic fuzzy information is computed via the new proposed accuracy function. Thus, we can rank all the alternatives according to the accuracy function and choose the optimal one(s). Finally, an illustrative example is given to demonstrate the practicality and effectiveness of the proposed approach.     

Intuitionistic preference relations and their application in group decision making

Intuitionistic fuzzy set, characterized by a membership function and a non-membership function, was introduced by Atanassov [Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986) 87-96]. In this paper, we define the concepts of intuitionistic preference relation, consistent intuitionistic preference relation, incomplete intuitionistic preference relation and acceptable intuitionistic preference relation, and study their various properties. We develop an approach to group decision making based on intuitionistic preference relations and an approach to group decision making based on incomplete intuitionistic preference relations respectively, in which the intuitionistic fuzzy arithmetic averaging operator and intuitionistic fuzzy weighted arithmetic averaging operator are used to aggregate intuitionistic preference information, and the score function and accuracy function are applied to the ranking and selection of alternatives. Finally, a practical example is provided to illustrate the developed approaches.     

An interactive method for dynamic intuitionistic fuzzy multi-attribute group decision making

This paper investigates the dynamic intuitionistic fuzzy multi-attribute group decision making (DIF-MAGDM) problems, in which all the attribute values provided by multiple decision makers (DMs) at different periods take the form of intuitionistic fuzzy numbers (IFNs), and develops an interactive method to solve the DIF-MAGDM problems. The developed method first aggregates the individual intuitionistic fuzzy decision matrices at different periods into an individual collective intuitionistic fuzzy decision matrix for each decision maker by using the dynamic intuitionistic fuzzy weighted averaging (DIFWA) operator, and then employs intuitionistic fuzzy TOPSIS method to calculate the individual relative closeness coefficient of each alternative for each decision maker and obtain the individual ranking of alternatives. After doing so, the method utilizes the hybrid weighted averaging (HWA) operator to aggregate all the individual relative closeness coefficients into the collective relative closeness coefficient of each alternative and obtain the aggregate ranking of alternatives, by which the optimal alternative can be selected. In addition, the spearman correlation coefficient for both the aggregate ranking and individual ranking of alternatives is calculated to measure the consensus level of the group preferences. Finally, a numerical example is used to illustrate the developed method.