Shu-Ping Wan

The extended VIKOR method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers

Triangular intuitionistic fuzzy numbers (TIFNs) are a special intuitionistic fuzzy set (IFS) on a real number set, which are very useful for decision makers (DMs) to depict their fuzzy preference information. In this work, we investigate multiple attribute group decision-making (MAGDM) problems in which the ratings of alternatives are expressed with TIFNs, and the weights of the attributes and DMs are completely unknown. Firstly, the crisp weighted possibility mean of TIFNs is defined, and the Hamming distance and Euclidean distance for TIFNs are defined based on Hausdorff distance. The triangular intuitionistic fuzzy weighted average (TIF-WA) operator is developed. Then, the weights of attributes are calculated by applying Shannon entropy measure and the weights of DMs are determined objectively combining the evidence theory with Bayes approximation. The individual decision matrixes for all DMs are aggregated into the group decision matrix by using the TIF-WA operator. Thereby, the classic Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method is extended for solving the MAGDM with TIFNs. Finally, the ranking order of alternative is given according to the closeness of alternative with respect to the ideal solution. The personnel selection example verifies the effectiveness of the proposed method.

Atanassov's Intuitionistic Fuzzy Programming Method for Heterogeneous Multiattribute Group Decision Making With Atanassov's Intuitionistic Fuzzy Truth Degrees

The aim of this paper is to develop a new Atanassovs intuitionistic fuzzy (A-IF) programming method to solve heterogeneous multiattribute group decision-making problems with A-IF truth degrees in which there are several types of attribute values such as A-IF sets (A-IFSs), trapezoidal fuzzy numbers, intervals, and real numbers. In this method, preference relations in comparisons of alternatives with hesitancy degrees are expressed by A-IFSs. Hereby, A-IF group consistency and inconsistency indices are defined on the basis of preference relations between alternatives. To estimate the fuzzy ideal solution (IS) and weights, a new A-IF programming model is constructed on the concept that the A-IF group inconsistency index should be minimized and must be not larger than the A-IF group consistency index by some fixed A-IFS. An effective method is developed to solve the new derived model. The distances of the alternatives to the fuzzy IS are calculated to determine their ranking order. Moreover, some generalizations or specializations of the derived model are discussed. Applicability of the proposed methodology is illustrated with a real supplier selection example.

2-Tuple linguistic hybrid arithmetic aggregation operators and application to multi-attribute group decision making

The focus of this paper is on multi-attribute group decision making (MAGDM) problems in which the attribute values, attribute weights, and expert weights are all in the form of 2-tuple linguistic information, which are solved by developing a new decision method based on 2-tuple linguistic hybrid arithmetic aggregation operator. First, the operation laws for 2-tuple linguistic information are defined and the related properties of the operation laws are studied. Hereby some hybrid arithmetic aggregation operators with 2-tuple linguistic information are developed, involving the 2-tuple hybrid weighted arithmetic average (THWA) operator, the 2-tuple hybrid linguistic weighted arithmetic average (T-HLWA) operator, and the extended 2-tuple hybrid linguistic weighted arithmetic average (ET-HLWA) operator. In the proposed decision method, the individual overall preference values of alternatives are derived by using the extended 2-tuple weighted arithmetic average operator (ET-WA). Utilized the ET-HLWA operator, all the individual overall preference values of alternatives are further integrated into the collective ones of alternatives, which are used to rank the alternatives. A real example of personnel selection is given to illustrate the developed method and the comparison analyses demonstrate the universality and flexibility of the method proposed in this paper.

A new method for Atanassov's interval-valued intuitionistic fuzzy MAGDM with incomplete attribute weight information

This paper develops a new method for solving multiple attribute group decision-making (MAGDM) problems with Atanassovs interval-valued intuitionistic fuzzy values (AIVIFVs) and incomplete attribute weight information. Firstly, we investigate the asymptotic property of the Atanassovs interval-valued intuitionistic fuzzy (AIVIF) matrix. It is demonstrated that after applying weights an infinite number of times, all elements in an AIVIF matrix will approach the same AIVIFV without regard to the initial values of elements. Then, the weight of each decision maker (DM) with respect to every attribute is determined by considering the similarity degree and proximity degree simultaneously. To avoid weighting an AIVIF matrix too many times, the collective decision matrix is transformed into an interval matrix using the risk coefficient of DMs. Subsequently, to derive the attribute weights objectively, we construct a multi-objective interval-programming model that is solved by transforming it into a linear program. The ranking order of alternatives is generated by the comprehensive interval values of alternatives. Finally, an example of a research and development (R&D) project selection problem is provided to illustrate the implementation process and applicability of the method developed in this paper.

Supplier selection using ANP and ELECTRE II in interval 2-tuple linguistic environment

In supply chain management, supplier selection can be treated as a type of hierarchical multi-criteria decision-making (MCDM) problems since it involves various criteria and hierarchical structure among criteria often exists. This paper investigates a kind of MCDM problems with two-level criteria and develops a novel hybrid method integrating TL-ANP (2-tuple linguistic analytic network process) and IT-ELECTRE II (interval 2-tuple Elimination and Choice Translating Reality II). Considering interactions among criteria, a TL-ANP approach, in which comparison matrices are consistent 2-tuple linguistic preference relations, is put forward to determine weights of criteria and sub-criteria. To deal with the case of criteria being not compensated, an IT-ELECTRE II approach is proposed. In this approach, ratings of alternatives on sub-criteria are represented as interval 2-tuple linguistic variables. A possible degree and a likelihood-based preference degree are respectively defined, followed by concordance, discordance and indifferent sets. Afterwards, concordance and discordance indices are identified and applied to establish net concordance and net discordance indices. Further, comprehensive dominant values of alternatives are obtained to rank alternatives. Thereby, a novel hybrid method is presented for MCDM with two-level criteria under interval 2-tuple linguistic environment. At length, a real case of supplier selection is examined and comparison analyses are conducted to illustrate the application and superiority of the proposed method.

A novel risk attitudinal ranking method for intuitionistic fuzzy values and application to MADM

The amount of information of an IFS is characterized by the closeness degree.The area of triangle is calculated to measure reliability of information of an IFS.It is proved that the closeness degree and triangle area just form an interval.A novel risk attitudinal measure is developed to rank IFS by C-OWA operator.Attributes weights are derived by constructing multi-objective fractional programming model. The ranking of intuitionistic fuzzy sets (IFSs) is very important for the intuitionistic fuzzy decision making. The aim of this paper is to propose a new risk attitudinal ranking method of IFSs and apply to multi-attribute decision making (MADM) with incomplete weight information. Motivated by technique for order preference by similarity to ideal solution (TOPSIS), we utilize the closeness degree to characterize the amount of information according to the geometrical representation of an IFS. The area of triangle is calculated to measure the reliability of information. It is proved that the closeness degree and the triangle area just form an interval. Thereby, a new lexicographical method is proposed based on the intervals for ranking the intuitionistic fuzzy values (IFVs). Furthermore, considered the risk attitude of decision maker sufficiently, a novel risk attitudinal ranking measure is developed to rank the IFVs on the basis of the continuous ordered weighted average (C-OWA) operator and this interval. Through maximizing the closeness degrees of alternatives, we construct a multi-objective fractional programming model which is transformed into a linear program. Thus, the attribute weights are derived objectively by solving this linear program. Then, a new method is put forward for MADM with IFVs and incomplete weight information. Finally, an example analysis of a teacher selection is given to verify the effectiveness and practicability of the proposed method.

Aggregating decision information into Atanassov's intuitionistic fuzzy numbers for heterogeneous multi-attribute group decision making

A new general method is developed to aggregate heterogeneous information into IFNs.A multiple objective IF programming is constructed for determining the attribute weights.A novel method is presented to solve heterogeneous MAGDM problems.Comparison analyses with existing methods are made.The proposed method is used to analyze a CCS provider evaluation problem. The aim of this paper is to propose a new aggregation method to solve heterogeneous MAGDM problem which involves real numbers, interval numbers, triangular fuzzy numbers (TFNs), trapezoidal fuzzy numbers (TrFNs), linguistic values and Atanassovs intuitionistic fuzzy numbers (AIFNs). Firstly, motivated by the relative closeness of technique for order preference by similarity to ideal solution (TOPSIS), we propose a new general method for aggregating crisp values, TFNs, TrFNs and linguistic values into AIFNs. Thus all the group decision matrices for each alternative which involves heterogeneous information are transformed into an Atanassovs intuitionistic fuzzy decision matrix which only contains AIFNs. To determine the attribute weights, a multiple objective Atanassovs intuitionistic fuzzy programming model is constructed and solved by converting it into a linear program. Subsequently, comparison analyses demonstrate that the proposed aggregated technology can overcome the drawbacks of existing methods. An example about cloud computing service evaluation is given to verify the practicality and effectiveness of the proposed method.

Aggregating decision information into interval-valued intuitionistic fuzzy numbers for heterogeneous multi-attribute group decision making

Multi-attribute group decision making (MAGDM) has attracted more and more attention in many fields. Correspondingly, a number of usable methods have been proposed for various MAGDM problems, nevertheless, very few research focus on the aggregation techniques of intuitionistic fuzzy information. The aim of this paper is to aggregate decision information into interval-valued intuitionistic fuzzy numbers (IVIFNs) to solve heterogeneous MAGDM problem in which the decision information involves real numbers, interval numbers, triangular fuzzy numbers (TFNs) and trapezoidal fuzzy numbers (TrFNs). There are three issues being addressed in this paper. The first is to propose a new general method to aggregate the attribute value vector into IVIFNs under heterogeneous MAGDM environment utilizing the relative closeness in technique for order preference by similarity to ideal solution (TOPSIS). The second is to construct a multiple objective intuitionistic fuzzy programming model to determine the attribute weights. Borrowing the results of the former two issues, the last is to present a new method to solve heterogeneous MAGDM problem. A comparison analysis with existing method is conducted to demonstrate the advantages of the proposed method. Two examples are provided to verify the practicality and effectiveness of the proposed method.

Extended VIKOR method for multiple criteria decision-making with linguistic hesitant fuzzy information

Abstract Linguistic hesitant fuzzy set (LHFS), a special hesitant fuzzy set (HFS) defined on linguistic term set (LTS), not only can express decision makers’ (DMs’) qualitative preferences, but can reflect their uncertainty and hesitancy. This paper develops a new LHF-VIKOR (linguistic hesitant fuzzy Vlsekriterijumska Optimizacija I Kompromisno Resenje) method for solving multiple criteria decision-making (MCDM) problems with LHFSs. Firstly, a new order relationship is proposed to rank LHFS by sufficiently considering the weights of membership degrees. Subsequently, a series of new distance measures of LHFS are defined including generalized distance, generalized Hausdorff distance, hybrid generalized distance, hybrid Hamming distance, and hybrid Euclidean distance. Some desirable properties of the defined distance measures are discussed in detail. Then, according to the maximizing deviation method, two optimization models are constructed to derive the criteria weights objectively for the case of completely unknown weight information and the case of incomplete weight information, respectively. Finally, by extending VIKOR method into LHF environment, a new LHF-VIKOR method is proposed to rank alternatives. An intelligent transportation system (ITS) evaluation example is analyzed to demonstrate the effectiveness and feasibility of the proposed method.

Power Average of Trapezoidal Intuitionistic Fuzzy Numbers Using Strict t-Norms and t-Conorms

As an extension of intuitionistic fuzzy number (IFN), trapezoidal intuitionistic fuzzy number (TrIFN) is one of the useful tools to deal with ill-known quantities in decision data and decision making problems. In this paper, based on the strict t-norms and t-conorms, new operation laws for the normalized TrIFNs are defined. Specially, the operation laws of TrIFNs take the speculative and radical principle and have the property of closeness in the set of normalized TrIFNs. Then, the power average operator for real numbers is extended to four power average operators for TrIFNs, i.e., the triangular (co)norms-based (t-based) power average for TrIFNs, t-based weighted power average operator for TrIFNs, t-based power ordered weighted average operator for TrIFNs, and t-based power hybrid average operator for TrIFNs. To show the feasibility and reasonability in the applications of multiple attributes group decision making using the developed operations for TrIFNs, a numerical example is provided. It is shown that there is more flexibility in the choice of the parameters associated with the degree of the risk one can bear.