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The aim of this paper is to develop a new methodology for solving bimatrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs), which are called TIFN bimatrix games for short. In this methodology, we define the concepts of the value-index and ambiguity-index and hereby develop a difference-index based ranking method, which is proven to be a total order. The parameterized bilinear programming models are derived from a pair of auxiliary TIFN mathematical programming models, which are used to determine solutions of TIFN bimatrix games. Validity and applicability of the models and method proposed in this paper are illustrated with a practical example.

The entropy of an intuitionistic fuzzy set (IFS) is a measure of uncertainty related to the IFS. The purpose of this paper is to develop a new axiomatical entropy for an IFS. The axioms for a new entropy of an IFS are defined and a mathematical expression/formula of the new entropy of the IFS is given. The newly defined entropy concerns both the amount of information and reliability of the IFS. It is proven that the new entropy has some remarkable and useful properties. The examples and comparison analysis show the validity and applicability of the new entropy proposed in this paper.

The purpose of this study is to identify the current research status on linguistic decision making through visualization method. The effective information visualization tool called CiteSpace was used to dig out how the research of linguistic decision making was conducted. A number of 2017 documents published between 1980 and 2015 were downloaded via Web of Science with the keyword “linguistic decision making” was used for topic search. The reference co-citation network was mapped to explore the reprehensive documents and research clusters in linguistic decision making area. The author co-citation network was generated to reveal the influential scholars in this area. The journal co-citation map was formulated to identify the dominant journals. The category network was mapped to excavate the most popular research category in linguistic decision making area. The results of this study have great significance to the researchers in linguistic fuzzy set, linguistic decision making and linguistic group decision making areas.

Imprecision and vagueness often occur in practical multi-attribute decision making MADM problems. Intuitionistic fuzzy IF sets are flexible to simulate these situations. The aim of this paper is to develop an effective method for solving MADM problems in which the attribute values are expressed with IF sets. Inspired by TOPSIS, we propose a new ranking function of IF sets, which takes into the amount and the reliability of an IF set. Hereby we develop a new MADM method. An example of the investment selection problem is examined to demonstrate applicability and feasibility of the proposed method. It is shown that the proposed method has some advantages over other methods.

The main objective of this paper is to develop a new ranking methodology for solving matrix games with intuitionistic fuzzy payoffs in terms of a value and ambiguity of triangular intuitionistic fuzzy numbers (TIFNs). In order to obtain an equilibrium solution of this matrix game, we construct two auxiliary TIFN programming models that are transformed into bi-objective linear programming models which are solved by a lexicographic methodology. The validity and applicability of the proposed methodology in this paper are illustrated with a numerical example.

The dual hesitant fuzzy set is an efficient mathematical approach to study imprecise, uncertain or incomplete information or knowledge. In this paper, we study the aggregation methods of the dual hesitant fuzzy information. Several aggregation operators are proposed, such as the generalized dual hesitant fuzzy weighted averaging operator (GDHFWA), the generalized dual hesitant fuzzy ordered weighted averaging operator (GDHFOWA) and the generalized dual hesitant fuzzy hybrid averaging operator (GDHFHA) operator for aggregating the dual hesitant fuzzy elements and establish various properties of these operators. A method is also proposed for multi-criteria decision making under dual hesitant fuzzy environment and applied it to teaching quality assessment.

Triangular intuitionistic fuzzy numbers TIFNs are useful to deal with ill-known quantities in decision making problems. The focus of this paper is on multi-attribute decision making MADM problems in which the attribute values are expressed with TIFNs and the information on attribute weights is incomplete, which are solved by developing a new decision method based on possibility mean and variance of TIFNs. The notions of possibility mean and variance for TIFNs are introduced as well as the possibility standard deviation. A new ranking approach for TIFNs is developed according to the ratio of the possibility mean to the possibility standard deviation. Hereby we construct a bi-objective programming model, which maximizes the ratios of the possibility mean to the possibility standard deviation for membership and non-membership functions on alternative's overall attribute values. Using the lexicographic approach, the bi-objective programming model is transformed into two non-linear programming models, which are further transformed into the linear programming models by using the variable transformation. Thus, we can obtain the maximum ratios of the possibility mean to the possibility standard deviation, s are used to rank the alternatives. A numerical example is examined to demonstrate applicability and implementation process of the proposed method.

Interval-valued intuitionistic fuzzy (IVIF) sets are a useful tool to deal with fuzziness inherent in decision data and decision making process. The aim of this paper is to develop a methodology for solving multiattribute decision making (MADM) with both ratings of alternatives on attributes and weights being expressed with IVIF sets. In this methodology, a weighted Euclidean distance between IF sets is defined using weights of IF sets. A pair of nonlinear programming models is constructed based on the concept of the relative closeness coefficients and the distance defined. Two simpler auxiliary nonlinear programming models are further derived to calculate the relative closeness coefficient intervals of alternatives to the IVIF positive ideal solution, which can be used to generate ranking order of alternatives based on the concept of likelihood of interval numbers. The method proposed in this paper is illustrated with a real example.