The purpose of this paper is to develop a methodology for solving a new type of matrix games in which payoffs are expressed with Triangular Intuitionistic Fuzzy Numbers (TIFNs). In this methodology, the concept of solutions for matrix games with payoffs of TIFNs is introduced. A pair of auxiliary Intuitionistic Fuzzy programming models for players are established to determine optimal strategies and the value of the matrix game with payoffs of TIFNs. Based on the cut sets and ranking order relations between TIFNs, the Intuitionistic Fuzzy programming models are transformed into linear programming models, which are solved using the existing simplex method. Validity and applicability of the proposed methodology are illustrated with a numerical example of the market share problem.

For many decision problems with uncertainty, Triangular Intuitionistic Fuzzy number is a useful tool in expressing illknown quantities. This paper develops a novel decision method based on zero-sum game for multiple attribute decision making problems where the attribute values take the form of Triangular Intuitionistic Fuzzy Numbers and the attribute weights are unknown. First, a new value index is defined for Triangular Intuitionistic Fuzzy Numbers on the basis of the centroid. Thereby, a new ranking approach is presented for comparing Triangular Intuitionistic Fuzzy Numbers. We formulate a multiple attribute decision making problem as a two-person zero-sum game with payoffs of Triangular Intuitionistic Fuzzy Numbers. Then, following the new ranking approach, the Fuzzy matrix game is converted as a pair of crisp linear programming models, and the optimal strategies are objectively derived by solving such models. Therefore, the ranking order of alternatives is determined by the expected scores of alternatives. An example of video monitoring system selection is demonstrated to illustrate the effectiveness of the proposed methodology.

Triangular Intuitionistic Fuzzy Numbers (TIFNs) is a special case of Intuitionistic Fuzzy (IF) set and the ranking of TIFNs is an important problem. The aim of this paper is to develop a new methodology for ranking TIFNs by using multiattribute decision making methods (MADM). In this methodology, the value and ambiguity indices of TIFNs may be considered as the attributes and the TIFNs in comparison are seen as the alternatives. A compromise ratio method for Fuzzy MADM is developed based on the concept that larger TIFN should close to the maximum value index and is far away from the minimum ambiguity index simultaneously. The proposed ranking method is applied to solve multiattribute decision making problems in which the ratings of alter- natives on attributes are expressed by using TIFNs. Numerical examples are examined to demonstrate the implementation process and applicability of the proposed method in this paper. Furthermore, a comparison analysis of the proposed method is conducted to show its advantages over other methods.

The Intuitionistic Fuzzy set has been applied to game theory very rarely since it was introduced by Atanassov in 1983. The aim of this paper is to develop an effective methodology for solving matrix games with payoffs of Atanassov's Triangular Intuitionistic Fuzzy Numbers (TIFNs). In this methodology, the concepts and ranking order relations of Atanassov's TIFNs are defined. A pair of bi-objective linear programming models for matrix games with payoffs of Atanassov's TIFNs is derived from two auxiliary Atanassov's Intuitionistic Fuzzy programming models based on the ranking order relations of Atanassov's TIFNs defined in this paper. An effective methodology based on the weighted average method is developed to determine optimal strategies for two players. The proposed method in this paper is illustrated with a numerical example of the market share competition problem.

Ranking Fuzzy Numbers(FNs) was a critical issue in Fuzzy computing field. Generally, Triangular FNs, trapezoidal FNs, and even interval-valued FNs(IVFNs) were often expressed in ranking. However, ranking Intuitionistic FNs(IFNs) were less mentioned due to the complicated components in membership functions. Herein, we will develop Fuzzy binary relation that is an extended Fuzzy preference relation(EFPR) to express the preference degree of two IFNs, and then the relation is improved to be a relative preference relation(RPR) used to rank a set of IFNs. Since EFPR on IFNs is a total ordering relation, RPR will be also a total ordering relation. Based on belonging and non-belonging components of membership functions in IFNs, using EFPR being also Fuzzy preference relation(FPR) is suitable to compare FNs on pairwise, but time complexity on Fuzzy operation of comparison computing is complicated. Hence, RPR is developed to avoid comparing on pairwise. Through yielding RPR values for a set of IFNs, IFNs are effectively and efficiently ranked to utilize related decision-making problems.

In this paper I will introduce the trapezoidal Intuitionistic Fuzzy Numbers (IF Numbers) and will prove some operations for them. Also I am going to propose a new ordering method for IF Numbers in which I will consider two characteristic values of membership and non-membership functions for an IF number. These values are defined by the integral of the inverse Fuzzy membership and non-membership functions multiplied by the grade with powered parameter.

The concept of an Intuitionistic Fuzzy number (I F N) is of importance for representing an ill-known quantity. Ranking Fuzzy Numbers plays a very important role in the decision process, data analysis and applications. The concept of an Intuitionistic Fuzzy number (IFN) is of importance for quantifying an ill-known quantity. Ranking of Intuitionistic Fuzzy Numbers plays a vital role in decision making and linear programming problems. Also, ranking of Intuitionistic Fuzzy Numbers is a very difficult problem. In this paper, a new method for ranking Intuitionistic Fuzzy number is developed by means of magnitude for different forms of Intuitionistic Fuzzy Numbers. In Particular ranking is done for trapezoidal Intuitionistic Fuzzy Numbers, Triangular Intuitionistic Fuzzy Numbers, symmetric trapezoidal Intuitionistic Fuzzy Numbers, and symmetric Triangular Intuitionistic Fuzzy Numbers. Numerical examples are illustrated for all the defined different forms of Intuitionistic Fuzzy Numbers. Finally some comparative numerical examples are illustrated to express the advantage of the proposed method.

Since the inception of Intuitionistic Fuzzy sets in 1986, many authors have proposed different methods for ranking Intuitionistic Fuzzy Numbers (IFNs). However, due to the complexity of the problem, a method which gives a satisfactory result to all situations is a challenging task. Most of them contained some shortcomings, such as requirement of complicated calculations, inconsistency with human intuition and indiscrimination and some produce different rankings for the same situation and some methods cannot rank crisp Numbers. For overcoming the above problems, in this paper, a new parametric ranking method for IFNs is proposed. It is developed based on the concept -cuts and -cuts and area on left side of IFNs. The proposed ranking method is applied to solve partner selection problem in which the rating of partner on attributes are expressed by using Triangular IFNs. The proposed method is much simpler and more efficient than other methods in the literature. Some comparative examples are also given to illustrate the advantages of the proposed method.