In the real world, the parameters of a problem may not be the crisp values. The fuzzy theory among the theories in which uncertainty plays a crucial role. Type-2 fuzzy sets generalize fuzzy sets. We consider a special type of such sets here. In this paper, we consider two issues. First, we review the method proposed by Javanmard and Mishmast Nehi for solving an interval type-2 triangular fuzzy linear programming problem, and improve it. Then, we express a bilevel linear programming problem, that, to the best of our knowledge, has not been investigated so far. We consider the bilevel linear programming problem with uncertainty where all the coefficients in the problem are interval type-2 triangular fuzzy numbers. We convert an interval type-2 triangular fuzzy bilevel linear programming problem into an interval bilevel linear programming problem using Grzegorzewski's nearest interval approximation method. Finally, we obtain five problems, and by solving them, we achieve the solution of interval type-2 triangular fuzzy bilevel linear programming problem as an interval type-2 triangular fuzzy number.

In this paper, we first use a fuzzy preference relation with a membership function representing preference degree for comparing two interval-valued fuzzy numbers and then utilize a relative preference relation improved from the fuzzy preference relation to rank a set of interval-valued fuzzy numbers. Since the fuzzy preference relation is a total ordering relation that satisfies reciprocal and transitive laws on interval-valued fuzzy numbers, the relative preference relation is also a total ordering relation. Practically, the fuzzy preference relation is more reasonable on ranking interval-valued fuzzy numbers than defuzzification because defuzzification does not present preference degree between fuzzy numbers and loses messages. However, fuzzy pair-wise comparison for the fuzzy preference relation is more complex and difficult than defuzzification. To resolve fuzzy pair-wise comparison tie, the relative preference relation takes the strengths of defuzzification and the fuzzy preference relation into consideration. The relative preference relation expresses preference degrees of interval-valued fuzzy numbers over average as the fuzzy preference relation does, and ranks fuzzy numbers by relative crisp values as defuzzification does. In fact, the application of relative preference relation was shown in traditional fuzzy numbers, such as triangular and trapezoidal fuzzy numbers, for previous approaches. In this paper, we extend and utilize the relative preference relation on interval-valued fuzzy numbers, especially for triangular interval-valued fuzzy numbers. Obviously, interval-valued fuzzy numbers based on the relative preference relation are easily and quickly ranked, and able to reserve fuzzy information.

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.