Matrix Game with Payoffs Represented by Triangular Dual Hesitant Fuzzy Numbers

Matrix Game with Payoffs RepresentedDue to the complexity of information or the inaccuracy of decision-makers’ cognition, it is difficult for experts to quantify the information accurately in the decision-making process. However, the integration of the fuzzy set and game theory provides a way to help decision makers solve the problem. This research aims to develop a methodology for solving matrix game with payoffs represented by triangular dual hesitant fuzzy numbers (TDHFNs). First, the definition of TDHFNs with their cut sets are presented. The inequality relations between two TDHFNs are also introduced. Second, the matrix game with payoffs represented by TDHFNs is investigated. Moreover, two TDHFNs programming models are transformed into two linear programming models to obtain the numerical solution of the proposed fuzzy matrix game. Furthermore, a case study is given to to illustrate the efficiency and applicability of the proposed methodology. Our results also demonstrate the advantage of the proposed concept of TDHFNs

A Laplace's principle based approach for solving fuzzy matrix games

We introduce a solution for matrix games with fuzzy payoffs via the α -cuts and the introduction of Nature as a third player expressing the uncertainty involved in the game. The beliefs of players about the behavior of Nature are based on the Laplace’s principle of “insufficient reason”. Moreover, we provide a procedure for computing the introduced solution

Multi-level Multi-objective Quadratic Fractional Programming Problem with Fuzzy Parameters: A FGP Approach

The motivation behind this paper is to present multi-level multi-objective quadratic fractional programming (ML-MOQFP) problem with fuzzy parameters in the constraints. ML-MOQFP problem is an important class of non-linear fractional programming problem. These type of problems arise in many fields such as production planning, financial and corporative planning, health care and hospital planning. Firstly, the concept of the -cut and fuzzy partial order relation are applied to transform the set of fuzzy constraints into a common crisp set. Then, the quadratic fractional objective functions in each level are transformed into non-linear objective functions based on a proposed transformation. Secondly, in the proposed model, separate non-linear membership functions for each objective function of the ML-MOQFP problem are defined. Then, the fuzzy goal programming (FGP) approach is utilized to obtain a compromise solution for the ML-MOQFP problem by minimizing the sum of the negative deviational variables. Finally, an illustrative numerical example is given to demonstrate the applicability and performance of the proposed approach

A method to solve two-player zero-sum matrix games in chaotic environment

This research article proposes a method for solving the two-player zero-sum matrix games in chaotic environment. In a fast growing world, the real life situations are characterized by their chaotic behaviors and chaotic processes. The chaos variables are defined to study such type of problems. Classical mathematics deals with the numbers as static and less value-added, while the chaos mathematics deals with it as dynamic evolutionary, and comparatively more value-added. In this research article, the payoff is characterized by chaos numbers. While the chaos payoff matrix converted into the corresponding static payoff matrix. An approach for determining the chaotic optimal strategy is developed. In the last, one solved example is provided to explain the utility, effectiveness and applicability of the approach for the problem.Abbreviations: DM= Decision Maker; MCDM = Multiple Criteria Decision Making; LPP = Linear Programming Problem; GAMS= General Algebraic Modeling System

Fuzzy linear programming problems : models and solutions

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, alpha-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately