Solving Fuzzy Bi-matrix Games Through a Interval Value Function Approach

Mapping Intimacies ◽

10.20944/preprints201802.0041.v1 ◽

2018 ◽

Author(s):

Kaisheng Liu ◽

Yumei Xing

Keyword(s):

Equilibrium Solution ◽

Optimization Problem ◽

Value Function ◽

Linear Optimization ◽

Function Approach ◽

Game Model ◽

Optimal Solutions ◽

Matrix Games ◽

Linear Optimization Problem ◽

Interval Value

This article puts forward the bi-matrix games with crisp parametric payoffs based on interval value function approach. We conclude that the equilibrium solution of the game model can converted into optimal solutions of the pair of the non-linear optimization problem. Finally, experiment results show the efficiency of the model.

Download Full-text

Solving Bi-Matrix Games Based on Fuzzy Payoffs via Utilizing the Interval Value Function Method

Mathematics ◽

10.3390/math7050469 ◽

2019 ◽

Vol 7 (5) ◽

pp. 469

Author(s):

Kaisheng Liu ◽

Yumei Xing

Keyword(s):

Nonlinear Optimization ◽

Function Method ◽

Value Function ◽

Optimization Problems ◽

Game Model ◽

Optimal Solutions ◽

Equilibrium Solutions ◽

Matrix Games ◽

Interval Value

In this article, we introduce a model of bi-matrix games based on crisp parametric payoffs via utilizing the method of interval value function. Then, we get that equilibrium solutions of bi-matrix games on the basis of fuzzy payoffs and equilibrium solutions of the game model are of equal value. Furthermore, it is concluded that equilibrium solutions of the game can be converted to optimal solutions of discrete nonlinear optimization problems with parameters. Lastly, the proposed methodology is illustrated by an example.

Download Full-text

Pessimistic Bilevel Linear Optimization

Journal of Nepal Mathematical Society ◽

10.3126/jnms.v1i1.42165 ◽

2018 ◽

Vol 1 (1) ◽

pp. 1-10

Author(s):

S. Dempe ◽

G. Luo ◽

S. Franke

Keyword(s):

Optimization Problem ◽

Value Function ◽

Linear Optimization ◽

Equivalent Transformation ◽

Optimal Solutions ◽

Linear Optimization Problem ◽

Optimal Value ◽

Nonconvex And Nonsmooth Optimization ◽

Bilevel Linear Optimization ◽

Nonsmooth Optimization Problem

In this paper, we investigate the pessimistic bilevel linear optimization problem (PBLOP). Based on the lower level optimal value function and duality, the PBLOP can be transformed to a single-level while nonconvex and nonsmooth optimization problem. By use of linear optimization duality, we obtain a tractable and equivalent transformation and propose algorithms for computing global or local optimal solutions. One small example is presented to illustrate the feasibility of the method.

Download Full-text

Efficiency of MOMA-plus Method to Solve Some Fully Fuzzy L-R Triangular Multiobjective Linear Programs

Journal of Mathematics Research ◽

10.5539/jmr.v10n2p77 ◽

2018 ◽

Vol 10 (2) ◽

pp. 77 ◽

Cited By ~ 1

Author(s):

Abdoulaye Compaoré ◽

Kounhinir Somé ◽

Joseph Poda ◽

Blaise Somé

Keyword(s):

Optimization Problem ◽

Optimization Problems ◽

Linear Optimization ◽

Linear Programs ◽

Pareto Optimal Solutions ◽

Optimal Solutions ◽

Linear Optimization Problem ◽

Novel Approach ◽

Linear Optimization Problems ◽

Single Objective

In this paper, we propose a novel approach for solving some fully fuzzy L-R triangular multiobjective linear optimization programs using MOMA-plus method (Kounhinir, 2017). This approach is composed of two relevant steps such as the converting of the fully fuzzy L-R triangular multiobjective linear optimization problem into a deterministic multiobjective linear optimization and the applying of the adapting MOMA-plus method. The initial version of MOMA-plus method is designed for multiobjective deterministic optimization (Kounhinir, 2017) and having already been tested on the single-objective fuzzy programs (Abdoulaye, 2017). Our new method allow to find all of the Pareto optimal solutions of a fully fuzzy L-R triangular multiobjective linear optimization problems obtained after conversion. For highlighting the efficiency of our approach a didactic numerical example is dealt with and obtained solutions are compared to Total Objective Segregation Method proposed by Jayalakslmi and Pandia (Jayalakslmi 2014).

Download Full-text