Open AccessOn Nash-Coalitive Fuzzy Continuous Differential Games
Author(s) -
Mohamed Abd El-Hady Kassem,
Nabil A. El-kholy,
Malak H. Eid,
Mohamed M. Ibrahim
Publication year - 2022
Publication title -
international journal emerging technology and advanced engineering
Language(s) - English
Resource type - Journals
ISSN - 2250-2459
DOI - 10.46338/ijetae0322_04
Subject(s) - fuzzy number , mathematics , nash equilibrium , differential game , mathematical optimization , fuzzy logic , fuzzy set operations , defuzzification , fuzzy classification , fuzzy set , computer science , artificial intelligence
This paper concentrates on providing a simple and effective technique to solve the Nash-coalitive fuzzy continuous differential games. These games are featured by having fuzzy coefficients, fuzzy controls, and fuzzy state functions. The proposed technique utilizes the α-cut set concept of fuzzy numbers to transform the problem under study into a corresponding interval problem. The latter one is sliced into two problems, lower problem and upper problem, to obtain the optimal solution for the Nash-coalitive fuzzy continuous differential games problem in a range form. The sufficient and necessary conditions for this problem are derived. A numerical example is provided to clarify the presented concepts. Keywords— fuzzy control, fuzzy differential games, fuzzy numbers, Nash-coalitive differential games