Linear optimization of fuzzy relation inequalities with max-Lukasiewicz ‎composition

Subject Areas : International Journal of Industrial Mathematics

E. Shivanian ¹

1 - Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran.

Received: 2015-04-16 Accepted : 2015-04-16 Published : 2015-04-01

Keywords: Linear objective function opti, Fuzzy relation equations, Fuzzy relation inequalities, max-Lukasiewicz ‎composition,

Abstract :

In this paper, we study the finitely many constraints of fuzzy relation inequalities problem and optimize the linear objective function on this region which is defined with fuzzy max-Lukasiewicz operator. In fact Lukasiewicz t-norm is one of the four basic t-norms. A new simplification technique is given to accelerate the resolution of the problem by removing the components having no effect on the solution process. Also, an algorithm and one numerical example are offered to abbreviate and illustrate the steps of the problem resolution ‎process.‎