Linear programming on SS-fuzzy inequality constrained problems

Document Type: Research Paper

Authors

1 University of Tehran, College of Engineering, Faculty of Engineering Science

2 Department of Algorithms and Computation, University of Tehran,Tehran, Iran.

Abstract

In this paper, a linear optimization problem is investigated whose constraints are defined with fuzzy relational inequality. These constraints are formed as the intersection of two inequality fuzzy systems and Schweizer-Sklar family of t-norms. Schweizer-Sklar family of t-norms is a parametric family of continuous t-norms, which covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. Firstly, we investigate the resolution of the feasible region of the problem and studysome theoretical results. A necessary and sufficient condition and three other necessary conditions are derived for determining the feasibility. Moreover, in order to simplify the problem, some procedures are presented. It is proved that the optimal solution of the problem is always resulted from the unique maximum solution and a minimal solution of the feasible region. A method  is proposed to generate random feasible max-Schweizer-Sklar fuzzy relational inequalities and an algorithm is presented to solve the problem. Finally, an example is described to illustrate these algorithms.

Keywords