Fuzzy relational inequalities and equations, fuzzy quasi-orders, closures and openings of fuzzy sets

Fuzzy relation equations and subsystems of fuzzy transition systems

In this paper we study subsystems, reverse subsystems and double subsystems of a fuzzy transition system. We characterize them in terms of fuzzy relation inequalities and equations, as eigen fuzzy sets of the fuzzy quasi-order Qδ and the fuzzy equivalence Eδ generated by fuzzy transition relations, and as linear combinations of aftersets and foresets of Qδ and equivalence classes of Eδ. We also...

Solving a non-convex non-linear optimization problem constrained by fuzzy relational equations and Sugeno-Weber family of t-norms

Sugeno-Weber family of t-norms and t-conorms is one of the most applied one in various fuzzy modelling problems. This family of t-norms and t-conorms was suggested by Weber for modeling intersection and union of fuzzy sets. Also, the t-conorms were suggested as addition rules by Sugeno for so-called  $lambda$–fuzzy measures. In this paper, we study a nonlinear optimization problem where the fea...

Linear optimization on Hamacher-fuzzy relational inequalities

In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated where the feasible region is formed as the intersection of two inequality fuzzy systems and Hamacher family of t-norms is considered as fuzzy composition. Hamacher family of t-norms is a parametric family of continuous strict t-norms, whose members are decreasing functions of ...

Openings and closures of fuzzy preorderings: theoretical basics and applications to fuzzy rule-based systems

Images of fuzzy sets under fuzzy relations have been investigated mainly in two contexts: on the one hand, mostly under the term “full image” (Gottwald, 1993), they can be regarded as very general tools for fuzzy inference, leading to the so-called “compositional rule of inference” (Gottwald, 1993; Bauer et al., 1995). The theory of fuzzy relational equations makes direct use of this fundamenta...

On the max - ``Fuzzy Or'' composition fuzzy inequalities systems