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 ...

We introduce and discuss a notion of fuzzy uniform structure that provides a direct link with the classical theory of uniform spaces. More exactly, for each continuous t-norm we prove that the category of all fuzzy uniform spaces in our sense (and fuzzy uniformly continuous mappings) is isomorphic to the category of uniform spaces (and uniformly continuous mappings) by means of a covariant func...

Recently, the distributivity of fuzzy implications over t-norms, t-conorms and uninorms was studied in many articles. In this paper we characterize functions which satisfy one of the four generalized distributivity equations of classical implication in the case when t-conorms are continuous and Archimedean. Using the obtained characterizations we describe some solutions which are fuzzy implicat...

Min-independence has been proved to be a sufficient condition of a vector of fuzzy random variables to be a fuzzy random vector. The objective of this paper is to study further on the independence condition for fuzzy random vector based on continuous triangular norms. We first discuss measurability criteria for fuzzy random vector, and present two more new equivalent formulations of the measura...

In this paper are introduced some concepts of interval-valued fuzzy relations and some of their properties: reflexivity, symmetry, T-transitivity, composition and local reflexivity. The existence and uniqueness of T-transitive closure of interval-valued fuzzy relations is proved. An algorithm to compute the T-transitive closure of finite interval-valued fuzzy relations is showed. Some propertie...

Uninorms are a generalization of t-norms and tconorms for which the neutral element is an element of [0,1] which is not necessarily equal to 0 (as for t-norms) or 1 (as for t-conorms). Uninorms on the unit interval are either conjunctive or disjunctive, i.e. they aggregate the pair (0,1) to either 0 or 1. In reallife applications, this kind of aggregation may be counter-intuitive. Atanassov’s i...

In this paper, line search based on Sequential Quadratic Programming is implemented in order to find a solution to Fuzzy Relation Equations. Sequential Quadratic Programming is a gradient-based method that uses a quadratic estimation of the objective function in each iteration’s neighborhood. Unlike analytical approaches, the method can handle equations with any combinations of t-norms and t-co...

Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and their residua as truth functions for implication. In these logics, a negation is also definable from the implication and the truth constant 0, namely ¬φ isφ → 0. However, this negation behaves quite differently depending on the t-norm. For a nilpotent t-norm (a t-norm which i...

Intuitionistic fuzzy rough sets are investigated in a general framework which includes generalizations of many related results in early literatures. A new definition of intuitionistic fuzzy rough sets is given with the analysis of its basic properties based on the notion of two universes, general binary relations, and a pair ðT , IÞ of intuitionistic fuzzy t-norm T and intuitionistic fuzzy impl...