In this paper, we introduce and study fuzzy variational-like inclusion, fuzzy resolvent equation and $H(cdot,cdot)$-$phi$-$eta$-accretive operator in real  uniformly smooth Banach spaces. It is established that fuzzy variational-like inclusion is equivalent to a fixed point problem as well as to a fuzzy resolvent equation. This equivalence is used to define an iterative algorithm for solving fu...

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 starting point of this paper is given by priestley’s papers, where a theory of representation of distributive lattices is presented. the purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. in this way, some results of priestley’s papers are extended. in the main theorem, we show that the category of finite fuzzy priestley space...

in this paper, we study the finitely many constraints of the fuzzyrelation inequality problem and optimize the linear objectivefunction on the region defined by the fuzzy max-product operator.simplification operations have been given to accelerate theresolution of the problem by removing the components having noeffect on the solution process. also, an algorithm and somenumerical and applied exa...

Operations between two granules and inclusion measure are two important issues in granular computing. Two operations between two granules, named join operation and meet operation, are formed to realize the transformation between granule spaces with different granularities, and the fuzzy inclusion measure is induced by the aforementioned operations. The granule set, operations, and fuzzy inclusi...

It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. Some basic operations on functions such as the inverse and composition are applicable to binary relations as well. Depending on the domain or range or both are fuzzy value fuzzy set, i...

We characterize a fuzzy partial order relation using its level set, find sufficient conditions for the image of a fuzzy partial order relation to be a fuzzy partial order relation, and find sufficient conditions for the inverse image of a fuzzy partial order relation to be a fuzzy partial order relation. Also we define a fuzzy lattice as fuzzy relations, characterize a fuzzy lattice using its l...

In this article, we introduce four fuzzy relations and the composition, and some useful properties are shown by them. In section 2, the definition of converse relation R of fuzzy relation R and properties concerning it are described. In the next section, we define the composition of the fuzzy relation and show some properties. In the final section we describe the identity relation, the universe...

In fuzzy set theory, comparison of fuzzy sets plays an important role. Among the several ways to compare fuzzy sets, we address the logical theoretic approach using fuzzy implications. We propose a general framework allowing to generate many measures of comparison: inclusion, similarity and distance, and study their properties. Since the literature on the use fuzzy implications for defining suc...