A new framework which extends the concepts of soft mathematical morphology into fuzzy sets is presented. Images can be considered as arrays of fuzzy singletons on the Cartesian grid. Based on this notion the definitions for the basic fuzzy soft morphological operations are derived. Compatibility with binary soft mathematical morphology as well as the algebraic properties of fuzzy soft operation...

There are fast known algorithms to compute the transitive closure of a fuzzy relation, but there are only a few different algorithms that compute T-transitive low approximations of a fuzzy relation. A fast method to compute a T-transitive low approximation of a reflexive and symmetric fuzzy relation is given for any continuous tnorm, spending O(n) time.

We introduce and study the construction of commutative fundamental relation in fuzzy hypersemigroups and investigate its basic properties. We will determine some necessary and sufficient conditions so that this relation is transitive in fuzzy hypersemigroups. Also we show that this relation is transitive in every fuzzy hypergroup.

Abstract Extending the belongs to (∈) relation and quasi-coincidence with(q) relation between fuzzy points and a fuzzy subsets, the concept of (α, β)-fuzzy filters and (α, β)-fuzzy filters of lattice implication algebras are introduced, where α, β ∈ {∈h , qδ, ∈h ∨qδ, ∈h ∧qδ}, α, β ∈ {∈h, qδ, ∈h ∨ qδ, ∈h ∧ qδ} but α ∈h ∧qδ, α ∈h ∧ qδ, respectively, and some related properties are investigated. S...

Systems which use a fuzzy rule base and an inference mechanisms are quite frequently used in many applications. Fuzzy rules and inference mechanisms can be described by a system of fuzzy relation equations. A solution to a given system of fuzzy relation equations can serve us a proper model of fuzzy rules (fuzzy model for short). But only two particular solutions, let us call them disjunctive a...

In this paper, we introduce the definition of E-inversive E-semigroup with fuzzy φ-kernel normal systems. It is described that the fuzzy regular congruences on the E-inversive E-semigroup with fuzzy φ-kernel normal systems.

In this paper, we endow set S with the structure of an ordered semigroup and define “intuitionistic fuzzy” analogous for several notions that have been proved to be useful in the theory of ordered semigroups and give some equivalent conditions of these definitions. Then we characterize the completely regular and the strongly regular ordered semigroups by means of intuitionistic fuzzy bi-ideals.