*Correspondence: [email protected] 1Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, 710121, China Full list of author information is available at the end of the article Abstract This study aims to explore modular inequalities of interval-valued fuzzy soft sets characterized by Jun’s soft J-inclusions. Using soft product operations...

This paper considers the relations among L -fuzzy sets, rough sets and hyperring theory. Based on a complete residuated lattice, the concept of (invertible) L-fuzzy hyperideals of a hyperring is introduced and some related properties are presented. The notions of lower and upper L-fuzzy rough approximation operators with respect to an L-fuzzy hyperideal are provided and some significant propert...

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...

Maji et al. introduced the concept of intuitionistic fuzzy soft sets, which is an extension to the soft set and intuitionistic fuzzy set. In this paper, we apply the concept of intuitionistic fuzzy soft sets to semigroup theory. The notion of intuitionistic fuzzy soft ideals over a semigroup is introduced and their basic properties are investigated. Some lattice structures of the set of all int...

In this paper, we shall introduce generalized fuzzy compactness in L-spaces where L is a complete de Morgan algebra. This definition does not rely on the structure of basis lattice L and no distributivity is required. The intersection of a generalized fuzzy compact L-set and a generalized closed Lset is a generalized fuzzy compact L-set. The generalized irresolute image of a generalized fuzzy c...

Ordered fuzzy numbers (OFN) invented by the second author and his two coworkers in 2002 make possible to utilize the fuzzy arithmetic and to construct the Abelian group of fuzzy numbers and then an ordered ring. The definition of OFN uses the extension of the parametric representation of convex fuzzy numbers. Fuzzy implication is proposed with the help of algebraic operations and a lattice stru...

In this paper we introduce the notions of regular and strongly regular intuitionistic fuzzy relations on hypergroupoids, studying some related properties and connections with the classical case. Then we investigate the lattice structure of these kinds of intuitionistic fuzzy equivalences.