The concept of quasi-coincidence of an interval-valued fuzzy set is considered. By using this new idea, the notion of interval-valued (α, β)−fuzzy k−ideals of semirings is introduced, which is a generalization of a fuzzy k−ideal. Also some related properties are studied and in particular, the interval-valued (∈,∈ ∨q)−fuzzy k−ideals in a semiring will be investigated. Finally, the concept of imp...

In this study, ?-interval valued set is defined whose elements are closed sub-intervals including ? of unit interval that I = [0, 1]. With different order relation on set, the properties examined. By help relation, it shown complete lattice. Negation function given in to study theoretical set. means discussions fundamental features studied. fuzzy sets defined. The algebraic these level subsets ...

The notion of a rough set was originally proposed by Pawlak [Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences 11 (5) (1982) 341–356]. Later on, Dubois and Prade [D. Dubois, H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General System 17 (2–3) (1990) 191–209] introduced rough fuzzy sets and fuzzy rough sets as a generalization of rough...

Abstract In the present paper, the interval-valued pP, P_ qq-fuzzy LI-ideal theory in lattice implication algebras is further studied. Some new properties of interval-valued pP, P_ qq-fuzzy LI-ideals are given. Representation theorem of interval-valued pP, P_ qq-fuzzy LI-ideal which is generated by an interval-valued fuzzy set is established. It is proved that the set consisting of all interval...

In this paper, we introduce the concept of interval valued (α, β)-fuzzy subnear-rings and ideal of near-rings, where α, β any two of the {∈, q,∈ ∨q,∈ ∧q} with α 6=∈ ∧q, by using belongs to relation ∈ and quasi-coincidence with relation q between interval valued fuzzy points and interval valued fuzzy sets. We also discussed some characterizations of interval valued (α,∈ ∨q)-fuzzy ideals(subnear-...

The relationship between the intuitionistic fuzzy sets and the algebraic hyperstructures is described in this paper. The concept of the quasi-coincidence of an intuitionistic fuzzy interval valued with an interval-valued intuitionistic fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of an intuitionistic fuzzy point in intuitionistic fuzzy sets. By using thi...

We define the Cartesian product, composition, union and join on interval-valued fuzzy graphs and investigate some of their properties. We also introduce the notion of interval-valued fuzzy complete graphs and present some properties of self complementary and self weak complementary interval-valued fuzzy complete graphs.