∈ , ∈ ∨ q ) – fuzzy ideal (prime) of bounded lattice is introduced and its properties are studied. Mathematics Subject Classifications: 06B10, 06D72

he theory of fuzzy sets was ntroduced by Zadeh [22] in 1965 as an attempt to study the vagueness and uncertainity in real world problems. A.Rosenfeld [16] applied the notion of fuzzy sets and introduced the notion of fuzzy subgroups in groups. Since then various classical algebraic systems have been fuzzified. The theory of rough sets introduced by Z.Pawlak [14] in 1982 is another independent m...

In this paper we introduce the notion of interval-valued (i.v.) fuzzy prime and semiprime ideals of a hypersemiring and study different properties of these two ideals. Finally, we examine the strongly irreducibility and irreducibility of an i.v. fuzzy ideal of a hypersemiring and characterize the equivalence of primeness, strongly irreducibility and irreducibility of an i.v. fuzzy ideal of a fu...

In this paper, we count the number of fuzzy subgroups of cyclic group G = Zp × Zq × Zr × Zs with p, q, r, s are distinct prime numbers. We define an equivalence relation on the fuzzy subgroups of any groups G and determine all of its subgroups. Then we draw the diagram of lattice subgroups of G. The number of fuzzy subgroups of G by observing the diagram then will be counted. Mathematics Subjec...

Fuzzy groups and fuzzy theory have a lot of applications in several sciences such as mathematics, computer science, computer and electrical engineering. Hence, counting the number of fuzzy subgroups of finite groups to classify them is an important issue in fuzzy theory. The Main goal of this paper is to give an explicit formula for the number of fuzzy subgroups of a finite cyclic group 1 2 3 k...