Interval Valued Intuitionistic (S, T)–fuzzy H v –submodules

Abstract

Abstract. On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K.Atanassov, the notion of interval valued intuitionistic fuzzy H v -submodules of an H v -module with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated.In particular, the connections between interval valued intuitionistic (S, T )-fuzzy H v -submodules and interval valued intuitionistic (S, T )-fuzzy submodules are discussed.

The L-fuzzy hypermodules

“…This approach can be extended to fuzzy hypergroups. For example, given a crisp hypergroup (H, •) and a fuzzy subset µ in H, then we say that µ is a fuzzy subhypergroup of H if every cut set of µ say µ t , is a (crisp) subhypergroup of H. This was initiated by Zahedi et al [13] and continued by Ameri and Hedayati [14], Davvaz and Corsini [15], Davvaz et al [16], Zhan et al [17][18][19][20][21] and so on. The third approach involves the definition and study of fuzzy hyperoperations.…”

Fuzzy roughness of n-ary hypergroups based on a complete residuated lattice

“…The relationships between the fuzzy sets and algebraic hyperstructures have been considered by Corsini, Davvaz, Kehagias, Leoreanu, Vougiouklis, Yin, Zhan and others. The reader is refereed to [5,22,26,28,40,43,48,50,51]. Also, the relationships between the fuzzy sets and n-ary algebraic hyperstructures have been considered by Corsini et al in [10-12, 20, 29, 46].…”

Connections between interval valued fuzzy graphs and fuzzy groups with (S,T)-norms

“…Such fuzzy sets have some applications in the technological scheme of the functioning of a silo-farm with pneumatic transportation, in a plastic products company and in medicine (for more details see [3], [7][8][9][10][11] and [19]). The fuzzy algebraic structures play a prominent role in mathematics with wide applications in many other branches such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, topological spaces, logic, set theory, group theory, groupoids, real analysis, measure theory etc (For instance see [13], [18] and [22]). Also graph theory has numerous applications to problems in systems analysis, operations research, transportation, and economics.…”