On interval-valued fuzzy soft set theory applied to ternary semigroups. (English) Zbl 1473.20076
Summary: In this paper, we focus on combining the theories of interval-valued fuzzy soft sets over ternary semigroups, and establishing a new framework for interval-valued fuzzy soft ternary semigroups. The aim of this manuscript is to apply interval-valued fuzzy soft set for dealing with several kinds of theories in ternary semigroups. First, we present the concepts of interval-valued fuzzy soft sets, interval-valued fuzzy soft ternary semigroups and interval-valued fuzzy soft ideals. Meanwhile, some illustrative examples are given to show the rationality of the definitions introduced in this paper. Second, several new kinds of generalized fuzzy soft sets over ternary semigroups are proposed, and related properties and mutual relationships are also investigated. Finally, our goal is to establish a relation between different types of ternary subsemigroups (left ideal, right ideal, lateral ideal, two-sided ideal, ideal) of a ternary semigroup and interval-valued fuzzy soft subsemigroups (interval-valued fuzzy soft left ideal, interval-valued fuzzy soft right ideal, interval-valued fuzzy soft lateral ideal, interval-valued fuzzy soft two-sided ideal, interval-valued fuzzy soft two-sided ideal) over a ternary semigroup and also characterize these notions in terms of soft sets in ternary semigroups.
MSC:
| 20N25 | Fuzzy groups |
| 20N10 | Ternary systems (heaps, semiheaps, heapoids, etc.) |
| 20M75 | Generalizations of semigroups |
Keywords:
ternary semigroup; interval-valued fuzzy soft ideal; interval-valued fuzzy soft set; interval-valued fuzzy soft ternary semigroup; interval-valued fuzzy soft bi-idealReferences:
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