Abstract

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.

中文翻译：

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三元半群的区间值模糊软集理论

摘要

在本文中，我们着重于结合三元半群上的区间值模糊软三元理论，并建立一个新的区间值模糊软三元半群框架。该手稿的目的是将区间值模糊软集应用于处理三元半群中的几种理论。首先，我们介绍了区间值模糊软集，区间值模糊软三元半群和区间值模糊软理想的概念。同时，给出了一些说明性的例子来说明本文介绍的定义的合理性。其次，提出了三元半群上的几种新型广义模糊软集，并研究了它们的相关性质和相互关系。最后，