Abstract
The notion of bipolar soft sets has already been defined, but in this article, the notion of bipolar soft sets has been redefined, called T-bipolar soft sets. It is shown that the new approach is more close to the concept of bipolarity as compared to the previous ones, and further it is discussed that so far in the study of soft sets and their generalizations, the concept introduced in this manuscript has never been discussed earlier. We have also discussed the operational laws of T-bipolar soft sets and their basic properties. In the end, we have deliberated the algebraic structures associated with T-bipolar soft sets and the applications of T-bipolar soft sets in decision-making problems.
Highlights
To handle the uncertainty has always been a problem for the researchers and decision makers as it appears in almost every field of real life and all sciences including basic sciences, management sciences, social sciences, and information sciences
After the remarkable start of the era of soft sets, many researchers put their share in the progress of the theory of soft sets, for example, Acar et al [8] presented the notion of soft rings, Sezer and Atagun [9] originated soft vector spaces, Ali et al [10] represented graphs based on neighbourhoods and soft sets, Shabir and Naz [11] opened the notion of soft topological spaces, Sezer et al [12] worked on soft intersection semigroups, Ali et al [13] initiated the notion of lattice ordered soft sets, and Cagman [14] initiated a new approach in soft set theory
(2) e definitions of intuitionistic fuzzy sets and that of double framed soft sets have same characteristics in the sense that (i) Both are characterized by two functions (ii) Both have a single set as domain set for both the functions (iii) Both have a single set, which is a lattice in either case, as codomain set for both the functions
Summary
To handle the uncertainty has always been a problem for the researchers and decision makers as it appears in almost every field of real life and all sciences including basic sciences, management sciences, social sciences, and information sciences. Naz and Shabir [26] instigated the study of algebraic structures associated with fuzzy soft sets. In 2013, Shabir and Naz [37] instigated the idea of bipolar soft sets, and keeping this concept in view, Naz and Shabir [38] familiarized the idea of fuzzy bipolar soft sets and studied their algebraic structures and their applications. We come to know that in both approaches, the conception of bipolar soft sets has some shortcomings, which we will discuss in our upcoming sections of the article (see Remark 1). (2) In Section 3 of the article, the notion of T-bipolar soft sets is familiarized, its basic operational laws are given, and related results are conferred. (5) In Section 6, conclusion of the work presented is drawn and some future directions are discussed
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