A Novel Approach Toward TOPSIS Method Based on Lattice Ordered T-Bipolar Soft Sets and Their Applications

The notion of the T-bipolar soft set defined by Mahmood is a novel approach that can explain bipolarity more effectively than the other notions of bipolar soft sets. But in our daily life there are some situations in which we have to discuss some order between terms like good, satisfactory, excellent, etc. For example, to order the positions of students in a certain class, the teacher ordered the grades like decent, unsatisfactory, really nice, and tremendous. This type of standing is essential to explain the order of students’ positions in a class. In these situations, the T-bipolar soft set fails because it cannot discuss the ordered between terms. So, there is a need for such a notion that can handle these kinds of limitations. Moreover, note that although the concept of lattice ordered soft set is already defined but it discusses only one dimension. The two-dimensional opinions are essential in many decision making problems for ranking some criteria of eligibility and non-eligibility options. Therefore, to cover these mentioned drawbacks, in this article, we have elaborated a new idea of lattice (anti-lattice) ordered T-bipolar soft sets that can consider the order among parameters and it is a more valuable structure for certain situations in decision-making problems. Therefore, when we define the ranking among the set of parameters, the concept of decision making becomes very helpful under the conception of lattice (anti-lattice) ordered T-bipolar soft sets. Moreover, basic operations are defined based on introduced notions like restricted union and restricted intersection. Furthermore, the extended union and the extended intersection of introduced notions have been established. To use the introduced notion to decision making problems, we have established the application in this regard. Furthermore, we have proposed a TOPSIS method that can strengthen the study of the introduced notion and verify the results obtained from introduced notions as well. The comparative analysis of introduced work show the superiority and effectiveness of established work than that of existing notions.