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

Abstract

The notion of the T-Bipolar soft set defined by Mahmood is a fundamental notion that not only considers positive or negative aspects, but it can deal with parameterization tools as well. However, note that in our daily life there is some situation in which we have to discuss some order between terms like good, satisfactory, excellent, etc. In these situations, the T-bipolar soft set fails and there is a need for such a notion that can handle these kinds of situations. 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 for ranking some criteria of eligibility and non-eligibility options. Therefore, due to these reasons, 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 for lattice ordered T-bipolar soft sets. Moreover, the restricted union and restricted intersection of lattice (anti-lattice) ordered T-Bipolar soft sets have been proposed. Moreover, the extended union and the extended intersection of introduced notions have been established. We have proposed the application of the initiated notions to support our work. Furthermore, a TOPSIS method is introduced to strengthen the study of the introduced notion. We have compared our work with some existing notions that shows that our work is more efficient and valuable.