Multi-criteria decision-making using connection number based TOPSIS method under tripolar fuzzy environment

Tripolar fuzzy sets offer a robust framework that integrates the aspects of intuitionistic fuzzy sets and bipolar fuzzy sets. Complex decision-making problems often involve multiple attributes with specific properties that reflect both negative and positive aspects. In such cases, intuitionistic fuzzy sets (IFS) and bipolar fuzzy sets (BFS) may be insufficient to handle these complexities that makes tripolar fuzzy sets an essential tool for identifying optimal solutions. In our study, we introduce a Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method using connection number of set pair analysis under the tripolar fuzzy environment. Initially, we express tripolar fuzzy number as a connection number, which is a pivotal concept in set pair analysis. We then extend the TOPSIS method based on the connection number of set pair analysis within the realm of tripolar fuzzy sets. By applying the proposed methodology, we provide the computational framework for the problem related to multi-criteria decision making. Moreover, we observe that our proposed technique also satisfies the existing test criterions. In this context, we conduct the comparative study of the newly established technique with the other ones existing in intuitionistic fuzzy and bipolar fuzzy environments. Finally, we show that our proposed technique is superior than the others.