Correlation coefficients for T-spherical fuzzy sets and their applications in clustering and multi-attribute decision making

The framework of T-spherical fuzzy set is a generalization of fuzzy set, intuitionistic fuzzy set and picture fuzzy set having a great potential of dealing with uncertain events with no limitation. A T-spherical fuzzy framework can deal with phenomena of more than yes or no type; for example, consider the scenario of voting where one's voting interest is not limited to in favor'' or against'' rather there could be some sort of abstinence or refusal degree also. The objective of this paper is to develop some correlation coefficients for T-spherical fuzzy sets due to the non-applicability of correlations of intuitionistic fuzzy sets and picture fuzzy sets in some certain circumstances. The fitness of new correlation coefficients has been discussed, and their generalization is studied with the help of some results. Clustering and multi-attribute decision-making algorithms have been proposed in the environment of T-spherical fuzzy sets. To demonstrate the viability of proposed algorithms and correlation coefficients, two real-life problems including a clustering problem and a multi-attribute decision-making problem have been solved. A comparative study of the newly presented and pre-existing literature is established showing the superiority of proposed work over the existing theory. Some advantages of new correlation coefficients and drawbacks of the pre-existing work are demonstrated with the help of numerical examples.