Type-2 intuitionistic fuzzy matrix games based on a new distance measure: Application to biogas-plant implementation problem

Abstract

In reality, to deal with uncertain information, researchers have introduced several extensions of fuzzy sets. But, in most cases, two-dimensional fuzzy sets (considering elements with their membership degree) are considered. However, it fails to capture all types of incomplete information. Occasionally, the inadequacy of the data depends upon the large span of source or time or both. In that case, two-dimensional fuzzy sets or type-1 fuzzy sets (T1FSs) are not sufficient to portray the situation. Type-2 fuzzy set (T2FS), a three-dimensional extent of the fuzzy set, appears here to bridge this gap. Type-2 intuitionistic fuzzy set (T2IFS) is a novel extension of T2FS. It can express the fuzzy preference of the decision-makers toward their decisions under different parameters. It also considers both the acceptance and non-acceptance of decision-makers. In the present study, we aim to develop matrix games in T2IF environment. To do this, we first define Hamacher aggregation operators in T2IF environment with their properties. We also propose the Minkowski distance of T2IFSs based on the Hausdorff metric. Then a similarity measure of T2IFS is formed. Next, we solve the matrix games by utilizing the proposed distance measure. The proposed methodology has been delineated with the biogas-plant implementation problem to check the applicability and validity.