A distance measure for optimistic viewpoint of the information in interval-valued intuitionistic fuzzy sets and its applications

Abstract

Distance measures in interval-valued intuitionistic fuzzy sets are useful tools for a wide range of decision-making, pattern recognition, and clustering problems. However, so far, only a few distance measures have been developed. Furthermore, the developed distance measure takes a moderate view of the information held in the interval-valued intuitionistic fuzzy sets. It is frequently necessary to be optimistic about the information contained in interval-valued intuitionistic fuzzy sets. Furthermore, in decision-making problems, cross-time information is an important parameter. As a result, a new distance measure has been developed to fill this gap in the literature. The developed distance measure takes into account the optimistic viewpoint of the information held in the interval-valued intuitionistic fuzzy sets as well as the cross-time information via the difference between the maximum and minimum cross-information factors. Numerical and comparative studies are being conducted to demonstrate the superiority of the proposed distance measure. Furthermore, to establish the validity and applicability of the proposed distance measure, it is being used to solve multi-attribute decision making problems, pattern recognition problems, and clustering problems in an interval-valued intuitionistic fuzzy environment. The results of the multi-attribute decision making problem of recruiting a marketing expert have been found to be equivalent to the majority of existing methods. Furthermore, the pattern recognition and clustering problems of building material classification are based on the same data set, with the pattern recognition problem determining that polyvinyl chloride flooring belongs to carpet, and the clustering problem determining that polyvinyl chloride flooring and carpet belong to the same class with a very high confidence interval. These demonstrate the proposed distance measure’s validity and applicability. In general, this work highlights on decision making, pattern recognition, and clustering of engineering problems under interval-valued intuitionistic fuzzy environment from an optimistic point of view.