Distance measure on intuitionistic fuzzy sets and its application in decision-making, pattern recognition, and clustering problems

Decision-making under uncertainty is consistently an essential fear and the most challenging circle of exploration. To manage the uncertainty, the intuitionistic fuzzy set (IFS) assumes a critical part in taking care of the conditions wherein decision-makers furnish an alternative with a grade of membership and a nonmembership. Distance measures of IFSs are apparatuses used in different decision-making problems, such as medical investigation, pattern recognition, multicriteria decision-making, clustering problems, and other real-world problems. As such, various distance measures were developed by different researchers and applied to decision-making problems with situation-based deficiencies. Motivated by this, in this paper, a symmetric distance formula is being proposed for effectively determining the distance between the information held by IFSs. The distance formula involves membership degree, nonmembership degree, the difference of the minimum of the cross-evaluation factor, and the difference of the maximum of the cross-evaluation factor. Furthermore, it is being proved that the proposed distance formula follows all the axiomatic definitions of a distance measure. Numerical examples depict the efficiency of the proposed distance measure. Hence, this measure is being applied to practical problems of decision-making, pattern recognition, and clustering problems. This measure is not restricted to a particular domain of study; it can be effectively applied in diverse decision-making problems.