A 3D Distance Measure for Intuitionistic Fuzzy Sets and its Application in Pattern Recognition and Decision-Making Problems

Abstract

The distance measure as an information measure helps in processing incomplete and confusing data to arrive at a conclusion by assessing the degree of difference between pairs of variables. Reviewing distance measures for Intuitionistic Fuzzy Sets (IFSs), we have pointed out several drawbacks of the existing measures. To overcome these, this paper presents a new distance measure between IFSs based on the probabilistic divergence measure. Several mathematical properties of the proposed metric are established and validated via numerical examples. This proposed definition is further used to devise several similarity measures. Applicability and consistency of the introduced measures have been corroborated by various examples. In addition to that, rationality of the proposed metric is established by applying it to pattern recognition applications, Multi-Attribute-Decision-Making (MADM) problems and medical & pathological diagnoses. Analysis of the results establishes that the suggested measure overcomes shortcomings associated with existing measures and thereby authenticates the superiority of the proposed measure.