Distance Measure Approaches to Rank Interval-Valued Trapezoidal Intuitionistic Fuzzy Sets

Abstract

Similarity/Distance measures are proven to be potential in evaluating uncertain information. It compares the objects with ambiguous and imprecise feature by measuring the degree of deviation of objects.  It is observed that the existing Euclidean distance measure on Interval-Valued Trapezoidal Intuitionistic Fuzzy Sets (IVTrIFSs) is failing to discriminating fuzzy sets in some cases. This paper proposes, a modified Euclidean distance measure by redefining the terms of non-memberships in the existing ED. Further a new distance measure-Jaccard distance is proposed by using the modified Euclidean distance. The desirable properties of the measure have been proven. Numerical examples are provided to demonstrate the applicability of the distance measure.  Comparative study is done. The results show that the proposed distance measures effectively ranking IVTrIFSs and the ranking is close to human intuition.