The Generalized Similarity Measures Based on Complex Interval-Valued Hesitant Fuzzy Sets and Their Applications in Pattern Recognition and Medical Diagnosis

Abstract

In this study, we investigate a novel conception called complex interval-valued hesitant fuzzy set (CIvHFS) as the modification of some prevailing conceptions such as interval-valued complex fuzzy set (IvCFS) and interval-valued hesitant fuzzy set (IvHFS), to tickle the data or information which have intricate and haziness in the genuine life dilemmas. The CIvHFS carries the membership grade in the model of a finite subset of numerous interval values which contains in the unit disc of a complex plane. We also propound the operational laws of the investigated conception. Further, we establish certain vector similarity measures (VSMs) and weighted VSMs (WVSMs) in the setting of CIvHFS, including the Jaccard similarity measure (JSM), Dice similarity measure (DSM), and Cosine SM (CSM), etc. Along with this, we also investigate hybrid VSM and weighted hybrid VSM relying on the CIvHFS. Moreover, we present some generalized exponential and non-exponential based SMs for CIvHFS. To portray the usefulness and advantages of the developed SMs in genuine life, we employ these SMs to solve pattern recognition and medical diagnosis. Finally, to assess the dependability and rationality of the developed SMs, we compare the investigated SMs with certain prevailing SMs.

Keywords

• Complex interval-valued hesitant fuzzy set
• similarity measures
• pattern recognition
• medical diagnosis