On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition

Kifayat Ullah,Naeem Jan,Zeeshan Ali,Tahir Mahmood

doi:10.1007/s40747-019-0103-6

Kifayat Ullah, Naeem Jan + Show 2 more

Open Access

https://doi.org/10.1007/s40747-019-0103-6

Copy DOI

Abstract

The concept of complex fuzzy set (CFS) and complex intuitionistic fuzzy set (CIFS) is two recent developments in the field of fuzzy set (FS) theory. The significance of these concepts lies in the fact that these concepts assigned membership grades from unit circle in plane, i.e., in the form of a complex number instead from [0, 1] interval. CFS cannot deal with information of yes and no type, while CIFS works only for a limited range of values. To deal with these kinds of problems, in this article, the concept of complex Pythagorean fuzzy set (CPFS) is developed. The novelty of CPFS lies in its larger range comparative to CFS and CIFS which is demonstrated numerically. It is discussed how a CFS and CIFS could be CPFS but not conversely. We investigated the very basic concepts of CPFSs and studied their properties. Furthermore, some distance measures for CPFSs are developed and their characteristics are studied. The viability of the proposed new distance measures in a building material recognition problem is also discussed. Finally, a comparative study of the proposed new work is established with pre-existing study and some advantages of CPFS are discussed over CFS and CIFS.

Highlights

Handling of uncertain and imprecise information has always been a challenge
Greenfield et al [11] proposed a novel concept of complex interval valued FS (CIVFS) which certainly improved the idea of complex fuzzy set (CFS) and generalizes the framework of interval valued fuzzy set (IVFS)
Some distance measures for complex intuitionistic fuzzy soft sets (CIFSSs) are developed by Kumar and Bajaj in [13], whereas the theory of power aggregation operators for complex intuitionistic fuzzy set (CIFS) is proposed by Rani and Garg [14] which was further utilized in multiattribute decision making (MADM)

Summary

Introduction

Handling of uncertain and imprecise information has always been a challenge. Many theories are presented to cope with imprecision and uncertainty that exists in almost all the reallife problems such as theory of soft sets [1], theory of rough sets [2], and theory of FSs [3]. 7. On the other hand, none of the existing tools can be applied to problems lying in the environment of CPFSs. we demonstrate the advantages of working in the area of CPFS and DMs of CPFSs. Our claim is that the proposed distance measures can solve the problem lies in the region of PFSs, CIFSs, IFSs, CFSs, and FS. Such problem can be solved using the restricted version of DMs proposed in Remark 1. Such problem can be solved using the restricted version of DMs proposed in Remark 4. All this discussion shows the superiority of our proposed work and the limitations of existing structures

Conclusion

Compliance with ethical standards