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

By Kifayat Ullah, Tahir Mahmood, Zeeshan Ali, Naeem Jan. Complex & Intelligent Systems, 2019

350 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/2af2f477590f5693c8be50e97269463749acd36d

How researchers see this paper

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In Computational Theory and Mathematics

1. Tahir Mahmood
2. Qaisar Khan
3. Kifayat Ullah
4. Zeeshan Ali

In Management Science and Operations Research

1. Zeeshan Ali
2. Kifayat Ullah
3. Qaisar Khan
4. Tahir Mahmood
5. Irik Z. Mukhametzyanov

Citations in the corpus

• Einstein Geometric Aggregation Operators using a Novel Complex Interval-valued Pythagorean Fuzzy Setting with Application in Green Supplier Chain Management (2021, methodology): “Ullah et al. (2020) only explored some measures based on CPFSs, but to determine the relationship among any number of attributes when they are in the form of interval-valued, then the existing theories have been failed, similarly, aggregation operators is one of the important techniques to manage…”