A novel approach towards bipolar complex fuzzy sets and their applications in generalized similarity measures

Abstract

The notions of the bipolar complex fuzzy set (BCFS) and complex bipolar fuzzy set (CBFS) have been already given, but these notions of BCFS and CBFS have the problem that they contradict the basic definition of the complex numbers which we discussed in this article, and then we defined the new definition of BCFS. Our defined notion of BCFS is more closed to bipolarity as compared with already existing BCFS and CBFS, and more accurate. BCFS is the fusion of bipolar fuzzy set (BFS) which a decision analyst needs to describe the positive and negative aspects of an object and complex fuzzy set (CFS) which a decision analyst needs to handle two‐dimensional (two variables) information. When there is information of two variables with positive and negative aspects then a decision analyst needs BCFS to handle this information. In this article, we also interpreted some basic operations on BCFS like a complement, intersection, and union and explained them with the help of examples. Additionally, we defined the concept of type‐1 partially BCFS and type‐2 partially BCFS. Further, we interpreted some generalized trigonometric similarity measures such as generalized cosine similarity measure, generalized tangent similarity measure, generalized cotangent similarity measure, and generalized hybrid trigonometric similarity measure for BCFS. The weighted generalized trigonometric similarity measures are also presented in this article. After that, we applied these similarity measures (SMs) in two real‐life applications (pattern recognition and medical diagnosis) to show the benefits and advantages of our proposed SMs. Finally, we did a comparison of our demonstrated SMs with some existing SMs to show the superiority, usefulness, and effectiveness of our proposed SMs.

Identification and Prioritization of DevOps Success Factors Using Bipolar Complex Fuzzy Setting With Frank Aggregation Operators and Analytical Hierarchy Process

“…By including the parameters Frank introduced t-norm and t-conorm to become more flexible in combining the data and appropriate to address the real-life issues. The Frank t-norm and t-conorm are presented as Definition 1: [47] The Frank t-norm and Frank t-conorm are diagnosed as [43] The conception of BCFS over a fixed set 𝔅 is described as follows…”

“…Finally, we compared the diagnosed operators with various existing theories to improve the worth of the invented approaches. Enhancing the worth of the diagnosed operators with the help of comparative analysis, for this, we selected some prevailing theories explained in Ref [25,43,58,59,60,44,45]. The comparative result of the diagnosed operators with selected prevailing theories is explained in Table XV.…”

“…Certain features with the perspective of bipolarity in the genuine chinses food system control with sorts of food continues to have a stable body. The main theme of this paragraph is to recall the wellknown and dominant idea of bipolar CFS (BCFS) which was diagnosed by Mahmood and Ur Rehman [43]. The main mathematical shape of BCFS is dependent on two basic terms called positive and negative supporting grades whose values lie among [0, 1] × [0, 1] and [−1, 0] × [−1, 0].…”

A Novel Approach Toward TOPSIS Method Based on Lattice Ordered T-Bipolar Soft Sets and Their Applications

“…The idea of bipolar fuzzy SS in K-algebra is defined by Akram et al [21]. Moreover, Mahmood and Rehman [22] defined the idea of bipolar complex FS and their applications in generalized similarity measures. The utilization of bipolar fuzzy SS in DM obstacle and its operation was introduced by Abdullah et al [23].…”

Bipolar Complex Fuzzy Hamacher Aggregation Operators and Their Applications in Multi-Attribute Decision Making

“…Mahmood and Ur Rehman [45] presented a bipolar complex fuzzy set (BCFS). The theory of BCFS has a powerful structure in the shape of complex numbers whose real and unreal terms are belonging to unit intervals.…”