Exponential and Non-Exponential Similarity Measures for Bipolar Complex Fuzzy Sets and Their Application in CRM Software

Authors

  • Tahir Mahmood Department of Mathematics and Statistics, International Islamic University Islamabad, Pakistan
  • Muhammad Nusrallah Department of Mathematics and Statistics, International Islamic University Islamabad, Pakistan
  • Ubaid Ur Rehman Department of Mathematic, University of Management and Technology, C-II, Johar Town, Lahore, Punjab, 54700, Pakistan
  • Jabbar Ahmmad Department of Mathematics, Faculty of Engineering and Computer Science, National University of Modern Languages (NUML), Islamabad, H-9, Pakistan
  • Dragan Pamucar Széchenyi István University, Győr, Hungary https://orcid.org/0000-0001-8522-1942

DOI:

https://doi.org/10.37256/cm.7120267363

Keywords:

customer relationship management software, bipolar complex fuzzy set, similarity measures, exponentialbased and non-exponential-based Similarity Measures (SMs)

Abstract

Throughout the customer lifecycle, organizations monitor and analyze relationships with their current and potential customers using an approach and set of procedures called Customer Relationship Management (CRM). The main objective of CRM is to raise customer happiness, retention, and loyalty while promoting corporate expansion and profitability. The utilization of positive and negative aspects is necessary in many real-life situations, for example, the attributes of CRM have both their effects and side effects and also contain extra information. In this regard, Bipolar Complex Fuzzy Set (BCFS) is the only structure that can model such information that has dual aspects and extra information. Thus, the purpose of this article is to analyze the study of Similarity Measures (SMs) in the environment of BCFS, such as exponential, non-exponential based SMs and weighted exponential, non-exponential based SMs. Afterward, we anticipate a technique of Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) by employing the invented SMs in the framework of BCFS and then we investigate an application “selection of finest CRM software” with the assistance of the diagnosed approach of TOPSIS. In the last part of this article, we anticipate the comparison of our devised theory with current theories to reveal the advantages and superiority.

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Published

2026-01-05

How to Cite

1.
Mahmood T, Nusrallah M, Rehman UU, Ahmmad J, Dragan Pamucar. Exponential and Non-Exponential Similarity Measures for Bipolar Complex Fuzzy Sets and Their Application in CRM Software. Contemp. Math. [Internet]. 2026 Jan. 5 [cited 2026 Jan. 8];7(1):326-64. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/7363