Bipolar Complex Fuzzy Sets

This book offers a comprehensive review of bipolar complex fuzzy sets theory. It investigates the algebraic structures such as lattices, semigroup, groups, semirings and rings. In turn, it discusses distance measures, similarity measures, correlation coefficient and entropy measures, together with the associated properties for bipolar complex fuzzy sets. Further, it describes the aggregation operators such as Hamy mean operators and power generalized Heronian mean operators in the environment of bipolar complex fuzzy set. Last but not least, it shows an application in supply chain management. The book addresses mathematicians and computer science working with imprecise, unclear information, and set the basis for new applications of fuzzy sets in the field of Intelligent Data-Driven Systems and Artificial Intelligence.

Author Biography

Ubaid ur Rehman working as an assistant professor at the Department of Mathematics, University of Management and Technology, Lahore, Pakistan. He received his Ph.D. degree in Mathematics from the International Islamic University Islamabad, Pakistan in 2023. His research interests include fuzzy sets and their generalizations, algebraic structures, aggregation operators, similarity measures, fuzzy decision-making, rough sets, soft sets, decision-making theory, and Machine learning. He has published more than 100 articles in well-reputed peer-reviewed journals with 320+ impact factor. He has been a member of the academic board of Global Open Share Publishing since 2024 and Editorial Board member of “Mathematics and System Science” journal.

Tahir Mahmood is Associate Professor of Mathematics at Department of Mathematics and Statistics, International Islamic University Islamabad, Pakistan. He received his Ph.D. degree in Mathematics from Quaid-i-Azam University Islamabad, Pakistan in 2012 in the field of Fuzzy Algebra. His areas of interest are Algebraic structures, Fuzzy Algebraic structures, Decision making and generalizations of fuzzy sets. Around 400 research publications are on his credit with more than 12700 citations, 900 impact factor, 56 h-index and around 221 i10-index. He has produced 65 MS students and 10 Ph.D. students.  Currently he is working as editorial board member of 3 impact factor journals and as editor-in-chief of the journal “Journal of Innovative Research in Mathematical and Computational Sciences”.