Complex bipolar fuzzy sets: An application in a transport’s company

Gulistan, Muhammad and Yaqoob, Naveed and Ahmed, Elmoasry and Jawdat, Alebraheem Complex bipolar fuzzy sets: An application in a transport’s company. Journal of Intelligent & Fuzzy Systems: JIFS-20023. pp. 1-17. ISSN 1064-1246 / 1875-8967 (In Press)

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Abstract

Zadeh’s fuzzy sets are very useful tool to handle imprecision and uncertainty, but they are unable to characterize
the negative characteristics in a certain problem. This problem was solved by Zhang et al. as they introduced the concept
of bipolar fuzzy sets. Thus, fuzzy set generalizes the classical set and bipolar fuzzy set generalize the fuzzy set. These
theories are based on the set of real numbers. On the other hand, the set of complex numbers is the generalization of the
set of real numbers so, complex fuzzy sets generalize the fuzzy sets, with wide range of values to handle the imprecision
and uncertainty. So, in this article, we study complex bipolar fuzzy sets which is the generalization of bipolar fuzzy set and
complex fuzzy set with wide range of values by adding positive membership function and negative membership function to
unit circle in the complex plane, where one can handle vagueness in a much better way as compared to bipolar fuzzy sets.
Thus this paper leads us towards a new direction of research, which has many applications in different directions.We develop
the notions of union, intersection, complement, Cartesian product and De-Morgan’s Laws of complex bipolar fuzzy sets.
Furthermore, we develop the complex bipolar fuzzy relations, fundamental operations on complex bipolar fuzzy matrices
and some operators of complex bipolar fuzzy matrices. We also discuss the distance measure on complex bipolar fuzzy sets
and complex bipolar fuzzy aggregation operators. Finally, we apply the developed approach to a numerical problem with the
algorithm.

Item Type:	Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Engineering and Applied Sciences (FEAS) > Department of Basic Sciences Islamabad
Depositing User:	Dr Naveed Yaqoob
Date Deposited:	01 Feb 2021 06:32
Last Modified:	01 Feb 2021 06:32
URI:	http://research.riphah.edu.pk/id/eprint/1120

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