Journal of Prime Research in Mathematics

# Complex Bipolar Fuzzy Soft Expert Sets

Abd Ulzeez Alkouri$$^{a,*}$$

$$^a$$Mathematics Department, Science College, Ajloun National University, P.O. Box 43, 26810, Ajloun, Jordan.

Correspondence should be addressed to: alkouriabdulazeez@gmail.com

### Abstract

The idea of representing information with its periodic nature has been extensively studied and applied in many fields. Many researchers have developed several tools to transfer uncertainty information that has the same data but with different meanings that happening in different phases/times. The novelty of combining complex numbers and uncertainty information appears in its ability to represent two values uncertainty and periodicity semantics in one mathematical tool. In this paper, we generalize existence concept of bipolar fuzzy soft expert sets (BFSES) from real number to complex numbers to be complex bipolar fuzzy soft expert sets (CBFSES). This generalization allows us to convey data that carry benefits, features, and specifications of BFSES in different phases or carrying periodic nature of the BFSE information to mathematical formula and vice versa without losing full meaning of information. The range of value becomes to be in unit disk in a complex plane for both positive and negative membership functions of BFSES. The main benefit of CBFSES that amplitude and phase terms can convey bipolar fuzzy information. Moreover, formal definition of CBFSES and illustration examples are introduced. Also, we define basic operations and their properties on CBFSES. Finally, OR and AND operations are generalized to the form of CBFSES.

#### Keywords:

Bipolar fuzzy set, Bipolar fuzzy soft expert set, complex bipolar fuzzy soft expert set, fuzzy set, complex fuzzy set.