On bipolar complex fuzzy sets and its application

Abstract

Many factors with the perspective of bipolarity in the traditional Chinese food system 'Yin and Yang food system' manipulate with types of food simultaneously to have a balanced body. This research studies the multiple attributes decision making (MADM) problem that measuring the 'bipolarity of periodic' variation in bipolar information with an illustration example in order to find an optimal nutrition program for a person X. To convey this type of data to a mathematical formula and vice versa without losing the full meaning of human knowledge, we use bipolar fuzzy set in a complex geometry by extending the range of bipolar fuzzy set to the realm of a complex number. This extension needs to be successful to study and introduce intensely a new mathematical structure called a bipolar complex fuzzy set (BCFS) with its properties. Ranges of values are extended to [0, 1] eiα[0,1] and [-1, 0] eiα[-1,0] for both positive and negative membership functions, respectively, as a replacement for [-1, 0] × [0, 1], as in the bipolar fuzzy set. The main benefit of BCFS that the amplitude and phase terms of BCFSs can convey bipolar fuzzy information. Moreover, the formal definition of BCF distance measure and illustration application are introduced. Some basic mathematical operations on BCFS are also proposed and study its properties with arithmetical examples.