Complex Generalised Fuzzy Soft Set and its Application

Abstract

Human knowledge and mentality of experts may be changed with the time making the time a very important factor to the decision-makers. Therefore, different decisions for exact problem can be made by decision-makers in different times. We introduce here a new mathematical tool called complex generalized fuzzy soft set (CGFSS), which is a combination of the concept of generalized fuzzy soft set (GFSS) and complex fuzzy set (CFS). The importance of CGFSS may be appeared in the ability to convey the parametric nature in the concept of GFSS that happening periodically without losing the full meaning of human knowledge. While the uncertainty values lie in GFSS may be affected by different factors/phases/levels, CGFSS represents two values for each parameter (i) the degree of membership “belongingness of uncertainty and periodicity for elements in universe of discourse” and (ii) the degree of uncertainty and periodicity for the possibility of such belongingness which are represented by using complex membership form. Some CGFSS’s basic operations and its properties are introduced with the definition of relation on this tool and its application to illustrate the novelty of CGFSS in the decision-making problem. Finally, a comparison between several uncertainty sets and CGFSS is illustrated.