Constructing the Membership Function of a Fuzzy Set with Objective and Subjective Information

Abstract

Abstract: A methodology to derive the membership function of a fuzzy set with objective and subjective information about a fuzzy event is introduced in this paper, This systematic framework makes use of the fuzzy calculus, the program‐evaluation and review technique (PERQ, in operations research, and the outstanding concept of special relativity theory to transform these types of information into a fuzzy set with a resultant membership function. The subjective information can be the multi‐inputs of expert knowledge. The objective part is the statistical data with their known probability‐density function (pdf); however, this probability measure partly reflects the uncertainty assessment and is considered insufficient to describe an actual fuzzy event. If objective information is absent, this transforming or fuzzifving process can also be used to combine the different viewpoints of expertise.