Generating fuzzy sets from the families of sets

Article type: Research Article

Authors: Wu, Hsien-Chung^{; *}

Affiliations: Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, Taiwan

Correspondence: [*] Corresponding author. Hsien-Chung Wu, Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan. E-mail: hcwu@nknucc.nknu.edu.tw.

Abstract: The main purpose of this paper is to establish a mechanical procedure to determine the membership functions using the data collected from the economic and engineering problems. Determining the membership functions from the collected data may depend on the subjective viewpoint of decision makers. The mechanical procedure proposed in this paper can get rid of the subjective bias of decision makers. The concept of solid families is also proposed by regarding the sets in a family to be continuously varied. The desired fuzzy sets will be generated in the sense that its α-level sets will be identical to the sets of the original family. In order to achieve this purpose, any arbitrary families will be rearranged as the nested families by applying some suitable functions to the original families that are formulated from the collected data.

Keywords: Nested families, non-normal fuzzy sets, solid families

DOI: 10.3233/JIFS-210201

Journal: Journal of Intelligent & Fuzzy Systems, vol. 41, no. 2, pp. 3061-3082, 2021