Computing with words and its relationships with fuzzistics

• Published in: Information sciences Vol. 177; no. 4; pp. 988 - 1006
• Main Author: Mendel, Jerry M.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.02.2007
• Subjects: Computing with words; Fuzzistics; Interval type-2 fuzzy sets; Inverse problems; Type-2 fuzzy sets; Interval type-2 fuzzy sets; Inverse problems; Type-2 fuzzy sets; Fuzzistics; Computing with words
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2006.06.008

Words mean different things to different people, and so are uncertain. We, therefore, need a fuzzy set model for a word that has the potential to capture their uncertainties. In this paper I propose that an interval type-2 fuzzy set (IT2 FS) be used as a FS model of a word, because it is characterized by its footprint of uncertainty (FOU), and therefore has the potential to capture word uncertainties. Two approaches are presented for collecting data about a word from a group of subjects and then mapping that data into a FOU for that word. The person MF approach, in which each person provides their FOU for a word, is limited to fuzzy set experts because it requires the subject to be knowledgeable about fuzzy sets. The interval end-points approach, in which each person provides the end-points for an interval that they associate with a word on a prescribed scale is not limited to fuzzy set experts. Both approaches map data collected from subjects into a parsimonious parametric model of a FOU, and illustrate the combining of fuzzy sets and statistics—type-2 fuzzistics.