On Advanced Computing With Words Using the Generalized Extension Principle for Type-1 Fuzzy Sets

• Published in: IEEE transactions on fuzzy systems Vol. 22; no. 5; pp. 1245 - 1261
• Main Authors: Rajati, Mohammad Reza, Mendel, Jerry M.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Advanced Computing with Words (ACWW); Computation; Computational modeling; Frequency selective surfaces; Fuzzy; Fuzzy logic; Fuzzy set theory; Fuzzy sets; Generalized Extension Principle; Intervals; Mathematical models; Methodology; Optimization; Perceptual Computing; Pragmatics; Similarity; type-1 fuzzy sets; Uncertainty; validation; Vocabulary; Zadeh's challenge problems
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2013.2287028

In this paper, we propose and demonstrate an effective methodology for implementing the generalized extension principle to solve Advanced Computing with Words (ACWW) problems. Such problems involve implicit assignments of linguistic truth, probability, and possibility. To begin, we establish the vocabularies of the words involved in the problems, and then collect data from subjects about the words after which fuzzy set models for the words are obtained by using the Interval Approach (IA) or the Enhanced Interval Approach (EIA). Next, the solutions of the ACWW problems, which involve the fuzzy set models of the words, are formulated using the Generalized Extension Principle. Because the solutions to those problems involve complicated functional optimization problems that cannot be solved analytically, we then develop a numerical method for their solution. Finally, the resulting fuzzy set solutions are decoded into natural language words using Jaccard's similarity measure. We explain how ACWW problems can solve some potential prototype engineering problems and connect the methodology of this paper with Perceptual Computing.