Volume 22, Issue 13 pp. 20-27
Article
Full Access

A proposal on approximate reasoning based on revision principle and fixed value law

Liya Ding

Liya Ding

Institute of Systems Science, National University of Singapore, Heng Mui Keng Terrace, Kent Ridge, Singapore 0511

Liya Ding obtained a B.E. in Computer Engineering from Shanghai University of Technology in China in 1982. She obtained a Ph.D. in Computer Science from Meiji University, Kawasaki, Japan, in 1991. She was appointed an Associate on the research staff,Institute of Systems Science, National University of Singapore, in 1991 and was a Visiting Scholar, School of Science and Technology, Meiji University, from 1986 to 1991. Her areas of researchinterest are in intelligent languages, fuzzy theory, knowledge engineering, compiler technology,and understanding natural languages.

Search for more papers by this author
Masao Mukaidono

Masao Mukaidono

School of Science and Technology, Meiji University, Kawasaki, Japan 214

Masao Mukaidono received a B.E., an M.E., and a Dr. of Eng. degree in Electrical Engineering from Meiji University, Kawasaki, Japan, in 1965, 1968, and 1973, respectively. He is currently a Professor in the Department of Computer Science, Faculty of Science and Technology, Meiji University. His main research interests are in multiple-valued logic, fuzzy set theory and its applications, fault-tolerant computing systems, and computer-aided logic design. Dr. Mukaidono is a member of the IEEE Computer Society; the Institute of Electronics, Information, and Communication Engineers of Japan; the Information Processing Society of Japan; and the Japan Society of Fuzzy Theory and Systems. He is a director of the Japan Society of Fuzzy Theory and Systems.

Search for more papers by this author
First published: 1991
Citations: 2

Abstract

When a rule P Q and a fact P' that is an approximation of P are given, how to obtain the conclusion Q' approximately is an interesting topic on approximate reasoning. This paper proposes a new approach based on the revision principle and fixed value law. The basic idea on revision principle is to deduce Q' from Q based on the deviation of P' from P.

When the revision principle is applied on fuzzy set, there are two laws for obtaining a deviation from P' to P. The first law is called the fixed point law. Its basic idea is to fix an element × in the universe of discourse × of P and P' to obtain the deviation between the membership functions m̈p(x) and m̈p(x). The second law is called the fixed value law. Its basic idea is to fix a value such that the membership functions m̈p(x)= m̈p(x') to obtain the shift from point × to x' on the universe of discourse X.

According to the fixed value law, it will become possible to deduce Q' from Q by shifting the membership function. As an example of the fixed value law, a set of linear revising formulas will be given.

The full text of this article hosted at iucr.org is unavailable due to technical difficulties.