Some theoretical aspects of fuzzy-relation equations describing fuzzy systems

Antonio Di Nola; Witold Pedrycz; Salvatore Sessa

doi:10.1016/0020-0255(84)90051-3

Some theoretical aspects of fuzzy-relation equations describing fuzzy systems

Antonio Di Nola
, Witold Pedrycz
, Salvatore Sessa

Department of Measurements and Control Systems (RAU/RAU2)

University of Naples Federico II

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

Abstract

This paper contains some theoretical results on fuzzy-relation equations and applications to analysis of fuzzy systems as well as identification and control problems. If A_i, 1 ≤ i ≤ k, are fuzzy inputs, B is a fuzzy output, and R is a fuzzy relation describing the system, the above problems are illustrated by means of a max-min multidimensional equation of type B = A₁ {A figure is presented} ... {A figure is presented} A_k {A figure is presented} R. Furthermore, we investigate some properties of fuzzy systems described by fuzzy-relation equations, focusing our attention on energy and entropy measures of fuzziness of solutions of the class of equations under discussion.

Original language	English
Pages (from-to)	241-264
Number of pages	24
Journal	Information Sciences
Volume	34
Issue number	3
DOIs	https://doi.org/10.1016/0020-0255(84)90051-3
Publication status	Published - Dec 1984

ASJC Scopus subject areas

Control and Systems Engineering
Software
Theoretical Computer Science
Computer Science Applications
Information Systems and Management
Artificial Intelligence

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10.1016/0020-0255(84)90051-3

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AU - Pedrycz, Witold

AU - Sessa, Salvatore

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N2 - This paper contains some theoretical results on fuzzy-relation equations and applications to analysis of fuzzy systems as well as identification and control problems. If Ai, 1 ≤ i ≤ k, are fuzzy inputs, B is a fuzzy output, and R is a fuzzy relation describing the system, the above problems are illustrated by means of a max-min multidimensional equation of type B = A1 {A figure is presented} ... {A figure is presented} Ak {A figure is presented} R. Furthermore, we investigate some properties of fuzzy systems described by fuzzy-relation equations, focusing our attention on energy and entropy measures of fuzziness of solutions of the class of equations under discussion.

AB - This paper contains some theoretical results on fuzzy-relation equations and applications to analysis of fuzzy systems as well as identification and control problems. If Ai, 1 ≤ i ≤ k, are fuzzy inputs, B is a fuzzy output, and R is a fuzzy relation describing the system, the above problems are illustrated by means of a max-min multidimensional equation of type B = A1 {A figure is presented} ... {A figure is presented} Ak {A figure is presented} R. Furthermore, we investigate some properties of fuzzy systems described by fuzzy-relation equations, focusing our attention on energy and entropy measures of fuzziness of solutions of the class of equations under discussion.

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JO - Information Sciences

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ER -

Some theoretical aspects of fuzzy-relation equations describing fuzzy systems

Abstract

ASJC Scopus subject areas

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