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Resolution of finite fuzzy relation equations. (English) Zbl 0553.04006
The authors study general schemes for solving finite fuzzy relation equations whose membership functions assume values in [0,1]. The algorithms presented determine the maximum solution of E. Sanchez [Inf. Control 30, 38-48 (1976; Zbl 0326.02048)] and the minimal solutions. An extensive comparison between the results of this paper and those of M. Prévot [Fuzzy Sets Syst. 5, 319-322 (1981; Zbl 0451.04004)] and of E. Czogala, J. Drewniak and W. Predrycz [Fuzzy Sets Syst. 7, 89-101 (1982; Zbl 0483.04001)] is discussed. A suitable numerical example showing how the different schemes work is also given.
Reviewer: A.Di Nola

MSC:
03E20 Other classical set theory (including functions, relations, and set algebra)
03-04 Software, source code, etc. for problems pertaining to mathematical logic and foundations
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References:
[1] Birkhoff, G., Lattice theory, (1967), AMS Colloquium Publications Providence, RI · Zbl 0126.03801
[2] Czogaiła, E.; Drewniak, J.; Pedrycz, W., Fuzzy relation equations on a finite set, Fuzzy sets and systems, 7, 89-101, (1982) · Zbl 0483.04001
[3] Prévot, M., Algorithm for the solution of fuzzy relations, Fuzzy sets and systems, 5, 319-322, (1981) · Zbl 0451.04004
[4] Sanchez, E., Equations de relations floves, (1972), Thèse Biologie Humaine Marseille, France
[5] Sanchez, E., Resolution of composite fuzzy relation equations, Inform. and control, 30, 38-48, (1976) · Zbl 0326.02048
[6] Zadeh, L.A., Fuzzy sets, Inform. control, 8, 338-353, (1965) · Zbl 0139.24606
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