The fuzzy relation equation with union or intersection preserving operator. (English) Zbl 0651.04005
The paper deals with finding extremal solutions of fuzzy relation equations. The composition of those relations is based on some binary operations on the unit interval. The discussion of those operations can be performed over an arbitrary complete lattice and has, indeed, been performed by G. Birkhoff [Lattice theory, 3rd ed., Chap. XIV, § 5 (1967; Zbl 0153.025)]. Theorems 3 and 6 of the paper should be compared with those of J. Drewniak [Fuzzy Sets Syst. 14, 237-247 (1984; Zbl 0553.04003)]. The remaining results are completely new. In particular, a new method of construction of extremal solutions of matrix equations is presented.
Reviewer: T.Kubiak
MSC:
| 03E99 | Set theory |
| 03E20 | Other classical set theory (including functions, relations, and set algebra) |
| 94D05 | Fuzzy sets and logic (in connection with information, communication, or circuits theory) |
References:
| [1] | Sanchez, E., Resolution of composite fuzzy relation equations, Inform. and Control, 30, 38-48 (1976) · Zbl 0326.02048 |
| [2] | Pedrycz, W., Fuzzy relational equations with generalized connectives and their applications, Fuzzy Sets and Systems, 5, 185-201 (1983) · Zbl 0525.04004 |
| [3] | Lichun, Cheng, The minimal inverse image of fuzzy mapping, Fuzzy Mathematics, 1, 21-31 (1984) · Zbl 0561.04004 |
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