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Keywords:
Bandler - Kohout compositions of relation; mixed associativity
Bandler - Kohout compositions of relation; mixed associativity
Summary:
This paper considers compositions of relations based on the notion of the afterset and the foreset, i. e., the subproduct, the superproduct and the square product introduced by Bandler and Kohout with modification proposed by De Baets and Kerre. There are proven all possible mixed pseudo-associativity properties of Bandler – Kohout compositions of relations.
References:
[1] Bandler W., Kohout L. J.: Fuzzy relational products as a tool for analysis and synthesis of the behaviour of complex natural and artificial systems. In: Fuzzy Sets. Theory and Applications to Policy Analysis and Information Systems (P. P. Wang and S. K. Chang, eds.), Plenum Press, New York 1980, pp. 341–367
[2] Baets B. De, Kerre E. : A revision of Bandler – Kohout compositions of relations. Math. Pannon. 4 (1993), 59–78 MR 1226174 | Zbl 0772.04002
[3] Baets B. De, Kerre E. : Fuzzy relational compositions. Fuzzy Sets and Systems 60 (1993), 109–120 MR 1254585 | Zbl 0794.04004
[4] Kohout L. J.: Relational semiotic methods for design of intelligent systems. In: IEEE-ISIC/CIRA/ISAS98, Gaithersburg 1998, pp. 1–62
[5] Kohout L. J.: Defining Homomorphisms and Other Generalized Morphisms of Fuzzy Relations in Monoidal Fuzzy Logics by Means of BK-Products. ArXiv Mathematics e-prints, math/0310175, (2003), pp. 1–13
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