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On compositions of lattice matrices. (English) Zbl 1014.15011

The paper examines the inf-sup product of matrices over a lattice (the dual product), which brings a generalization of results of M. Z. Ragab and E. G. Emam [Fuzzy Sets Syst. 75, No. 1, 83-92 (1995; Zbl 0860.15013)] in the lattice \(([0,1],\max,\min)\). In the case of the pseudocomplemented lattice (infinitely distributive lattice) properties of the residuated coimplication are examined [cf. B. De Baets, Tatra M. Math. Publ. 12, 229-240 (1997; Zbl 0954.03029)]. The obtained results have some consequences in the associated matrix lattice.

MSC:

15B33 Matrices over special rings (quaternions, finite fields, etc.)
06D15 Pseudocomplemented lattices
08A72 Fuzzy algebraic structures
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References:

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