## 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

### Citations:

Zbl 0860.15013; Zbl 0954.03029
Full Text:

### References:

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