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.


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


[1] Birkhoff, G., Lattice theory, (1967), American Mathematical Society Providence, RI · Zbl 0126.03801
[2] Charcron, M., A note on matrices with entries in a distributive lattice, Bull. soc. math. belg., 22, 143-145, (1970) · Zbl 0283.15003
[3] Give’on, Y., Lattice matrices, Inform. control, 7, 477-481, (1964) · Zbl 0154.01103
[4] Hashimato, H., Decomposition of fuzzy matrices, SIAM. J. algebraic discrete methods, 6, 32-38, (1985)
[5] Ragab, M.Z.; Emam, E.G., On the min – max composition of fuzzy matrices, Fuzzy sets and systems, 75, 83-92, (1995) · Zbl 0860.15013
[6] Skornyakov, L.A., Invertible matrices over distributive structures, Sibirsk mat. zh., 27, 289-292, (1986) · Zbl 0609.15001
[7] Tan, Y.J., Eigenvalues and eigenvectors for matrices over distributive lattices, Linear algebra appl., 283, 257-272, (1998) · Zbl 0932.15005
[8] Zhao, C.K., On matrix equations in a class of complete and completely distributive lattices, Fuzzy sets and systems, 22, 303-320, (1987) · Zbl 0621.06006
[9] Zhao, C.K., Inverse of L-fuzzy matrices, Fuzzy sets and systems, 34, 103-116, (1990) · Zbl 0687.15011
[10] Zhao, C.K., Invertible conditions for a matrix over a distributive lattices, Acta sci. natur. univ. intramongolicae, 22, 477-480, (1991) · Zbl 1332.15018
[11] Zhang, K.L., Determinant theory for D01-lattice matrices, Fuzzy sets and systems, 62, 347-353, (1994) · Zbl 0836.15002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.