Two new operators on fuzzy matrices.
Matrices over lattices were firstly considered by \textit{M. Yoeli} [Am Math. Monthly 68, 552--557 (1961; Zbl 0115.02103)] and \textit{T. S. Blyth} [J. Lond. Math. Soc. 39, 427--432 (1964; Zbl 0154.01104)]. \textit{M. G. Thomason} [J. Math. Anal. Appl. 57, 476--480 (1977; Zbl 0345.15007)] considered the particular case: matrices over the lattice \(([0,1],\max,\min)\) and called them `fuzzy matrices'. This paper deals with such matrices as matrices of fuzzy relations on a finite set (relation notions are used for matrices). The title `new operators' were introduced by \textit{L. A. Zadeh} [Inf. Control 8, 338--353 (1965; Zbl 0139.24606)] as algebraic union and intersection of fuzzy sets and fuzzy relations, and examined in details by \textit{L. T. Kóczy} and \textit{M. Hajnal} [Probl. Control Inform. Theory 6, 47--66 (1977; Zbl 0358.02017)]. Now, the authors prove (Properties 2 and 6), that fuzzy relation properties as symmetry, reflexivity and irreflexivity are preserved by the decribed union and intersection of fuzzy relations (cf. also \textit{V. Peneva} and \textit{I. Popchev} [Fuzzy Sets Syst. 139, 615--633 (2003; Zbl 1054.91021)]).
scientific article; zbMATH DE number 2103973