Fuzzy matrices of permanent one
The paper deals with square matrices over the semiring \(([0,1], \max, \min)\). Matrices with permanent one [max-min determinant, cf. \textit{J. B. Kim}, \textit{A. Baartmans} and \textit{N. S. Sahadin}, ibid. 29, No. 3, 349- 356 (1989; Zbl 0668.15004)] are considered as a generalization of reflexive fuzzy relations on a finite set [cf. \textit{A. Kaufmann}, Fuzzy sets theory (1975; Zbl 0456.68081)]. The notion of the generalized inverse [cf. \textit{P. S. S. N. V. Prasada Rao}, \textit{K. P. S. Bhaskara Rao}, Linear Algebra Appl. 11, 135-153 (1975; Zbl 0322.15011)] is characterized for these matrices and applied to study of idempotent matrices and fuzzy linear mappings.
scientific article; zbMATH DE number 496181