Resolution of matrix equations over arbitrary Brouwerian lattices

Authors:
Song-Chol Han;Hong-Xing Li;Jia-Yin Wang
Affiliations:
Department of Mathematics and Mechanics, Kim Il Sung University, Pyongyang, Democratic People's Republic of Korea and School of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR ...;School of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR China and School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116023, PR China;School of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR China
Venue:
Fuzzy Sets and Systems
Year:
2008

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Abstract

This paper studies the problem of solving a matrix equation over an arbitrary (not necessarily complete) Brouwerian lattice. A criterion for the solvability and a method for finding all solutions of the equation are obtained. Over an arbitrary self-dual Brouwerian lattice, an equivalent condition for the unique solution, a necessary and sufficient condition for the minimal solution and a procedure for constructing minimal solutions less than or equal to any given solution of the equation are presented. It is shown that the results of the paper can be applied to the determination of generalized inverses of a matrix over an arbitrary Brouwerian lattice.