On Matrix Equations In V-T Composition Over Complete Lattices And Their Applications

In this paper,using an infinitely distributive t -norm T on a complete lattice L ,we study the matrix equation A T XTB= C in ∨ -T composition.First,we obtain a necessary and sufficient condition for the solvability of this equation.In order to find an algorithm of the entire solution set for the equation A T XTB= C in the case that this equation is solvable,we begin with some simple forms of the equation A T X= B,and then consider its complex form and obtain an algorithm of the entire solution set for the equation A T X= B.Finally,we obtain an algorithm of the entire solution set for the equation A T XTB= C.Also,as an application of the solution set for the equation A T XTB= C.we consider necessary and sufficient conditions for the existence of generalized inverses of matrices in ∨ -T composition over the lattice L .Algorithms for finding the generalized inverses are given.Finally,we consider the perturbation issues of fuzzy matrix equations by the fuzzy solution-invariant matrix and obtain some lower perturbed elements and their perturbed interval to these equations.