Optimization of generalized finite non-stationary minimax fuzzy automata

Abstract

In the paper it is theoretically ground and elaborated a special method for minimization of the states number and construct a minimal form of a generalized finite non-stationary minimax fuzzy automata which is based on the previously proven theorem about maximin and minimax fuzzy matrices product and elaborated matrix method for optimization of a generalized finite non-stationary maximin fuzzy automata. It is proved that from the given generalized finite non-stationary minimax fuzzy automaton may be turn to generalized finite non-stationary maximin fuzzy automata, which is an addition to the initial minimax automaton. It is also proved that if given the generalized finiten on-stationary minimaxand maximin fuzzy automata are addition of each other, their minimalformshave the same number of states, which allows first turn from the generalized finitenon-stationary minimax fuzzy auto matonto generalized finite non-stationary maximin fuzzy automaton, then to minimizethis obtained generalized maxmin fuzzy automaton by known method of transform matrix and turn back to its addition, get a minimal form of initial generalized finite non-stationary minimax fuzzy automaton. As a result, the procedure and the corresponding algorithm of minimization of the number of states and construct a minimal form of a generalized finitenon-stationary minimax fuzzy auto maton worked out. Finally, an example of application of the proposed special method of minimization to the given generalized finite non-stationary minimax fuzzy automatonisgiven.

Keywords:

generalized finite non-stationary minimax (“optimistic”) fuzzy automaton, generalized finite nonstationary maximin (“pessimistic”) fuzzy automaton, addition of a finite non-stationary minimax fuzzy automaton, a minimal form of a finite non-stationary minimax fuzzy automaton