On Possibilistic Automata

. General automata are considered with respect to normalization over semirings. Possibilistic automata are defined as normal pessimistic fuzzy automata. Possibilistic automata are analogous to stochastic automata where stochastic (+=\Theta) semirings are replaced by possibilistic (=) semirings; but where stochastic automata must be normal, fuzzy automata may be (resulting in possibilistic automata) or may not be (resulting in fuzzy automata proper). While possibilistic automata are direct generalizations of nondeterministic automata, stochastic automata are not. Some properties of possibilistic automata are considered, and the identity of possibilistic automata strongly consistent with stochastic automata is shown. 1 Introduction Fuzzy automata were introduced and examined in the late 1960's in a series of papers by Santos [20], Santos and Wee [22], and Wee and Fu [25]. Their most commonly considered form is the pessimistic max-min fuzzy automata, a system e A : =\Omega Q; A; F; ¯ ..