Determinization of Fuzzy Automata by Means of the Degrees of Language Inclusion

Abstract

Determinization of fuzzy finite automata is understood here as a procedure of their conversion into equivalent crisp-deterministic fuzzy automata, which can be viewed as being deterministic with possibly infinitely many states, but with fuzzy sets of terminal states. Particularly significant determinization methods are those that provide a minimal crisp-deterministic fuzzy automaton equivalent to the original fuzzy finite automaton, called canonization methods. One canonization method for fuzzy finite automata, the Brzozowski type determinization, has been developed recently by Jančić andĆirić in [10]. Here we provide another canonization method for a fuzzy finite automaton A = (A, σ, δ, τ ) over a complete residuated lattice L, based on the degrees of inclusion of the right fuzzy languages associated with states of A into the left derivatives of the fuzzy language recognized by A. The proposed procedure terminates in a finite number of steps whenever the membership values taken by δ, σ and τ generate a finite subsemiring of the semiring reduct of L. This procedure is generally faster than the Brzozowski type determinization, and if the basic operations in the residuated lattice L can be performed in constant time, it has the same computational time as all other determinization procedures provided in [8], [11], [12].

Improved algorithms for computing the greatest right and left invariant Boolean matrices and their application

“…They have been used to model the indistinguishability of states of fuzzy finite automata, and have been applied in the state reduction and determinization of fuzzy automata (cf. above mentioned references and also [31,35,44]). The greatest right and left invariant fuzzy quasi-orders and equivalences were calculated in [14,15,43] by algorithms that approximate the greatest fixpoint by the means of the Kleene fixpoint theorem, and in [36] by partition refinement algorithms.…”

Minimal Determinization Procedure for Fuzzy Automata

“…In [18], Jančić and Ćirić apply the construction N (r(N (r(A)))) 1 to obtain an equivalent minimal cDFfA to A. In [19], Micić et al propose the method of a degree of language inclusion and obtain a minimal cDFfA. Determinization methods whose objective is to convert a FfA to an equivalent (minimal) cDFfA do not achieve the main goal of this paper by the argument given in (i) above.…”

Application of Fuzzy Pushdown Automaton on Prediction of Quality Control for Spinning Yarn

“…Fuzzy reasoning had been widely used in the fields of control systems and intelligence [10]. Using fuzzy sets and using closed intervals to represent uncertain data had similar functions [4,13]. Therefore, in the early 1980s, the Polish school proposed the interval analysis method as a tool to be used together with the fuzzy set method [18].…”