State Minimization of General Finite Fuzzy Automata

The minimization of automaton is important to reduce space and computational time. Reduction in number of states and transitions leads to equivalent automaton with less number of states and transitions. In this paper, state minimization of General Finite Fuzzy Automata (GFFA) is discussed. To obtain minimal equivalent GFFA we have removed redundant states and transitions using substitution property (SP) partition and quotient machine. The algorithm to find membership values of states of the GFFA is described and algorithm to associate states with quotient machine to obtain minimal machine with less number of states is discussed.

Study of Weak Fuzzy Automaton Homomorphisms on Single Input Fuzzy Automata

In this paper we have defined input-connected fuzzy automaton and established that in an input connected fuzzy automaton, element of an orbit maps to an element of the orbit under the weak fuzzy automaton endomorphism. Further, if an input x is unicore in the fuzzy automaton, then the number of weak fuzzy automaton endomorphisms of A(x) is equal to the number of states.

Semigroup of Finite-State Deterministic Intuitionistic Fuzzy Automata with Application in Fault Diagnosis of an Aircraft Twin-Spool Turbofan Engine

The twin-spool turbofan engine is an important component of almost every modern aircraft. Fault detection at an early stage can improve engine performance and health. The current research is based on the construction of an inference system for fault diagnosis in a generalized fuzzy environment. For such an inference system, finite-state deterministic intuitionistic fuzzy automata (FDIFA) are established. A semigroup of FDIFA and its algebraic properties including substructures and structure-preserving maps are studied. The FDIFA semigroups are used as variables for the inference system, and FDIFA semigroup homomorphisms are used to indicate the relation between variables. The newly established model is then applied to diagnose the possible fault and their nature in aircraft twin-spool turbofan engines by modelling the performance of the supercharger and air cooler.

Computing crisp simulations for fuzzy labeled transition systems

The problem of checking whether a state in a finite fuzzy labeled transition system (FLTS) crisply simulates another is one of the fundamental problems of the theory of FLTSs. This problem is of the same nature as computing the largest crisp simulation between two finite FLTSs. A naive approach to the latter problem is to crisp the given FLTSs and then apply one of the currently known best methods to the obtained crisp labeled transition systems. The complexity of the resulting algorithms is of order O (l (m + n) n), where l is the number of fuzzy values occurring in the specification of the input FLTSs, m is the number of transitions and n is the number of states of the input FLTSs. In the worst case, l can be m + n and O (l (m + n) n) is the same as O ((m + n) 2 n). In this article, we design an efficient algorithm with the complexity O ((m + n) n) for computing the largest crisp simulation between two finite FLTSs. This gives a significant improvement. We also adapt our algorithm to computing the largest crisp simulation between two finite fuzzy automata.

Minimization of Hesitant L-Fuzzy Automaton

In this paper, we study a new generalization for the notion of fuzzy automata, which we called hesitant L-fuzzy automaton (HLFA). We present the formulations of the mathematics framework for the theory of HLFA. Moreover, we present the concepts of hesitant L-fuzzy behavior and inverse hesitant L-fuzzy behavior recognized by a type of HLFA. After that, for any hesitant L-fuzzy language we present a minimal complete accessible deterministic hesitant L-fuzzy automaton recognizing that. Finally, we present an algorithm, which determines states of the minimal hesitant L-fuzzy automaton and we present the time complexity of the algorithm.

On the Categories of L-Valued and Q-Valued Deterministic Fuzzy Automata

Automata and languages have been studied in the context of different lattice structures by several authors. This paper is toward the categorical study of deterministic lattice-valued ([Formula: see text]-valued) fuzzy automata and deterministic quantale-valued ([Formula: see text]-valued) fuzzy automata. The existence of initial and final objects in the subcategory of category of deterministic lattice-valued fuzzy automata is shown. We also show that there is an adjunction between the category of deterministic lattice-valued and quantale-valued fuzzy automata.