An intuitionistic fuzzy finite state automaton assigns a membership and nonmembership values in which there is a unique membership transition on an input symbol (IFA-UM) is considered. It is proved that the fuzzy behaviors of IFA-UM is closed under union, product, intersection and reversal.

Dynamic Fault Trees (DFTs) are powerful tools for deriving fault-tolerant system designs. However, deterministic approaches to DFTs suffer from semantic struggles with problems such as spare races. In this paper, we discuss the added complexity in the state-space representation of a non-deterministic DFT model and propose a modularized approach for synthesizing recovery automata. Finally, we give an implementation and evaluate it on the Fault tree FOResT (FFORT) benchmark. The results show that non-deterministic semantics with modularization can scale for literature case studies.

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An intuitionistic fuzzy finite automaton with a unique membership transition on an input symbol is considered. It is shown that, if h : Γ * → Σ * is a morphism and h −1 (1) = 1, then the image of a recognizable subset of Γ * is a recognizable subset of Σ * and if h is fine, then the inverse image of recognizable subset of Σ * is recognizable. It is also proved that the shuffle product of any two recognizable sets is recognizable.Index Terms-Intuitionistic fuzzy sets, Intuitionistic fuzzy behavior, Intuitionistic fuzzy finite automaton, fine morphism, shuffle product.

Intuitionistic fuzzy recognizers and intuitionistic fuzzy finite automata are discussed. The notions of intuitionistic fuzzy finite automata with unique transition on an input symbol is introduced. It is shown that for any intuitionistic fuzzy finite automaton (IFA) there exists an equivalent intuitionistic fuzzy finite automaton with unique membership transitions on an input symbol such that membership values for recognized strings are the same. The concepts are proved and illustrated with examples.Index Terms-Intuitionistic fuzzy sets, Intuitionistic fuzzy languages, Intuitionistic fuzzy finite automaton.