The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

Fuzzy Switching and Automata Theory and Applications

The notion of (normal) m-polar ( ∈ , ∈ ) -fuzzy p-ideals of BCI-algebras is introduced, and several properties are investigated. Relations between an m-polar ( ∈ , ∈ ) -fuzzy ideal and an m-polar ( ∈ , ∈ ) -fuzzy p-ideal are displayed, and conditions for an m-polar ( ∈ , ∈ ) -fuzzy ideal to be an m-polar ( ∈ , ∈ ) -fuzzy p-ideal are provided. Characterization of m-polar ( ∈ , ∈ ) -fuzzy p-ideals are considered. Given an m-polar ( ∈ , ∈ ) -fuzzy ideal (resp., m-polar ( ∈ , ∈ ) -fuzzy p-ideal), a normal m-polar ( ∈ , ∈ ) -fuzzy ideal (resp., normal m-polar ( ∈ , ∈ ) -fuzzy p-ideal) is established. Using an m-polar ( ∈ , ∈ ) -fuzzy ideal, the quotient structure of BCI-algebras is constructed.

https://www.mdpi.com/2227-7390/7/11/1094/pdf

Multipolar Fuzzy p-Ideals of BCI-Algebras

m-polar fuzzy q-ideals in BCI-algebras

The aim of this paper is testing the directability of a given fuzzy automaton. A fuzzy automaton is directable if there exists a word, a directing word, which takes each state of a fuzzy automaton to a single state with some membership value. In this paper, we proposed a method for testing the directability of a fuzzy automaton using the mergeability relation.

/pdf/directable-fuzzy-automata-2wb7pr1be9.pdf

Directable Fuzzy Automata

In this paper we introduced homomorphism, strong homomorphism in bipolar fuzzy finite state machines and discuss their properties using bipolar-valued fuzzy set. Mathematics Subject Classification: 18B20, 68Q45, 68Q70, 03E72

/pdf/homomorphism-in-bipolar-fuzzy-finite-state-machines-2yujlph0v3.pdf

Homomorphism in Bipolar Fuzzy Finite State Machines

The purpose of this paper to study homomorphism of γ- synchronized automata and proved that every homomorphic image of a γsynchronized automata is also a γ-synchronized automata.

in Fuzzy Automata

In this paper we introduce some properties of homomorphism in Intuitionistic Fuzzy Automata. AMS subject classification: 18B20.

Homomorphism in Intuitionistic Fuzzy Automata

This paper presents a contribution to minimization of intuitionistic fuzzy automata. In this paper the concept of substitution property (SP) partition for a finite intuitionistic fuzzy automaton is formulated, and the quotient automaton with respect to an SP partition is defined.

M. Rajasekar

Papers

Directable Fuzzy Automata

Homomorphism in Bipolar Fuzzy Finite State Machines

in Fuzzy Automata

Homomorphism in Intuitionistic Fuzzy Automata

Intuitionistic fuzzy automaton and the minimal machine