# Implication-Based Intuitionistic Fuzzy Finite State Machine over a Finite Group

## TL;DR

This paper introduces and investigates a new type of fuzzy finite state machine over finite groups, focusing on implication-based intuitionistic fuzzy structures and their algebraic properties.

## Contribution

It defines implication-based intuitionistic fuzzy semiautomata over finite groups and explores their kernels and subsemiautomata using fuzzy subgroup concepts.

## Key findings

- Characterization of implication-based intuitionistic fuzzy kernels.
- Conditions for fuzzy subsemiautomata and normal subgroups.
- Theoretical framework for fuzzy automata over finite groups.

## Abstract

In this paper implication-based intuitionistic fuzzy finite state machine otherwise called as Implication-based intuitionistic fuzzy semiautomaton (IB-IFSA) over a finite group is defined and investigated intensively. The abstraction of implication-based intuitionistic fuzzy kernel and implication-based intuitionistic fuzzy subsemiautomaton of an IB-IFSA over a finite group are brought about using the notion of implication-based intuitionistic fuzzy subgroup and implication-based intuitionistic fuzzy normal subgroup. The necessary and sufficient condition for an implication-based intuitionistic fuzzy normal subgroup to be an implication-based intuitionistic fuzzy kernel as well as the necessary and sufficient condition for an implication-based intuitionistic fuzzy subgroup} to be an implication-based intuitionistic fuzzy subsemiautomaton of an IB-IFSA are studied.

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Source: https://tomesphere.com/paper/1906.10521