Further improvements of determinization methods for fuzzy finite automata

TL;DR

This paper introduces combined determinization and state reduction algorithms for fuzzy finite automata that outperform previous methods by producing smaller automata without increasing computation time.

Contribution

The paper presents novel two-in-one algorithms that simultaneously determinize and reduce states in fuzzy automata, improving efficiency over existing methods.

Findings

Produce smaller automata than previous algorithms

Require the same computation time as earlier methods

Can enhance the performance of Brzozowski type algorithms

Abstract

In this paper we combine determinization and state reduction methods into two-in-one algorithms that simultaneously perform determinization and state reduction. These algorithms perform better than all previous determinization algorithms for fuzzy finite automata, developed by Belohlavek [Inform Sciences 143 (2002) 205-209], Li and Pedrycz [Fuzzy Set Syst 156 (2005) 68-92], Ignjatovi\'c et al. [Inform Sciences 178 (2008) 164-180], and Jan\v{c}i\'c et al. [Inform Sciences 181 (2011) 1358-1368], in the sense that they produce smaller automata, while require the same computation time. The only exception is the Brzozowski type determinization algorithm developed recently by Jan\v{c}i\'c and \'Ciri\'c [Fuzzy Set Syst (2014), to appear], which produces a minimal crisp-deterministic fuzzy automaton, but the algorithms created here can also be used within the Brzozowski type algorithm and improve its performances.