A formal model of computing with words

Abstract

Classical automata are formal models of computing with values. Fuzzy automata are generalizations of classical automata where the knowledge about the system's next state is vague or uncertain. It is worth noting that like classical automata, fuzzy automata can only process strings of input symbols. Therefore, such fuzzy automata are still (abstract) devices for computing with values, although a certain vagueness or uncertainty are involved in the process of computation. In this paper, we introduce a new kind of fuzzy automata whose inputs are instead strings of fuzzy subsets of the input alphabet. These new fuzzy automata may serve as formal models of computing with words. We establish an extension principle from computing with values to computing with words. This principle indicates that computing with words can be implemented with computing with values with the price of a big amount of extra computations.

New Construction Method for the Equivalence between Two Forms of Deterministic Fuzzy Finite Automata1

“…It is worthy noting that automata theory with membership values in more general structures, such as lattice-ordered monoids L ( Birkhoff 1967; Sheng and Li 2006), and set the formal models of computing with words on the L-fuzzy finite automata (L-FFAs) (Li and Pedrycz 2005). Also, fuzzy finite automata have many important applications such as in learning systems, the model of computing with words, pattern recognition and data base theory (Mordeson and Malik 2002;Pedrycz et al2001;Lin and Ying 2002;Ying 2002;Guerra et al 2021;Bhatia and Zheng 2020;Jastrzab et al 2020;Joseph and Dersanambika 2019;Micic et al 2018;Li and Pedrycz 2006;Zhang and Li 2009).…”

Human Activities Recognition Based on Neuro-Fuzzy Finite State Machine

“…Thus, the system can be in more than one state at any time based on the membership values or degree of belonging to each state [5,6]. Readers are referred to [9] for the theoretical definition of the FFSM with some recent developments reported in [10,11].…”

On fuzzy multiset regular languages

“…In the last few years many researchers greatly contributed the considerable literature to this field, such as Malik and Mordeson [19,20,22] have established a fundamental framework of algebraic fuzzy automata theory. Thereafter, there were number of authors having contributed to this field (cf., [15,24,26,29,30,35]). In application point of view, fuzzy regular language have been shown to be useful in numerous engineering applications such as learning systems, computing with word, fuzzy discrete event systems, pattern recognition, database theory, lexical analysis in programming language compilation, user-interface translations, circulation design and text editing (cf., [1,7,16,17,25]).…”