TY - JOUR

T1 - Novel neural algorithms based on fuzzy δ rules for solving fuzzy relation equations

T2 - Part III

AU - Ruan, Da

PY - 2000/2/1

Y1 - 2000/2/1

N2 - In our previous work (Li and Ruan, 1997) we proposed a max-min operator network and a series of training algorithms, called fuzzy δ rules, which could be used to solve fuzzy relation equations. The most basic and important result is the convergence theorem of fuzzy perceptron based on max-min operators. This convergence theorem has been extended to the max-times operator network in (Li and Ruan 1997). In this paper, we will further extend the fuzzy δ rule and its convergence theorem to the case of max-* operator network in which * is a t-norm. An equivalence theorem points out that the neural algorithm in solving this kind of fuzzy relation equations is equivalent to the fuzzy solving method (non-neural) in Di Nola et al. (1984) and Gottwald (1984). The proof and simulation will be given.

AB - In our previous work (Li and Ruan, 1997) we proposed a max-min operator network and a series of training algorithms, called fuzzy δ rules, which could be used to solve fuzzy relation equations. The most basic and important result is the convergence theorem of fuzzy perceptron based on max-min operators. This convergence theorem has been extended to the max-times operator network in (Li and Ruan 1997). In this paper, we will further extend the fuzzy δ rule and its convergence theorem to the case of max-* operator network in which * is a t-norm. An equivalence theorem points out that the neural algorithm in solving this kind of fuzzy relation equations is equivalent to the fuzzy solving method (non-neural) in Di Nola et al. (1984) and Gottwald (1984). The proof and simulation will be given.

KW - Fuzzy relation equation

KW - Fuzzy δ

KW - Max-

KW - Operator network

KW - Rule

UR - http://www.scopus.com/inward/record.url?scp=0001666681&partnerID=8YFLogxK

U2 - 10.1016/s0165-0114(98)00104-3

DO - 10.1016/s0165-0114(98)00104-3

M3 - Article

AN - SCOPUS:0001666681

SN - 0165-0114

VL - 109

SP - 355

EP - 362

JO - Fuzzy sets and systems

JF - Fuzzy sets and systems

IS - 3

ER -