Arithmetic operators in interval-valued fuzzy set theory

被引：127
|
作者：
Deschrijver, Glad [1 ]
机构：
[1] Univ Ghent, Dept Math & Comp Sci, Fuzziness & Uncertainty Modelling Res Unit, B-9000 Ghent, Belgium
来源：
INFORMATION SCIENCES | 2007年 / 177卷 / 14期
关键词：
t-norm on L-1; arithmetic operators on L-1; sum; difference; product; quotient; addition; subtraction; multiplication;
D O I：
10.1016/j.ins.2007.02.003
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We introduce the addition, subtraction, multiplication and division on L-1, where L-1 is the underlying lattice of both interval-valued fuzzy set theory [R. Sambuc, Fonctions Phi-floues. Application l'aide au diagnostic en pathologie thyroidienne, Ph.D. Thesis, Universite de Marseille, France, 1975] and intuitionistic fuzzy set theory [K.T. Atanassov, Intuitionistic, fuzzy sets, 1983, VII ITKR's Session, Sofia (deposed in Central Sci. Technical Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian)]. We investigate some algebraic properties of these operators. We show that using these operators the pseudo-t-representable extensions of the Lukasiewicz t-norm and the product t-norm on the unit interval to L-1 and some related operators can be written in a similar way as their counterparts on ([0,1],<=). (c) 2007 Elsevier Inc. All rights reserved.
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页码：2906 / 2924
页数：19
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