Additive and Multiplicative Generators in Interval-Valued Fuzzy Set Theory

Author

Deschrijver, Glad

Author_Institution

Dept. of Appl. Math. & Comput. Sci., Ghent Univ.

Volume

15

Issue

2

fYear

2007

fDate

4/1/2007 12:00:00 AM

Firstpage

222

Lastpage

237

Abstract

In this paper, we introduce the notion of additive and multiplicative generator on L^I, which is the underlying lattice of interval-valued fuzzy set theory. A special class of generators on L^I is the class of representable generators which can be represented using generators on ([0,1],les). A representation of involutive negators on L^I by means of continuous additive generators which is similar to the representation of involutive negators on ([0,1], les) is given. We also investigate additive and multiplicative generators of t-norms on L^I

Keywords

fuzzy set theory; continuous additive generator; interval-valued fuzzy set theory; involutive negators; multiplicative generator; Additives; Character generation; Computer science; Fuzzy set theory; Fuzzy sets; Lattices; Mathematical model; Mathematics; Set theory; Uncertainty; $t$-norm on ${cal L}^{I}$; Addition on ${cal L}^{I}$; additive generator on ${cal L}^{I}$; involutive negator; multiplication on ${cal L}^{I}$; multiplicative generator on ${cal L}^{I}$; representable generator;

fLanguage

English

Journal_Title

Fuzzy Systems, IEEE Transactions on

Publisher

ieee

ISSN

1063-6706

Type

jour

DOI

10.1109/TFUZZ.2006.879999

Filename

4142752