Title :
Additive and Multiplicative Generators in Interval-Valued Fuzzy Set Theory
Author :
Deschrijver, Glad
Author_Institution :
Dept. of Appl. Math. & Comput. Sci., Ghent Univ.
fDate :
4/1/2007 12:00:00 AM
Abstract :
In this paper, we introduce the notion of additive and multiplicative generator on LI, which is the underlying lattice of interval-valued fuzzy set theory. A special class of generators on LI is the class of representable generators which can be represented using generators on ([0,1],les). A representation of involutive negators on LI 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 LI
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;
Journal_Title :
Fuzzy Systems, IEEE Transactions on
DOI :
10.1109/TFUZZ.2006.879999
