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C-sets of n-uninorms

Authors :
Prabhakar Akella
Source :
Fuzzy Sets and Systems. 160:1-21
Publication Year :
2009
Publisher :
Elsevier BV, 2009.

Abstract

The concept of n-uninorms was introduced in our earlier paper which is based on the existence of an n-neutral element for an associative, monotone non-decreasing in both variables and commutative (AMC) binary operator on [0,1]. There it was shown that the number of subclasses of n-uninorms is the (n+1)th Catalan number. An expression for the arbitrary member of each subclass was also given which is recursive in nature. In this paper we introduce a unique ordered set of distinct integers between 0 and n, called C-sets, for each subclass of n-uninorms. This enables us to(1)obtain an expression for arbitrary member of each subclass which is non-recursive in nature, (2)identify the minimum and the maximum members in general and of idempotent members in particular in each subclass, (3)relate C-sets of De Morgan pairs (for strict negation) of n-uninorms from different subclasses, (4)convert theoretical results into construction procedures which are algorithmic in nature. In process we generalize some of the existing results for uninorms in the literature.

Details

ISSN :
01650114
Volume :
160
Database :
OpenAIRE
Journal :
Fuzzy Sets and Systems
Accession number :
edsair.doi...........86fe8f000d4477d2c960018fd4948ef7
Full Text :
https://doi.org/10.1016/j.fss.2008.04.011