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C-sets of n-uninorms
- 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