Akella, P
(2013)
Binary Tree Based Construction of NUninorm Aggregation Operators.
In: IEEE International Conference on Fuzzy Systems, FUZZIEEE 2013, 710, July 2013, Hyderabad; India.
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Abstract
The concept of nuninorm aggregation operators was introduced as generalization of uninorms and nullnorms. The structure of the operator is based on the existence of an nneutral element for an associative, monotone increasing in both variables and commutative binary operator on [0, 1]. It has been shown that the number of subclasses of nuninorms is the (n + 1) th Catalan number. Stack sortable permutations and binary trees are well studied as combinatorial objects whose total number are also enumerated by Catalan numbers. We give a onetoone correspondence between nuninorms, stack sortable permutations and binary trees and use it to give an iterative algorithm to construct the operator on [0, 1]2 for any of its Catalan number of subclasses
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