Title :
Binary tree based construction of n-uninorm aggregation operators
Author :
Akella, Prabhakar
Author_Institution :
Dept. of Math., Indian Inst. of Technol. Hyderabad, Hyderabad, India
Abstract :
The concept of n-uninorm aggregation operators was introduced as generalization of uninorms and nullnorms. The structure of the operator is based on the existence of an n-neutral 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 n-uninorms 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 one-to-one correspondence between n-uninorms, 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.
Keywords :
iterative methods; mathematical operators; number theory; trees (mathematics); (n + 1)th Catalan number; binary tree based construction; combinatorial objects; commutative binary operator; iterative algorithm; n-neutral element; n-uninorm aggregation operator; nullnorms generalization; one-to-one correspondence; stack sortable permutations; uninorms generalization; Arrays; Binary trees; Equations; Indexes; Iterative methods; Production facilities; Aggregation operators; Catalan numbers; binary trees; n-uninorms; stack sortable permutations;
Conference_Titel :
Fuzzy Systems (FUZZ), 2013 IEEE International Conference on
Conference_Location :
Hyderabad
Print_ISBN :
978-1-4799-0020-6
DOI :
10.1109/FUZZ-IEEE.2013.6622403