Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10323692 | Fuzzy Sets and Systems | 2005 | 24 Pages |
Abstract
Associativity of a two place function T(x,y)=f(-1)(f(x)+f(y)) where f:[0,1]â[0,â] is a strictly monotone function andf(-1):[0,â]â[0,1] is the pseudo-inverse of f depends only on properties of the range of f. The following question is answered: what property of the range of an additive generator f is necessary and sufficient for associativity of the corresponding generated function T? We also introduce the characterization of all additive generators f of T with property T(â¦T(T(x1,x2),x3),â¦,xn)=f(-1)(f(x1)+â¯+f(xn)) for all nâN,n⩾2 and for all x1,â¦,xnâ[0,1]. Some constructions of non-continuous additive generators of associative functions are presented.
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Peter VicenÃk,