Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6855800 | Fuzzy Sets and Systems | 2018 | 24 Pages |
Abstract
Commutativity is an important property in two-step information merging procedure. It is shown that the result obtained from the procedure should not depend on the order in which signal steps are performed. In the case of a bisymmetric aggregation operator with the neutral element, Saminger et al. have provided a full characterization of commutative n-ary operator by means of unary distributive functions. Further, characterizations of these unary distributive functions can be viewed as resolving a kind of the Cauchy-like equations f(xây)=f(x)âf(y), where f:[0,1]â[0,1] is a monotone function, â is a bisymmetric aggregation operator with the neutral element. In this paper, we are still devoted to investigating and fully characterizing the Cauchy-like equation f(U(x,y))=U(f(x),f(y)), where f:[0,1]â[0,1] is an unknown function but not necessarily monotone, U is a uninorm continuous in (0,1)2. These results show the key technology is how to find a transformation from this equation into several known cases. Moreover, this equation has completely different and non-monotone solutions in comparison with the obtained results.
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Feng Qin, Yuan-Yuan Zhao, Jing Zhu,