On a functional equation connected to the distributivity of fuzzy implications over triangular norms and conorms

Title:

On a functional equation connected to the distributivity of fuzzy implications over triangular norms and conorms

Creator:

Baczyński, Michal, Szostok, Tomasz, and Niemyska, Wanda

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:c32fb7b4-d448-4f5a-a5c6-e08b632b56aa
uuid:c32fb7b4-d448-4f5a-a5c6-e08b632b56aa

Subject:

fuzzy connectives, fuzzy implication, distributivity, and functional equations

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Distributivity of fuzzy implications over different fuzzy logic connectives have a very important role to play in efficient inferencing in approximate reasoning, especially in fuzzy control systems (see \cite{Combs_Andrews_1998,Jayaram2008} and \cite{Baczynski_Jayaram_2008}). Recently in some considerations connected with these distributivity laws, the following functional equation appeared (see \cite{Baczynski_Jayaram_2009}) f(min(x+y,a))=min(f(x)+f(y),b), where a,b>0 and f:[0,a]→[0,b] is an unknown function. In this paper we consider in detail a generalized version of this equation, namely the equation f(m1(x+y))=m2(f(x)+f(y)), where m1,m2 are functions defined on some intervals of \R satisfying additional assumptions. We analyze the cases when m2 is injective and when m2 is not injective.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[679]-695

Source:

Kybernetika | 2014 Volume:50 | Number:5

Harvested from:

CDK

Metadata only:

false