Complete subobjects of fuzzy sets over $MV$-algebras

Title:

Complete subobjects of fuzzy sets over $MV$-algebras

Creator:

Močkoř, Jiří

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:c553e052-0366-4798-95c0-64612f4aa3e6
uuid:c553e052-0366-4798-95c0-64612f4aa3e6

Subject:

fuzzy set over $MV$-lagebra, complete subobjects, and subobjects classification

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

A subobjects structure of the category $\Omega $- of $\Omega $-fuzzy sets over a complete $MV$-algebra $\Omega =(L,\wedge ,\vee ,\otimes ,\rightarrow )$ is investigated, where an $\Omega $-fuzzy set is a pair ${\mathbf A}=(A,\delta )$ such that $A$ is a set and $\delta \:A\times A\rightarrow \Omega $ is a special map. Special subobjects (called complete) of an $\Omega $-fuzzy set ${\mathbf A}$ which can be identified with some characteristic morphisms ${\mathbf A}\rightarrow \Omega ^*=(L\times L,\mu )$ are then investigated. It is proved that some truth-valued morphisms $\lnot _{\Omega }\:\Omega ^*\rightarrow \Omega ^*,\cap _{\Omega }$, $\cup _{\Omega } \:\Omega ^*\times \Omega ^*\rightarrow \Omega ^*$ are characteristic morphisms of complete subobjects.

Language:

English

Rights:

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

Coverage:

379-392

Source:

Czechoslovak Mathematical Journal | 2004 Volume:54 | Number:2

Harvested from:

CDK

Metadata only:

false