On Contradiction and Inclusion Using Functional Degrees

DOI

10.2991/ijcis.d.200409.001How to use a DOI?

Keywords

Fuzzy sets; Inclusion measure; Contradiction measure; Galois connections

Abstract

The notion of inclusion is a cornerstone in set theory and therefore, its generalization in fuzzy set theory is of great interest. The degree of f-inclusion is one generalization of such a notion that differs from others existing in the literature because the degree of inclusion is considered as a mapping instead of a value in the unit interval. On the other hand, the degree of f-weak-contradiction was introduced to represent the contradiction between two fuzzy sets via a mapping and its definition has many similarities with the f-degree of inclusion. This suggests the existence of relations between both f-degrees. Specifically, following this line, we analyze the relationship between the f-degree of inclusion and the f-degree of contradiction via the complement of fuzzy sets and Galois connections.

Copyright

© 2020 The Authors. Published by Atlantis Press SARL.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Nicolás Madrid
AU  - Manuel Ojeda-Aciego
PY  - 2020
DA  - 2020/04/24
TI  - On Contradiction and Inclusion Using Functional Degrees
JO  - International Journal of Computational Intelligence Systems
SP  - 464
EP  - 471
VL  - 13
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.200409.001
DO  - 10.2991/ijcis.d.200409.001
ID  - Madrid2020
ER  -