Some notes on the category of fuzzy implications on bounded lattices

Amin Yousefi; Mashaallah Mashinchi; Radko Mesiar

Kybernetika (2021)

  • Issue: 2, page 332-351
  • ISSN: 0023-5954

Abstract

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In this paper, we introduce the product, coproduct, equalizer and coequalizer notions on the category of fuzzy implications on a bounded lattice that results in the existence of the limit, pullback, colimit and pushout. Also isomorphism, monic and epic are introduced in this category. Then a subcategory of this category, called the skeleton, is studied. Where none of any two fuzzy implications are Φ -conjugate.

How to cite

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Yousefi, Amin, Mashinchi, Mashaallah, and Mesiar, Radko. "Some notes on the category of fuzzy implications on bounded lattices." Kybernetika (2021): 332-351. <http://eudml.org/doc/297893>.

@article{Yousefi2021,
abstract = {In this paper, we introduce the product, coproduct, equalizer and coequalizer notions on the category of fuzzy implications on a bounded lattice that results in the existence of the limit, pullback, colimit and pushout. Also isomorphism, monic and epic are introduced in this category. Then a subcategory of this category, called the skeleton, is studied. Where none of any two fuzzy implications are $\Phi $-conjugate.},
author = {Yousefi, Amin, Mashinchi, Mashaallah, Mesiar, Radko},
journal = {Kybernetika},
keywords = {fuzzy implication; t-norm; category; skeleton of category},
language = {eng},
number = {2},
pages = {332-351},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Some notes on the category of fuzzy implications on bounded lattices},
url = {http://eudml.org/doc/297893},
year = {2021},
}

TY - JOUR
AU - Yousefi, Amin
AU - Mashinchi, Mashaallah
AU - Mesiar, Radko
TI - Some notes on the category of fuzzy implications on bounded lattices
JO - Kybernetika
PY - 2021
PB - Institute of Information Theory and Automation AS CR
IS - 2
SP - 332
EP - 351
AB - In this paper, we introduce the product, coproduct, equalizer and coequalizer notions on the category of fuzzy implications on a bounded lattice that results in the existence of the limit, pullback, colimit and pushout. Also isomorphism, monic and epic are introduced in this category. Then a subcategory of this category, called the skeleton, is studied. Where none of any two fuzzy implications are $\Phi $-conjugate.
LA - eng
KW - fuzzy implication; t-norm; category; skeleton of category
UR - http://eudml.org/doc/297893
ER -

References

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