Fundamental Properties of Fuzzy Implications

Fundamental Properties of Fuzzy Implications

In the article we continue in the Mizar system [8], [2] the formalization of fuzzy implications according to the monograph of Baczyński and Jayaram “Fuzzy Implications” [1]. We develop a framework of Mizar attributes allowing us for a smooth proving of basic properties of these fuzzy connectives [9]...

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Bibliographic Details
Main Author: Grabowski Adam
Format: Article
Language:English
Published: Sciendo 2018-12-01
Series:Formalized Mathematics
Subjects:
fuzzy implication
fuzzy set
fuzzy logic
03b52
68t37
03b35
Online Access:https://doi.org/10.2478/forma-2018-0023
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spelling doaj-4a6ce3b5cc0f49aeaa70227c1e96c28b2021-09-05T21:01:04ZengSciendoFormalized Mathematics1426-26301898-99342018-12-0126427127610.2478/forma-2018-0023forma-2018-0023Fundamental Properties of Fuzzy ImplicationsGrabowski Adam0Institute of Informatics, University of Białystok, PolandIn the article we continue in the Mizar system [8], [2] the formalization of fuzzy implications according to the monograph of Baczyński and Jayaram “Fuzzy Implications” [1]. We develop a framework of Mizar attributes allowing us for a smooth proving of basic properties of these fuzzy connectives [9]. We also give a set of theorems about the ordering of nine fundamental implications: Łukasiewicz (ILK), Gödel (IGD), Reichenbach (IRC), Kleene-Dienes (IKD), Goguen (IGG), Rescher (IRS), Yager (IYG), Weber (IWB), and Fodor (IFD).https://doi.org/10.2478/forma-2018-0023fuzzy implicationfuzzy setfuzzy logic03b5268t3703b35
collection DOAJ
language English
format Article
sources DOAJ
author Grabowski Adam
spellingShingle Grabowski Adam
Fundamental Properties of Fuzzy Implications
Formalized Mathematics
fuzzy implication
fuzzy set
fuzzy logic
03b52
68t37
03b35
author_facet Grabowski Adam
author_sort Grabowski Adam
title Fundamental Properties of Fuzzy Implications
title_short Fundamental Properties of Fuzzy Implications
title_full Fundamental Properties of Fuzzy Implications
title_fullStr Fundamental Properties of Fuzzy Implications
title_full_unstemmed Fundamental Properties of Fuzzy Implications
title_sort fundamental properties of fuzzy implications
publisher Sciendo
series Formalized Mathematics
issn 1426-2630
1898-9934
publishDate 2018-12-01
description In the article we continue in the Mizar system [8], [2] the formalization of fuzzy implications according to the monograph of Baczyński and Jayaram “Fuzzy Implications” [1]. We develop a framework of Mizar attributes allowing us for a smooth proving of basic properties of these fuzzy connectives [9]. We also give a set of theorems about the ordering of nine fundamental implications: Łukasiewicz (ILK), Gödel (IGD), Reichenbach (IRC), Kleene-Dienes (IKD), Goguen (IGG), Rescher (IRS), Yager (IYG), Weber (IWB), and Fodor (IFD).
topic fuzzy implication
fuzzy set
fuzzy logic
03b52
68t37
03b35
url https://doi.org/10.2478/forma-2018-0023
work_keys_str_mv AT grabowskiadam fundamentalpropertiesoffuzzyimplications
_version_ 1717781702641713152

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