<abstract xmlns="http://www.w3.org/1999/xhtml">In the article we continue in the Mizar system [8], [2] the formalization of fuzzy implications according to the monograph of Baczyński and Jayaram <italic>“Fuzzy Implications”</italic> [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 (<italic>I</italic>LK), Gödel (<italic>I</italic>GD), Reichenbach (<italic>I</italic>RC), Kleene-Dienes (<italic>I</italic>KD), Goguen (<italic>I</italic>GG), Rescher (<italic>I</italic>RS), Yager (<italic>I</italic>YG), Weber (<italic>I</italic>WB), and Fodor (<italic>I</italic>FD).This work is a continuation of the development of fuzzy sets in Mizar [6]; it could be used to give a variety of more general operations on fuzzy sets [13]. The formalization follows [10], [5], and [4].</abstract>

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).This work is a continuation of the development of fuzzy sets in Mizar [6]; it could be used to give a variety of more general operations on fuzzy sets [13]. The formalization follows [10], [5], and [4].

Fundamental Properties of Fuzzy Implications

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"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...

Fundamental Properties of Fuzzy Implications

Online veröffentlicht: 02. März 2019

Seitenbereich: 271 - 276

Akzeptiert: 29. Sept. 2018

DOI: https://doi.org/10.2478/forma-2018-0023

Schlüsselwörter
fuzzy implication, fuzzy set, fuzzy logic

© 2018 Adam Grabowski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fundamental Properties of Fuzzy Implications

Online veröffentlicht: 02. März 2019

Seitenbereich: 271 - 276

Akzeptiert: 29. Sept. 2018

DOI: https://doi.org/10.2478/forma-2018-0023

Schlüsselwörterfuzzy implication, fuzzy set, fuzzy logic

© 2018 Adam Grabowski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Schlüsselwörter
fuzzy implication, fuzzy set, fuzzy logic