<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We continue in the Mizar system [2] the formalization of fuzzy implications according to the book of Baczyński and Jayaram “Fuzzy Implications” [1]. In this article we define fuzzy negations and show their connections with previously defined fuzzy implications [4] and [5] and triangular norms and conorms [6]. This can be seen as a step towards building a formal framework of fuzzy connectives [10]. We introduce formally Sugeno negation, boundary negations and show how these operators are pointwise ordered. This work is a continuation of the development of fuzzy sets [12], [3] in Mizar [7] started in [11] and partially described in [8]. This submission can be treated also as a part of a formal comparison of fuzzy and rough approaches to incomplete or uncertain information within the Mizar Mathematical Library [9].</p></abstract>

We continue in the Mizar system [2] the formalization of fuzzy implications according to the book of Baczyński and Jayaram “Fuzzy Implications” [1]. In this article we define fuzzy negations and show their connections with previously defined fuzzy implications [4] and [5] and triangular norms and conorms [6]. This can be seen as a step towards building a formal framework of fuzzy connectives [10]. We introduce formally Sugeno negation, boundary negations and show how these operators are pointwise ordered. This work is a continuation of the development of fuzzy sets [12], [3] in Mizar [7] started in [11] and partially described in [8]. This submission can be treated also as a part of a formal comparison of fuzzy and rough approaches to incomplete or uncertain information within the Mizar Mathematical Library [9].

On Fuzzy Negations Generated by Fuzzy Implications

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License.

{"article-title":"On Fuzzy Negations Generated by Fuzzy Implications"}

We continue in the Mizar system [2] the formalization of fuzzy implications according to the book of Baczyński and Jayaram “Fuzzy Implications” [1]. In this...

On Fuzzy Negations Generated by Fuzzy Implications

Published Online: May 29, 2020

Page range: 121 - 128

Accepted: Feb 26, 2020

DOI: https://doi.org/10.2478/forma-2020-0011

Keywords
fuzzy set, fuzzy negation, fuzzy implication

© 2020 Adam Grabowski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License.

On Fuzzy Negations Generated by Fuzzy Implications

Published Online: May 29, 2020

Page range: 121 - 128

Accepted: Feb 26, 2020

DOI: https://doi.org/10.2478/forma-2020-0011

Keywordsfuzzy set, fuzzy negation, fuzzy implication

© 2020 Adam Grabowski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License.

Keywords
fuzzy set, fuzzy negation, fuzzy implication