A Method of Generating Fuzzy Implications with Specific Properties

In this paper we introduce a new method of generating fuzzy implications via known fuzzy implications. We focus on the case of generating fuzzy implications via a fuzzy connective and at least one known fuzzy implication. We present some basic desirable properties of fuzzy implications that are inva...

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Main Authors:	Dimitrios S. Grammatikopoulos, Basil K. Papadopoulos
Format:	Article
Language:	English
Published:	MDPI AG 2020-01-01
Series:	Symmetry
Subjects:	fuzzy implication t-norm t-conorm
Online Access:	https://www.mdpi.com/2073-8994/12/1/155

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spelling	doaj-6b0faf0379304f7199e9e761be177dfd2020-11-25T01:45:08ZengMDPI AGSymmetry2073-89942020-01-0112115510.3390/sym12010155sym12010155A Method of Generating Fuzzy Implications with Specific PropertiesDimitrios S. Grammatikopoulos0Basil K. Papadopoulos1Section of Mathematics and Informatics, Department of Civil Engineering, School of Engineering, Democritus University of Thrace, 67100 Kimeria, GreeceSection of Mathematics and Informatics, Department of Civil Engineering, School of Engineering, Democritus University of Thrace, 67100 Kimeria, GreeceIn this paper we introduce a new method of generating fuzzy implications via known fuzzy implications. We focus on the case of generating fuzzy implications via a fuzzy connective and at least one known fuzzy implication. We present some basic desirable properties of fuzzy implications that are invariant via this method. Furthermore, we suggest some ways of preservation or violation of these properties, based in this method. We show how we can generate not greater or not weaker fuzzy implications with specific properties. Finally, two subclasses of any fuzzy implication arise, the so called <i>T</i> and <i>S</i> subclasses.https://www.mdpi.com/2073-8994/12/1/155fuzzy implicationt-normt-conorm
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Dimitrios S. Grammatikopoulos Basil K. Papadopoulos
spellingShingle	Dimitrios S. Grammatikopoulos Basil K. Papadopoulos A Method of Generating Fuzzy Implications with Specific Properties Symmetry fuzzy implication t-norm t-conorm
author_facet	Dimitrios S. Grammatikopoulos Basil K. Papadopoulos
author_sort	Dimitrios S. Grammatikopoulos
title	A Method of Generating Fuzzy Implications with Specific Properties
title_short	A Method of Generating Fuzzy Implications with Specific Properties
title_full	A Method of Generating Fuzzy Implications with Specific Properties
title_fullStr	A Method of Generating Fuzzy Implications with Specific Properties
title_full_unstemmed	A Method of Generating Fuzzy Implications with Specific Properties
title_sort	method of generating fuzzy implications with specific properties
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2020-01-01
description	In this paper we introduce a new method of generating fuzzy implications via known fuzzy implications. We focus on the case of generating fuzzy implications via a fuzzy connective and at least one known fuzzy implication. We present some basic desirable properties of fuzzy implications that are invariant via this method. Furthermore, we suggest some ways of preservation or violation of these properties, based in this method. We show how we can generate not greater or not weaker fuzzy implications with specific properties. Finally, two subclasses of any fuzzy implication arise, the so called <i>T</i> and <i>S</i> subclasses.
topic	fuzzy implication t-norm t-conorm
url	https://www.mdpi.com/2073-8994/12/1/155
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A Method of Generating Fuzzy Implications with Specific Properties

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