A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict Components

A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict Components

We establish, by means of a large class of continuous t-representable intuitionistic fuzzy t-conorms, a factorization of an intuitionistic fuzzy relation (IFR) into a unique indifference component and a family of regular strict components. This result generalizes a previous factorization obtained by...

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Main Authors: Louis Aimé Fono, Gilbert Njanpong Nana, Maurice Salles, Henri Gwet
Format: Article
Language:English
Published: Hindawi Limited 2009-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2009/580918
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spelling doaj-6ca87aae078d48d78be4be53291e5a432020-11-24T21:44:24ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/580918580918A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict ComponentsLouis Aimé Fono0Gilbert Njanpong Nana1Maurice Salles2Henri Gwet3Département de Mathématiques et Informatique, Faculté des Sciences, Université de Douala, B.P. 24157 Douala, CameroonLaboratoire de Mathématiques Appliquées aux Sciences Sociales, Département de Mathématiques, Faculté des Sciences, Université de Yaoundé I, B.P. 15396 Yaoundé, CameroonMRSH, University of Caen, CREM-UMR 6211, CNRS, 14032 Caen Cedex, FranceDepartment of Mathematics, National Polytechnic Institute, P.O. Box 8390, Yaoundé, CameroonWe establish, by means of a large class of continuous t-representable intuitionistic fuzzy t-conorms, a factorization of an intuitionistic fuzzy relation (IFR) into a unique indifference component and a family of regular strict components. This result generalizes a previous factorization obtained by Dimitrov (2002) with the (max,min) intuitionistic fuzzy t-conorm. We provide, for a continuous t-representable intuitionistic fuzzy t-norm 𝒯, a characterization of the 𝒯-transitivity of an IFR. This enables us to determine necessary and sufficient conditions on a 𝒯-transitive IFR 𝑅 under which a strict component of 𝑅 satisfies pos-transitivity and negative transitivity.http://dx.doi.org/10.1155/2009/580918
collection DOAJ
language English
format Article
sources DOAJ
author Louis Aimé Fono
Gilbert Njanpong Nana
Maurice Salles
Henri Gwet
spellingShingle Louis Aimé Fono
Gilbert Njanpong Nana
Maurice Salles
Henri Gwet
A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict Components
International Journal of Mathematics and Mathematical Sciences
author_facet Louis Aimé Fono
Gilbert Njanpong Nana
Maurice Salles
Henri Gwet
author_sort Louis Aimé Fono
title A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict Components
title_short A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict Components
title_full A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict Components
title_fullStr A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict Components
title_full_unstemmed A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict Components
title_sort binary intuitionistic fuzzy relation: some new results, a general factorization, and two properties of strict components
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2009-01-01
description We establish, by means of a large class of continuous t-representable intuitionistic fuzzy t-conorms, a factorization of an intuitionistic fuzzy relation (IFR) into a unique indifference component and a family of regular strict components. This result generalizes a previous factorization obtained by Dimitrov (2002) with the (max,min) intuitionistic fuzzy t-conorm. We provide, for a continuous t-representable intuitionistic fuzzy t-norm 𝒯, a characterization of the 𝒯-transitivity of an IFR. This enables us to determine necessary and sufficient conditions on a 𝒯-transitive IFR 𝑅 under which a strict component of 𝑅 satisfies pos-transitivity and negative transitivity.
url http://dx.doi.org/10.1155/2009/580918
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