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: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/580918 |
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| author | Louis Aimé Fono Gilbert Njanpong Nana Maurice Salles Henri Gwet |
| author_facet | Louis Aimé Fono Gilbert Njanpong Nana Maurice Salles Henri Gwet |
| author_sort | Louis Aimé Fono |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-6ca87aae078d48d78be4be53291e5a43 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-6ca87aae078d48d78be4be53291e5a432025-02-03T01:21:00ZengWileyInternational 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2009/580918 |
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