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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
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 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |