Transitive closure of interval-valued relations

González-del-Campo, Ramón; Garmendia, Luis; López, Victoria

doi:10.1109/iske.2008.4731150

Cited by 1 publication

(6 citation statements)

References 12 publications

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“…Definition 2.12: [9] A generalized t-norm operator T : L 2 → L is t-representable if there exist two t-norms T 1 and T 2 that satisfy: [15] it is proved that T is the highest generalized t-norm.…”

Section: Preliminariesmentioning

confidence: 99%

“…Lemma 5.1: [15] Let R be an interval-valued fuzzy relation in a universe X and let T be an arbitrary generalized t-norm. Then the T -transitive closure of R, R T always exists.…”

Section: A T -Transitive Closures Of Ivfrsmentioning

confidence: 99%

“…Then the T -transitive closure of R, R T always exists. An algorithm to compute the T -transitive closure of any IVFR for any generalized t-norm T is given in [15].…”

Section: A T -Transitive Closures Of Ivfrsmentioning

confidence: 99%

“…However, the transitive property for interval-valued fuzzy relations [15] is a much stronger condition because it needs that all intervals must be comparable in the inequality that defines T -transitivity. Due to the fact that the set of intervals in [0,1] is a lattice, it is possible to relax the "classical" transitivity by satisfying the inequality just when the intervals are comparable.…”

Section: Introductionmentioning

confidence: 99%

“…Sometimes imposing fuzzy T -transitivity to FRs or IVFRs by computing the T -transitive closure [15] gives in a completely different IVFR, with much more higher interval degrees. So it looks important to look for a weaker condition to impose coherence not in contradiction to Ttransitivity and resulting in a much closer closure to a given IVFR.…”

Section: Introductionmentioning

confidence: 99%

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Weak T -transitivity and weak closures of interval-valued fuzzy relations

González-del-Campo

Garmendia

2012

2012 IEEE International Conference on Fuzzy Systems

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In this paper a new weak transitive property for interval-valued fuzzy relations (IVF Rs) is introduced. Weak T -transitivity is equivalent to T -transitivity when the IVFR is a fuzzy relation and T = (T, T ) for a triangular norm T . Otherwise it is a weaker property than T -transitive one relaxing the need that all intervals must be comparable and must satisfy all the transitive inequalities by just the need of not having comparable non T -transitive cycles. This paper also defines a weak concept of closure, and it is proved that it exists is just one T -transitive and weak T -transitive closure, it does not exists a T -transitive weak closure, but there are many weak T -transitive weak closures of an IVF Rs.

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Section: Preliminariesmentioning

confidence: 99%

“…Lemma 5.1: [15] Let R be an interval-valued fuzzy relation in a universe X and let T be an arbitrary generalized t-norm. Then the T -transitive closure of R, R T always exists.…”

Section: A T -Transitive Closures Of Ivfrsmentioning

confidence: 99%

“…Then the T -transitive closure of R, R T always exists. An algorithm to compute the T -transitive closure of any IVFR for any generalized t-norm T is given in [15].…”

Section: A T -Transitive Closures Of Ivfrsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations