On Comparability Relations in the Class of Interval-Valued Fuzzy Relations

Abstract In this paper, a new relation for the set of interval-valued fuzzy relations is introduced. This relation is an interval order for the family of intervals and for the family of interval-valued fuzzy relations in a given set, it has the reflexivity property. Consequences of considering such a relation are studied in the context of operations on interval-valued fuzzy relations. A new transitivity property, namely possible T-transitivity is studied (pos-T-transitivity for short). This transitivity property is connected with the new relation proposed in this paper. Preservation of this type of transitivity by some operations is also discussed.

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Transitive closure of L-fuzzy relations and interval-valued fuzzy relations

International Conference on Fuzzy Systems ◽

10.1109/fuzzy.2010.5584671 ◽

2010 ◽

Cited By ~ 1

Author(s):

Ramon Gonzalez-del-Campo ◽

L. Garmendia ◽

B. De Baets

Keyword(s):

Transitive Closure ◽

Fuzzy Relations ◽

Interval Valued

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Gray Scale Edge Detection using Interval-Valued Fuzzy Relations

International Journal of Computational Intelligence Systems ◽

10.1080/18756891.2015.1129588 ◽

2015 ◽

Vol 8 (sup2) ◽

pp. 16-27 ◽

Cited By ~ 5

Author(s):

Agustina Bouchet ◽

Pelayo Quirós ◽

Pedro Alonso ◽

Virginia Ballarin ◽

Irene Díaz ◽

...

Keyword(s):

Edge Detection ◽

Fuzzy Relations ◽

Gray Scale ◽

Interval Valued

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Interval-Valued Fuzzy Relations

Uncertainty Data in Interval-Valued Fuzzy Set Theory - Studies in Fuzziness and Soft Computing ◽

10.1007/978-3-319-93910-0_2 ◽

2018 ◽

pp. 21-89

Author(s):

Barbara Pȩkala

Keyword(s):

Fuzzy Relations ◽

Interval Valued

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INTERVAL-VALUED REPRESENTABILITY OF QUALITATIVE DATA: THE CONTINUOUS CASE

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488507004698 ◽

2007 ◽

Vol 15 (03) ◽

pp. 299-319 ◽

Cited By ~ 19

Author(s):

GIANNI BOSI ◽

MARIA JESÚS CAMPIÓN ◽

JUAN CARLOS CANDEAL ◽

ESTEBAN INDURÁIN

Keyword(s):

Qualitative Data ◽

Triangular Fuzzy Number ◽

Continuous Case ◽

Interval Order ◽

Interval Orders ◽

And Topology ◽

Study Interval ◽

Characteristic Interval ◽

Interval Valued

In the framework of the representability of ordinal qualitative data by means of interval-valued correspondences, we study interval orders defined on a nonempty set X. We analyse the continuous case, that corresponds to a set endowed with a topology that furnishes an idea of continuity, so that it becomes natural to ask for the existence of quantifications based on interval-valued mappings from the set of data into the real numbers under preservation of order and topology. In the present paper we solve a continuous representability problem for interval orders. We furnish a characterization of the representability of an interval order through a pair of continuous real-valued functions so that each element in X has associated in a continuous manner a characteristic interval or equivalently a symmetric triangular fuzzy number.

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Fuzzy Alexandrov Topologies Associated to Fuzzy Interval Orders

Asian Research Journal of Mathematics ◽

10.9734/arjom/2020/v16i1030227 ◽

2020 ◽

pp. 1-6

Author(s):

Gianni Bosi ◽

Chiaramaria Panozzo ◽

Magal`ı Ernestine Zuanon

Keyword(s):

Partial Order ◽

Interval Order ◽

Interval Orders ◽

The Family ◽

Fuzzy Interval

We characterize the fuzzy T0 - Alexandrov topologies on a crisp set X, which are associated to fuzzy interval orders R on X. In this way, we generalize a well known result by Rabinovitch (1978), according to which a crisp partial order is a crisp interval order if and only if the family of all the strict upper sections of the partial order is nested.

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