<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

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

Interdisciplinary Centre for Computational Modelling University of Rzeszów al. Rejtana 16c PL-35–959 Rzeszów,

KERMIT Research Unit Knowledge-based Systems Ghent University Coupure links 653 B–9000 Gent,

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"On Comparability Relations in the Class of Interval-Valued Fuzzy Relations"}

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...

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

Published Online: Jan 20, 2017

Page range: 91 - 101

Received: Jul 15, 2016

DOI: https://doi.org/10.1515/tmmp-2016-0023

Keywords
partial order, interval order, T-transitivity, pos-T-transitivity, interval-valued fuzzy relation

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Jan 20, 2017

Page range: 91 - 101

Received: Jul 15, 2016

DOI: https://doi.org/10.1515/tmmp-2016-0023

Keywordspartial order, interval order, T-transitivity, pos-T-transitivity, interval-valued fuzzy relation

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
partial order, interval order, T-transitivity, pos-T-transitivity, interval-valued fuzzy relation