Fuzzy Alexandrov Topologies Associated to Fuzzy Interval Orders

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Gianni Bosi
Chiaramaria Panozzo
Magal`ı Ernestine Zuanon


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.

Fuzzy Alexandrov topology, fuzzy partial order, T0 separation axiom.

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How to Cite
Bosi, G., Panozzo, C., & Zuanon, M. E. (2020). Fuzzy Alexandrov Topologies Associated to Fuzzy Interval Orders. Asian Research Journal of Mathematics, 16(10), 1-6. https://doi.org/10.9734/arjom/2020/v16i1030227
Original Research Article


Hutton B, Reilly I. Separation axioms in fuzzy topological spaces. Fuzzy Sets and Systems. 1980;3:93-104.

Srivastava R, Lal SN, Srivastava AK. On fuzzy T0 and R0 topological spaces. Journal of Mathematical Analysis and Applications. 1988;136:66-73.

Alexandrov P. Diskrete Ra¨ume. Mat. Sb. N.S. 1937;2:501-518.

Rabinovitch I. The dimansion of semiorders. Journal of Combinatorial Theory, Ser. A. 1988;25:50-61.

Wang CY. Topological characterizations of rough fuzzy sets. Fuzzy Sets and Systems. 2017;312:109-125.

Bosi G, Estevan A, Ravent´os-Pujol A. Topologies for semicontinuous Richter-Peleg multiutilities. Theory and Decision. 2020;88:457-470.

Qin B. Fuzzy approximating spaces. Journal of Applied Mathematics. 2014;2014:7. Article ID 405802

Zadeh LA. Fuzzy sets. Information and Control. 1975;8:338-353.

Wong CK. Fuzzy points and local properties of fuzzy Topology. Journal of Mathematical Analysis and Applications. 1974;46:316-328.

Zadeh LA. Similarity relations and fuzzy orderings. Inf. Sci. 1971;3:17-200.

Isler R, Bosi G. Topological characterizations of posets. In: Rios, S. Ed., Decision Theory and Decision Analysis: Trends and Challenges, Kluwer. 1994;139-145.

Mishra S, Srivastava R. Representabilty of fuzzy biorders and fuzzy weak orders. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems. 2016;24:917-935