ON INTERRELATIONSHIPS BETWEEN FUZZY METRIC STRUCTURES

Document Type : Research Paper

Authors

1 Department of Statistics and Operations Research, University of Jaen, Campus Las Lagunillas, s/n, E-23071, Jaen, Spain

2 Department of Mathematics, University of Jaen, Campus Las Lagunillas, s/n, E-23071, Jaen, Spain

3 Department of Statistics and Operations Research, University of Granada, Campus Fuentenueva s/n, E-18071, Granada, Spain

Abstract

Considering the increasing interest in fuzzy theory and possible applications,
the concept of fuzzy metric space concept has been introduced by several
authors from different perspectives. This paper interprets the theory in terms
of metrics evaluated on fuzzy numbers and defines a strong Hausdorff topology.
We study interrelationships between this theory and other fuzzy theories such
as intuitionistic fuzzy metric spaces, Kramosil and Michalek's spaces, Kaleva
and Seikkala's spaces, probabilistic metric spaces, probabilistic
metric co-spaces, Menger spaces and intuitionistic probabilistic metric
spaces, determining their position in the framework of theses different theories.

Keywords


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