Fuzzy proximal relator spaces

  • Mehmet Ali Öztürk
  • Ebubekir İnan
  • Özlem Tekin
  • James Francis Peters
Original Article


This paper introduces fuzzy Lodato–Smirnov proximal relator spaces. We define fuzzy proximity relation to evaluate the proximity of the sets. Also, it is shown that the max–min composition of fuzzy proximity relations is associative and the Smirnov proximity measure on the Lodato proximity space is a fuzzy spatial Lodato proximity relation. Fuzzy proximity relation approach can be applied to some problems. Therefore, it is used to solve a few issues such as precise sorting of near sets, solution of classification problems and given examples for the problems.


Proximity space Relator space Fuzzy relation Fuzzy proximity 

Mathematics Subject Classification

03E72 54E05 90B50 



The authors are thankful for financial support from the Research Fund of Adiyaman University by the Project FEFMAP/2015-0010.

Compliance with ethical standards

Conflict of interest

All authors of this article have no relationships or interests that could have direct or potential influence or impart bias on any aspect of this work.


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Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  • Mehmet Ali Öztürk
    • 1
  • Ebubekir İnan
    • 1
  • Özlem Tekin
    • 1
  • James Francis Peters
    • 2
  1. 1.Department of Mathematics, Faculty of Arts and SciencesAdıyaman UniversityAdıyamanTurkey
  2. 2.Computational Intelligence Laboratory, Department of Electrical and Computer EngineeringUniversity of ManitobaWinnipegCanada

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