Ordering fuzzy numbers using the centroid: Practical aspects

Authors

Keywords:

fuzzy numbers, ordering, centroid, databases, Haskell, fuzzy

Abstract

This paper corresponds to the second part of the study exploring the ordering of fuzzy numbers with the purpose of supporting the database queries configuration. In the first part: a new proposal was presented comparing two fuzzy numbers using the centroid abscissa; and it was shown to be a total order relation.  In this second part: study cases are addressed that include a vast diversity of possible situations for comparison fuzzy numbers with different representations; a Haskell implementation of the proposed method is presented; and thus, we demonstrate its adaptation to human intuition.

Downloads

Download data is not yet available.

Author Biographies

Soraya Carrasquel, Universidad Simón Bolivar, Venezuela

Lic. en Matemáticas, MSc. en Matemáticas. Profesora e investigadora adscrita al Departamento de Computación y Tecnología de la Información. Universidad Simón Bolivar, Venezuela. Correo: scarrasquel@usb.ve

David Coronado, Universidad Simón Bolivar, Venezuela

Lic. en Matemáticas, MSc. en Matemáticas, PhD. en Matemáticas. Profesor e investigador adcrito al Departamento de Computación y Tecnología de la Información de la Universidad Simón Bolivar, Venezuela. Correo: dcoronado@usb.ve

Ricardo Monascal, Universidad Simón Bolivar, Venezuela

Ing. en Computación, MSc. en Computación. Profesor e investigador en la Universidad Simón Bolivar, Caracas, Venezuela. Adscrito al Departamento de Computación y Tecnología de la Información. Correo: rmonascal@usb.ve

Rosseline Rodríguez, Universidad Simón Bolivar, Venezuela

Ing. en Computación, MSc. en Computación. Profesora e investigadora en la Universidad Simón Bolivar, Caracas, Venezuela. Adscrita al Departamento de Computación y Tecnología de la Información. Correo: crodrig@usb.ve

References

[1] L. A. Zadeh. The concept of a linguistic variable and its application to approximate reasoning—I. Information sciences, 8(3):199–249, 1975. OnLine.

[2] J. Galindo; A. Urrutia; M. Piattini. Fuzzy databases: Modeling, design and implementation. Idea Group Publishing Hershey, USA, 2006. OnLine.

[3] Pushpinder Singh. A novel method for ranking generalized fuzzy numbers. Journal of Information Science and Engineering, 31:1373–1385, 2015. OnLine.

[4] J.J Buckley; E. Eslami. Fuzzy ordering of fuzzy numbers. International Journal of Uncertainty, Fuzziness and Knowledge–Based Systems, 12(01):105–114, 2004. OnLine.

[5] Y. Yuan. Criteria for evaluating fuzzy ranking methods. Fuzzy Sets and Systems, 43(2):139–157, 1991. OnLine.

[6] S. H. Nasseri; F. Taleshian; Z. Alizadeh; J. Vahidi. A new method for ordering LR fuzzy number. The Journal of Mathematics and Computer Science, 4(3):283–294, 2012. OnLine.

[7] T.C. Chu; P. Charnsethikul. Ordering alternatives under fuzzy multiple criteria decision making via a fuzzy number dominance based ranking approach. International Journal of Fuzzy Systems, 15(3):263–273, 2013.

[8] S. Carrasquel; D. Coronado; R.Monascal; R. Rodriguez. Ordenamiento de números difusos usando centroides. aspectos teóricos. Publicaciones en Ciencia y Tecnología, 12(2):57–67, 2018. OnLine.

[9] P. Bushan Rao; N. R.Shankar. Ranking fuzzy numbers with a distance method using circumcenter of centroids and an index of modality. Advances in Fuzzy Systems, pages 1–7, 2011. OnLine.

[10] L. A. Zadeh. Fuzzy sets. Information and Control, 8(3):338–353, 1965. OnLine.

[11] Ching-Hsue Cheng. A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets and Systems, 95(3):307–317, 1998. OnLine.

[12] Y.M Wang; J.B. Yang; D.L. Xu; K.S. Chin. On the centroids of fuzzy numbers. Fuzzy sets and systems, 157(7):919–926, 2006. OnLine.

[13] Ta-Chung Chu; Chung-Tsen Tsao. Ranking fuzzy numbers with an area between the centroid point and original point. Computers &Mathematics with Applications, 43(1-2):111–117, 2002, OnLine.

[14] H. B. Mitchell; P. A. Schaefer. On ordering fuzzy numbers. International Journal of Intelligent Systems, 15(11):981–993, 2000. OnLine.

[15] A. H. Ganesh; M. Suresh. Ordering of generalised trapezoidal fuzzy numbers based on area method using euler line of centroids. Advances in Fuzzy Mathematics, 12(4):783–791, 2017.
Publicaciones en Ciencias y Tecnologia Vol 12 nro 2 año 20189

Published

2018-11-05

How to Cite

[1]
S. Carrasquel, D. Coronado, R. Monascal, and R. Rodríguez, “Ordering fuzzy numbers using the centroid: Practical aspects”, Publ.Cienc.Tecnol, vol. 12, no. 2, pp. 105-116, Nov. 2018.

Issue

Vol. 12 No. 2 (2018): July-December

Section

Research Article

Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacional (CC BY-NC-SA 4.0)

The opinions expressed by the authors do not necessarily reflect the position of the publisher of the publication or of UCLA. The total or partial reproduction of the texts published here is authorized, as long as the complete source and the electronic address of this journal are cited.

The authors fully retain the rights to their works, giving the journal the right to be the first publication where the article is presented. The authors have the right to use their articles for any purpose as long as it is done for non-profit. Authors are recommended to disseminate their articles in the final version, after publication in this journal, in the electronic media of the institutions to which they are affiliated or personal digital media.