International Journal of Computational Intelligence Systems

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Volume 12, Issue 2, 2019, Pages 833 - 841

An Algorithmic Approach for Computing Unions and Intersections Between Fuzzy Multisets

Authors
Ángel Riesgo1, Pedro Alonso2, Irene Díaz3, Susana Montes1, *
1Department of Statistics and O.R., University of Oviedo, Federico García Lorca, Oviedo, Asturias 33007, Spain
2Department of Mathematics, University of Oviedo, Federico García Lorca, Oviedo, Asturias 33007, Spain
3Computer Science Department, University of Oviedo, Jesús Arias de Velasco, Oviedo, Asturias 33005, Spain
*Corresponding author. E-mail: montes@uniovi.es
Corresponding Author
Susana Montes
Received 5 October 2018, Accepted 20 July 2019, Available Online 5 August 2019.
DOI
10.2991/ijcis.d.190724.001How to use a DOI?
Keywords
Fuzzy sets; Fuzzy multisets; Aggregate union; Aggregate intersection
Abstract

Fuzzy multisets represent a particularly challenging generalization of the concept of fuzzy sets. The membership degrees of fuzzy multisets are given by multisets in 0,1 rather than single values. Mathematically, they can be also seen as a generalization of the hesitant fuzzy sets. But in this general setting, the information about repetition is not lost with fuzzy multisets; and so, the opinions given by the experts are more reliably accounted for. The definitions of the complement, union, and intersection operations for these sets and their relation with other extensions of fuzzy sets, however, is not straightforward. Aggregate unions and intersections have been shown to be equivalent to the standard definitions of union and intersection for the typical hesitant fuzzy sets. But computing them is not simple because the definitions of the aggregate operations as multiset unions of sequences based on permutations can potentially result in a huge number of operations. In this paper, we propose a new formulation for the aggregate union and intersection of fuzzy multisets that is computationally less intensive, thereby providing two algorithms amenable to computer-based calculations.

Copyright
© 2019 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
International Journal of Computational Intelligence Systems
Volume-Issue
12 - 2
Pages
833 - 841
Publication Date
2019/08/05
ISSN (Online)
1875-6883
ISSN (Print)
1875-6891
DOI
10.2991/ijcis.d.190724.001How to use a DOI?
Copyright
© 2019 The Authors. Published by Atlantis Press SARL.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Ángel Riesgo
AU  - Pedro Alonso
AU  - Irene Díaz
AU  - Susana Montes
PY  - 2019
DA  - 2019/08/05
TI  - An Algorithmic Approach for Computing Unions and Intersections Between Fuzzy Multisets
JO  - International Journal of Computational Intelligence Systems
SP  - 833
EP  - 841
VL  - 12
IS  - 2
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.190724.001
DO  - 10.2991/ijcis.d.190724.001
ID  - Riesgo2019
ER  -