On some properties of the alpha-order and the weight distribution functions

Authors

  • Antonio Francisco Roldán López de Hierro University of Granada
  • Fernando Neres Departamento de Ciência e Tecnologia, Universidade Federal Rural do Semi-Árido, Caraúbas, Rio Grande do Norte, Brazil
  • Regivan H.N. Santiago Departamento de Informática e Matemática Aplicada, Universidade Federal do Rio Grande do Norte, Natal, Rio Grande do Norte, Brazil
  • Diego García-Zamora Department of Computing, University of Jaén, Jaén, Spain
  • Anderson Cruz Instituto Metropóle Digital, Universidade Federal do Rio Grande do Norte, Natal, Rio Grande do Norte, Brazil
  • Javier Fernández Departamento de Estadística, Informática y Matemáticas, Universidad P´ublica de Navarra, Pamplona, Navarra, Spain
  • Humberto Bustince Departamento de Estadística, Informática y Matemáticas, Universidad P´ublica de Navarra, Pamplona, Navarra, Spain

Keywords:

fuzzy set, Fuzzy number, alpha-order, aggregation function,, binary relation

Abstract

In this paper, we describe how it can be applied the \(\alpha\)-order to any fuzzy sets in a great class \(\mathscr{C}\) of fuzzy sets. Before that, we introduce the algebraic tools that are underlying to this construction, and we detail the mentioned class of fuzzy sets of the real line that can be ranked by using such fuzzy binary relation. Furthermore, we introduce some new properties both of the weight distribution functions and of the \(\alpha\)-orders. For the sake of completeness, we illustrate all processes by showing examples enough.

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A.F. Roldán López de Hierro, A. Cruz, R.H.N. Santiago, C. Roldán, D. García-Zamora, F. Neres, H. Bustince. Fuzzy dissimilarities and the fuzzy Choquet integral of triangular fuzzy numbers on [0, 1]. Accepted for publication.

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Published

2024-09-12

Issue

2 (2024) No. 3 - Early Pub Issue

Section

Articles

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Copyright (c) 2024 Letters in Nonlinear Analysis and its Applications

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