Some geometrical methods for constructing contradiction measures on Atanassov's intuitionistic fuzzy sets

Castiñeira Holgado, Elena and Torres Blanc, Carmen and Cubillo Villanueva, Susana (2011). Some geometrical methods for constructing contradiction measures on Atanassov's intuitionistic fuzzy sets. "International Journal of General Systems", v. 40 (n. 6); pp. 577-598. ISSN 0308-1079. https://doi.org/10.1080/03081079.2011.592040.

Description

Title: Some geometrical methods for constructing contradiction measures on Atanassov's intuitionistic fuzzy sets
Author/s:
  • Castiñeira Holgado, Elena
  • Torres Blanc, Carmen
  • Cubillo Villanueva, Susana
Item Type: Article
Título de Revista/Publicación: International Journal of General Systems
Date: 2011
Volume: 40
Subjects:
Freetext Keywords: Atanassov's intuitionistic fuzzy sets, contradiction measures, semicontinuous measures, semilattices, order isomorphism and automorphism
Faculty: Facultad de Informática (UPM)
Department: Matemática Aplicada
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

Trillas et al. (1999, Soft computing, 3 (4), 197–199) and Trillas and Cubillo (1999, On non-contradictory input/output couples in Zadeh's CRI proceeding, 28–32) introduced the study of contradiction in the framework of fuzzy logic because of the significance of avoiding contradictory outputs in inference processes. Later, the study of contradiction in the framework of Atanassov's intuitionistic fuzzy sets (A-IFSs) was initiated by Cubillo and Castiñeira (2004, Contradiction in intuitionistic fuzzy sets proceeding, 2180–2186). The axiomatic definition of contradiction measure was stated in Castiñeira and Cubillo (2009, International journal of intelligent systems, 24, 863–888). Likewise, the concept of continuity of these measures was formalized through several axioms. To be precise, they defined continuity when the sets ‘are increasing’, denominated continuity from below, and continuity when the sets ‘are decreasing’, or continuity from above. The aim of this paper is to provide some geometrical construction methods for obtaining contradiction measures in the framework of A-IFSs and to study what continuity properties these measures satisfy. Furthermore, we show the geometrical interpretations motivating the measures.

More information

Item ID: 12103
DC Identifier: http://oa.upm.es/12103/
OAI Identifier: oai:oa.upm.es:12103
DOI: 10.1080/03081079.2011.592040
Official URL: http://www.tandfonline.com/doi/abs/10.1080/03081079.2011.592040
Deposited by: Memoria Investigacion
Deposited on: 11 Sep 2012 13:07
Last Modified: 21 Apr 2016 11:17
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