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Grant support

This research has been partially supported by the Government of Spain (grants PID2021-122905NB-C22 and PID2020-112502RB-C41), Comunidad de Madrid (Convenio Plurianual con la Universidad Politecnica de Madrid en la linea de actuacion Programa de Excelencia para el Profesorado Universitario).

Analysis of institutional authors

Magdalena, LuisCorresponding AuthorTorres-Blanc, CarmenAuthorCubillo, SusanaAuthorMartinez-Mateo, JesusAuthor

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Different Types of Entropy Measures for Type-2 Fuzzy Sets

Publicated to:Axioms: Mathematical Logic And Mathematical Physics. 13 (8): 556- - 2024-08-01 13(8), DOI: 10.3390/axioms13080556

Authors: Magdalena, Luis; Torres-Blanc, Carmen; Cubillo, Susana; Martinez-Mateo, Jesus

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Abstract

In this work, we consider De Luca and Termini's notion of non-probabilistic entropy, and we extend some entropy-like measures of the degree of fuzziness to type-2 fuzzy sets. With this aim, we first study different entropy measures proposed in the frameworks of fuzzy, intuitionistic, and interval-valued fuzzy sets. Then, we propose three possible novel axiomatizations for entropy in type-2 fuzzy sets. The proposed types of entropy measures evaluate how much a type-2 fuzzy set is non-crisp, non-fuzzy, and non-interval-valued fuzzy. This can also be interpreted as how far a type-2 fuzzy set is from a crisp, fuzzy, or interval-valued fuzzy set. The present contribution is also novel, since we considered the interpretation of type-2 fuzzy sets that is closest to Zadeh's original conception.

Keywords

FuzzinessInclusionIntuitionistic fuzzyNegatioNon-probabilistic fuzzy entropyType-2 fuzzy seUncertainty

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Axioms: Mathematical Logic And Mathematical Physics due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2024 there are still no calculated indicators, but in 2023, it was in position 66/332, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics, Applied.

Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.

Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2025-06-07:

  • WoS: 1

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-06-07:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 1 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

    It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

    • The work has been submitted to a journal whose editorial policy allows open Open Access publication.

    Leadership analysis of institutional authors

    There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (MAGDALENA LAYOS, LUIS) and Last Author (MARTINEZ MATEO, JESUS).

    the author responsible for correspondence tasks has been MAGDALENA LAYOS, LUIS.