Averaging Functions on Triangular Fuzzy Numbers and an Application in Graphs

Nicolás Zumelzu; Roberto Díaz; Aldryn Aparcana; José Canumán; Álvaro Mella; Edmundo Mansilla; Diego Soto; Benjamín Bedregal

doi:10.1109/TFUZZ.2024.3473791

Averaging Functions on Triangular Fuzzy Numbers and an Application in Graphs

Nicolás Zumelzu, Roberto Díaz, Aldryn Aparcana, José Canumán, Álvaro Mella, Edmundo Mansilla, Diego Soto, Benjamín Bedregal

CIENCIAS

Research output: Contribution to journal › Article › peer-review

Abstract

Admissible orders on fuzzy numbers are total orders, which refine a basic and well-known partial order on fuzzy numbers. In this work, we define an admissible order on triangular fuzzy numbers (i.e., TFN's) and study some fundamental properties with its arithmetic and their relation with this admissible order. We also propose a new hyperstructure for ordered vector spaces and, in particular, consider the case of TFN. In addition, we also introduce the concepts of averaging functions on TFN, with emphasis on ordered weighted averaging functions on TFN equipped with an admissible order. Finally, the problem of joining central vertices is presented with an illustrative example where the previous concept is used.

Original language	English
Pages (from-to)	7025-7036
Number of pages	12
Journal	IEEE Transactions on Fuzzy Systems
Volume	32
Issue number	12
DOIs	https://doi.org/10.1109/TFUZZ.2024.3473791
State	Published - 2024

Bibliographical note

Publisher Copyright:
© 1993-2012 IEEE.

Keywords

Admissible orders
NI-vector space (NIVS)
ONI-vector space
ONI-vector weighted graph
average function
hyperstructure
ordered hyperstructure
ordered twofold commutative monoid
orders on fuzzy numbers
triangular fuzzy numbers (TFNs)
twofold commutative monoid

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10.1109/TFUZZ.2024.3473791

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title = "Averaging Functions on Triangular Fuzzy Numbers and an Application in Graphs",

abstract = "Admissible orders on fuzzy numbers are total orders, which refine a basic and well-known partial order on fuzzy numbers. In this work, we define an admissible order on triangular fuzzy numbers (i.e., TFN's) and study some fundamental properties with its arithmetic and their relation with this admissible order. We also propose a new hyperstructure for ordered vector spaces and, in particular, consider the case of TFN. In addition, we also introduce the concepts of averaging functions on TFN, with emphasis on ordered weighted averaging functions on TFN equipped with an admissible order. Finally, the problem of joining central vertices is presented with an illustrative example where the previous concept is used.",

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AU - Zumelzu, Nicolás

AU - Díaz, Roberto

AU - Aparcana, Aldryn

AU - Canumán, José

AU - Mella, Álvaro

AU - Mansilla, Edmundo

AU - Soto, Diego

AU - Bedregal, Benjamín

PY - 2024

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KW - ONI-vector weighted graph

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KW - twofold commutative monoid

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JO - IEEE Transactions on Fuzzy Systems

JF - IEEE Transactions on Fuzzy Systems

IS - 12

ER -

Averaging Functions on Triangular Fuzzy Numbers and an Application in Graphs

Abstract

Bibliographical note

Keywords

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