Connections between generalized fuzzy constraint interval representation and interactive fuzzy intervals

Estevão Esmi; Laécio Carvalho de Barros; Marina Mizukoshi; Yurilev Chalco-Cano; Weldon Alexander Lodwick

doi:10.1016/j.fss.2026.110095

Connections between generalized fuzzy constraint interval representation and interactive fuzzy intervals

Estevão Esmi
, Laécio Carvalho de Barros
, Marina Mizukoshi
, Yurilev Chalco-Cano
, Weldon Alexander Lodwick

Department of Mathematics

Universidade Estadual de Campinas
Universidade Federal de Goiás
University of Colorado Denver

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

Abstract

This article investigates the relationship between two representations of fuzzy intervals: interactive fuzzy intervals and generalized constraint fuzzy intervals. To this end, we construct a joint possibility distribution from generalized constraint representations of two or more fuzzy intervals. Using this joint distribution, we prove that, under certain weak conditions, the arithmetic of generalized constraint fuzzy intervals coincides with the sup- J extension principle of the corresponding arithmetic operation. Consequently, the two representation frameworks are shown to be closely related, allowing analytical results developed in one framework to be transferred to the other.

Original language	English
Article number	110095
Journal	Fuzzy Sets and Systems
Volume	546
DOIs	https://doi.org/10.1016/j.fss.2026.110095
State	Published - 1 Jan 2027

Keywords

Extension principle
Fuzzy arithmetic
Fuzzy constraint interval representation
Fuzzy interactivity

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10.1016/j.fss.2026.110095

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title = "Connections between generalized fuzzy constraint interval representation and interactive fuzzy intervals",

abstract = "This article investigates the relationship between two representations of fuzzy intervals: interactive fuzzy intervals and generalized constraint fuzzy intervals. To this end, we construct a joint possibility distribution from generalized constraint representations of two or more fuzzy intervals. Using this joint distribution, we prove that, under certain weak conditions, the arithmetic of generalized constraint fuzzy intervals coincides with the sup- J extension principle of the corresponding arithmetic operation. Consequently, the two representation frameworks are shown to be closely related, allowing analytical results developed in one framework to be transferred to the other.",

keywords = "Extension principle, Fuzzy arithmetic, Fuzzy constraint interval representation, Fuzzy interactivity",

author = "Estev{\~a}o Esmi and \{Carvalho de Barros\}, La{\'e}cio and Marina Mizukoshi and Yurilev Chalco-Cano and Lodwick, \{Weldon Alexander\}",

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doi = "10.1016/j.fss.2026.110095",

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T1 - Connections between generalized fuzzy constraint interval representation and interactive fuzzy intervals

AU - Esmi, Estevão

AU - Carvalho de Barros, Laécio

AU - Mizukoshi, Marina

AU - Chalco-Cano, Yurilev

AU - Lodwick, Weldon Alexander

PY - 2027/1/1

Y1 - 2027/1/1

N2 - This article investigates the relationship between two representations of fuzzy intervals: interactive fuzzy intervals and generalized constraint fuzzy intervals. To this end, we construct a joint possibility distribution from generalized constraint representations of two or more fuzzy intervals. Using this joint distribution, we prove that, under certain weak conditions, the arithmetic of generalized constraint fuzzy intervals coincides with the sup- J extension principle of the corresponding arithmetic operation. Consequently, the two representation frameworks are shown to be closely related, allowing analytical results developed in one framework to be transferred to the other.

AB - This article investigates the relationship between two representations of fuzzy intervals: interactive fuzzy intervals and generalized constraint fuzzy intervals. To this end, we construct a joint possibility distribution from generalized constraint representations of two or more fuzzy intervals. Using this joint distribution, we prove that, under certain weak conditions, the arithmetic of generalized constraint fuzzy intervals coincides with the sup- J extension principle of the corresponding arithmetic operation. Consequently, the two representation frameworks are shown to be closely related, allowing analytical results developed in one framework to be transferred to the other.

KW - Extension principle

KW - Fuzzy arithmetic

KW - Fuzzy constraint interval representation

KW - Fuzzy interactivity

UR - https://www.scopus.com/pages/publications/105048613534

U2 - 10.1016/j.fss.2026.110095

DO - 10.1016/j.fss.2026.110095

M3 - Article

AN - SCOPUS:105048613534

SN - 0165-0114

VL - 546

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

M1 - 110095

ER -

Connections between generalized fuzzy constraint interval representation and interactive fuzzy intervals

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Keywords

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