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Contracción de imágenes a través de estructuras de grafos outerplanare suaves difusas

Deivanai Jaisankar1, Sujatha Ramalingam2, Gizachew Bayou Zegeye3

  • 1Mathematics School of Science and Humanities, Shiv Nadar University Chennai, Rajiv Gandhi Salai (OMR), Kalavakkam, Chengalpattu, Tamil Nadu, 603110, India.

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|February 17, 2026
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Resumen

Este estudio presenta los grafos outerplanare suaves difusos (FSOG), un marco matemático novedoso que combina la teoría de conjuntos difusos y los conjuntos suaves con estructuras de grafos outerplanare para modelar la incertidumbre en redes de datos complejas.

Palabras clave:
grafos duales suaves difusosgrafos suaves difusosgrafos outerplanare suaves difusoscontracción de imágenessubgrafos outerplanare suaves difusos máximos y maximalessubgrafos outerplanare suaves difusos VD y ED

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Área de la Ciencia:

  • Teoría de Grafos
  • Teoría de Conjuntos
  • Matemáticas Computacionales

Sus antecedentes:

  • Los conjuntos difusos y los conjuntos suaves son marcos matemáticos establecidos para gestionar la incertidumbre y la vaguedad.
  • Los grafos outerplanare, un subconjunto de los grafos planares, ofrecen estructuras simplificadas para redes de datos complejas.
  • Los modelos de grafos existentes luchan por representar eficazmente relaciones ambiguas o parcialmente definidas.

Objetivo del estudio:

  • Presentar y definir los grafos outerplanare suaves difusos (FSOG) como una generalización de los grafos outerplanare nítidos.
  • Explorar las propiedades y aplicaciones de los FSOG en el manejo de la incertidumbre.
  • Extender los conceptos de la teoría de grafos para incorporar características de conjuntos difusos y suaves.

Principales métodos:

  • Integración de la teoría de conjuntos difusos para la asignación de membresía graduada a vértices y aristas.
  • Aplicación de parámetros de conjuntos suaves para representaciones de grafos dependientes del contexto.
  • Formulación de subgrafos de eliminación de vértices (VD) y eliminación de aristas (ED), incluidos los FSOG máximos y maximales.
  • Desarrollo del concepto dual para grafos planares suaves difusos.

Principales resultados:

  • Los FSOG modelan eficazmente las relaciones ambiguas combinando la difusidad y la flexibilidad de los conjuntos suaves.
  • Se establecen nuevos tipos de subgrafos (VD y ED) y conceptos de grafos duales para grafos planares suaves difusos.
  • Los hallazgos teóricos se sustentan con teoremas formales y ejemplos ilustrativos.
  • Se demuestra el potencial de aplicaciones en la contracción de imágenes.

Conclusiones:

  • Los FSOG proporcionan un marco matemático robusto para representar la incertidumbre en las estructuras de grafos.
  • Los conceptos desarrollados ofrecen capacidades mejoradas para analizar redes de datos complejas y vagas.
  • El estudio abre vías para futuras investigaciones en la teoría de grafos difusos y sus aplicaciones.