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Towards Interval Type-3 Intuitionistic Fuzzy Sets and Systems

Author

Listed:
  • Oscar Castillo

    (Tijuana Institute of Technology, TecNM, Tijuana 22414, Mexico)

  • Patricia Melin

    (Tijuana Institute of Technology, TecNM, Tijuana 22414, Mexico)

Abstract

In this work, several types of intuitionistic fuzzy sets, inspired by Type-2 and Type-3 concepts, are introduced. In particular, the newly proposed interval Type-3 intuitionistic sets are very interesting as they extend the opportunities of both interval Type-3 fuzzy sets and intuitionistic sets when capturing specific forms of uncertainty. A comparative study of interval Type-3 with respect to intuitionistic fuzzy is presented. Based on this comparison, a novel concept of an interval Type-3 intuitionistic fuzzy set is put forward to enhance the capabilities of modeling uncertainty with respect to the individual Type-3 and intuitionistic concepts. Basically, the secondary and tertiary membership functions are added to the intuitionistic fuzzy sets to build an interval Type-3 intuitionistic fuzzy set. An illustrative example dealing with controlling the imaging system of televisions is provided to envision the potential applicability and advantages of interval Type-3 intuitionistic fuzzy sets in real problems. For this application, the intuitionistic Type-3 approach shows the potential to outperform previous approaches in controlling this system.

Suggested Citation

  • Oscar Castillo & Patricia Melin, 2022. "Towards Interval Type-3 Intuitionistic Fuzzy Sets and Systems," Mathematics, MDPI, vol. 10(21), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4091-:d:961494
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    References listed on IDEAS

    as
    1. Krassimir Atanassov & Peter Vassilev & Olympia Roeva, 2021. "Level Operators over Intuitionistic Fuzzy Index Matrices," Mathematics, MDPI, vol. 9(4), pages 1-16, February.
    2. Krassimir Atanassov & Evgeniy Marinov, 2021. "Four Distances for Circular Intuitionistic Fuzzy Sets," Mathematics, MDPI, vol. 9(10), pages 1-8, May.
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    Cited by:

    1. Gerardo Maximiliano Méndez & Ismael López-Juárez & María Aracelia Alcorta García & Dulce Citlalli Martinez-Peon & Pascual Noradino Montes-Dorantes, 2023. "The Enhanced Wagner–Hagras OLS–BP Hybrid Algorithm for Training IT3 NSFLS-1 for Temperature Prediction in HSM Processes," Mathematics, MDPI, vol. 11(24), pages 1-33, December.

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