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An Interval-Valued Intuitionistic Hesitant Fuzzy Methodology and Application.

Shailendra Kumar Bharati1

  • 1Department of Mathematics, Kamala Nehru College, University of Delhi, New Delhi, 110049 India.

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Summary

This study introduces a novel optimization technique and algorithm using interval-valued intuitionistic hesitant fuzzy sets (IVIHFS) to address limitations in current methods for complex multiobjective optimization problems (MOOP). The new approach enhances decision-making in engineering and management sectors.

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Fuzzy setsHesitant fuzzy setsLinear programmingMultiple objectiveUncertainty and hesitation

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Area of Science:

  • Operations Research
  • Decision Sciences
  • Fuzzy Set Theory

Background:

  • Existing optimization techniques struggle with hesitant and intuitionistic expert decisions.
  • Limitations in prior research necessitate advanced methods for multiobjective optimization problems (MOOP).

Purpose of the Study:

  • Introduce a novel optimization technique and computational algorithm.
  • Develop a new operation for interval-valued intuitionistic hesitant fuzzy sets (IVIHFS).
  • Extend fuzzy and intuitionistic fuzzy optimization methodologies.

Main Methods:

  • Developed a new operation for interval-valued intuitionistic hesitant fuzzy sets (IVIHFS).
  • Constructed a stepwise computational algorithm based on the new IVIHFS operation.
  • Applied the algorithm to a real-world production planning problem.

Main Results:

  • The proposed algorithm effectively handles hesitant and intuitionistic expert data.
  • Demonstrated applicability in multiobjective optimization problems (MOOP) within engineering and management.
  • Achieved comparable or improved results compared to existing optimization techniques.

Conclusions:

  • The new IVIHFS-based optimization technique offers a robust extension to existing fuzzy and intuitionistic methods.
  • The developed computational algorithm provides a practical tool for complex real-life MOOP.
  • This research advances decision-making capabilities in uncertain and hesitant environments.