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Levitin–Polyak Well Posedness for Fuzzy Optimization Problems Through a Linear Ordering

Author

Listed:
  • Rattanaporn Wangkeeree

    (Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand)

  • Panatda Boonman

    (Department of Computing Science, Faculty of Science and Technology, Rajamangala University of Technology Suvarnabhumi, Phranakhon Si Ayutthaya 13000, Thailand)

  • Nithirat Sisarat

    (Naresuan University Secondary Demonstration School, Faculty of Education, Naresuan University, Phitsanulok 65000, Thailand)

Abstract

We propose a reformulated notion of Levitin–Polyak (abbreviated as LP) well posedness for fuzzy optimization problems formulated in the fuzzy order-preserving (FOP) setting, where minimizing sequences are governed by a total ordering defined on fuzzy intervals. Under this formulation, we present verifiable sufficient conditions that guarantee LP well-posed behavior. These conditions are derived using ranking mechanisms that maintain interval order relations and ensure solution comparability. One central contribution is an equivalence-based theoretical characterization of LP well posedness obtained through an examination of the topological properties of the approximate solution mapping, particularly its closed-graph structure and upper semicontinuity. In addition, convergence of approximating solution sequences is investigated under the upper Hausdorff metric, leading to stability results for the associated solution sets. The established criteria provide a comprehensive framework for analyzing the convergence performance of algorithms designed for fuzzy optimization environments.

Suggested Citation

  • Rattanaporn Wangkeeree & Panatda Boonman & Nithirat Sisarat, 2026. "Levitin–Polyak Well Posedness for Fuzzy Optimization Problems Through a Linear Ordering," Mathematics, MDPI, vol. 14(7), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:7:p:1143-:d:1908790
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