Sufficient conditions for the existence of minimizers of fuzzy variational problems with generalized Hukuhara differentiable functions

Mansi Verma; Chuei Yee Chen; Sie Long Kek; Mansi Verma; Chuei Yee Chen; Sie Long Kek

doi:10.3934/math.20261046

AIMS Mathematics

2026, Volume 11, Issue 8: 26120-26135. doi: 10.3934/math.20261046

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Research article

Sufficient conditions for the existence of minimizers of fuzzy variational problems with generalized Hukuhara differentiable functions

1.
Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
2.
School of Computer Science and Engineering, IILM University, 1, Knowledge Center, Golf Course Rd, Sector 53, 122011, Gurugram, Haryana, India
3.
Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
4.
Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, UTHM Kampus Cawangan Pagoh, Hab Pendidikan Tinggi Pagoh, KM 1, Jalan Panchor, 84600 Pagoh, Muar, Johor, Malaysia

Received: 09 February 2026 Revised: 22 July 2026 Accepted: 04 August 2026 Published: 21 August 2026
MSC : 49K21, 93C23

The study of fuzzy variational problems has received considerable attention in recent years due to their ability to handle the complexity and uncertainty of mathematical models in optimal control and image segmentation problems. The existing literature is focused on necessary conditions for finding minimizers, under the assumption that a minimizer always exists. This study establishes sufficient conditions for the existence of minimizers for generalized Hukuhara (gH) differentiable functions involving multivariable preinvex functions. Preinvexity, being a weaker notion than convexity, nevertheless retains the lower bound property that is sufficient for establishing the existence of minimizers.
- fuzzy variational problem,
- existence of minimizer,
- gH differentiable function,
- mul-tivariable preinvex gH differentiable functions
Citation: Mansi Verma, Chuei Yee Chen, Sie Long Kek. Sufficient conditions for the existence of minimizers of fuzzy variational problems with generalized Hukuhara differentiable functions[J]. AIMS Mathematics, 2026, 11(8): 26120-26135. doi: 10.3934/math.20261046

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Abstract

The study of fuzzy variational problems has received considerable attention in recent years due to their ability to handle the complexity and uncertainty of mathematical models in optimal control and image segmentation problems. The existing literature is focused on necessary conditions for finding minimizers, under the assumption that a minimizer always exists. This study establishes sufficient conditions for the existence of minimizers for generalized Hukuhara (gH) differentiable functions involving multivariable preinvex functions. Preinvexity, being a weaker notion than convexity, nevertheless retains the lower bound property that is sufficient for establishing the existence of minimizers.

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