Fuzzy-interval inequalities for generalized preinvex fuzzy interval valued functions

Area of Science:

• Mathematical Analysis
• Fuzzy Set Theory
• Interval Analysis

Background:

• Fuzzy-interval-valued functions (FIVFs) are an extension of interval-valued functions and fuzzy set theory.
• Hermite-Hadamard (H-H) inequalities are fundamental in convex analysis and have been extended to various function types.
• Preinvexity is a generalization of convexity with applications in optimization and inequality theory.

Purpose of the Study:

• To define and introduce the concept of h-preinvex fuzzy-interval-valued functions (h-preinvex FIVFs).
• To establish new Hermite-Hadamard type inequalities for h-preinvex FIVFs using fuzzy integrals and fuzzy order relations.
• To derive Hermite-Hadamard Fejér type inequalities for h-preinvex FIVFs.

Main Methods:

• Definition of h-preinvex fuzzy-interval-valued functions (h-preinvex FIVFs).
• Application of fuzzy integrals and fuzzy order relations.
• Development of novel inequalities based on the established function class.

Main Results:

• The paper establishes new Hermite-Hadamard type inequalities for h-preinvex FIVFs.
• New Hermite-Hadamard Fejér type inequalities for h-preinvex FIVFs are derived.
• The results are validated with illustrative examples, showing connections to existing inequalities.

Conclusions:

• The study successfully defines h-preinvex FIVFs and extends H-H inequalities to this new class of functions.
• The derived inequalities provide valuable tools for analyzing h-preinvex FIVFs in fuzzy analysis.
• The work contributes to the field of inequalities with potential applications in optimization and related areas.