Generalized Fractional Integral Inequalities for <i>p</i>-Convex Fuzzy Interval-Valued Mappings

The fuzzy order relation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced><mo>≽</mo></mfenced></mrow></semantics></math></inline-formula> and fuzzy inclusion relation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced><mo>⊇</mo></mfenced></mrow></semantics></math></inline-formula> are two different relations in fuzzy-interval calculus. Due to the importance of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>p</mi></semantics></math></inline-formula>-convexity, in this article we consider the introduced class of nonconvex fuzzy-interval-valued mappings known as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>p</mi></semantics></math></inline-formula>-convex fuzzy-interval-valued mappings (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>p</mi></semantics></math></inline-formula>-convex f-i-v-ms) through fuzzy order relation. With the support of a fuzzy generalized fractional operator, we establish a relationship between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>p</mi></semantics></math></inline-formula>-convex f-i-v-ms and Hermite–Hadamard (ℋ–ℋ) inequalities. Moreover, some related ℋ–ℋ inequalities are also derived by using fuzzy generalized fractional operators. Furthermore, we show that our conclusions cover a broad range of new and well-known inequalities for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>p</mi></semantics></math></inline-formula>-convex f-i-v-ms, as well as their variant forms as special instances. The theory proposed in this research is shown, with practical examples that demonstrate its usefulness. These findings and alternative methodologies may pave the way for future research in fuzzy optimization, modeling, and interval-valued mappings (i-v-m).