Some Refinements of Integral Inequalities over Triangular Fuzzy Co-Domain

Integral inequalities, in general, serve as powerful tools for various applications. Specifically, when an integral operator is used as a predictive tool, an integral inequality can play a key role in defining, quantifying, and analyzing such processes. Real-valued functions over a fuzzy domain, also referred to as real-valued fuzzy functions, offer a valuable approach for incorporating uncertainty into prediction models. In this paper, using a straightforward proof method over a newly defined triangular LPL_PLP​ fuzzy space, we establish several new refinements for integral forms of the classical Hölder’s and newly defined triangular Hölder’s-like inequality. Numerous existing inequalities linked with the triangular Hölder’s-like inequality over a fuzzy domain can be improved through the newly obtained ones, as illustrated through applications such as the triangular Hölder’s power-mean-like integral inequality, triangular Cauchy–Schwarz-like inequality, triangular Minkowski’s-like inequality, and triangular Beckenbach’s-like inequality over a fuzzy domain. Additionally, our outcomes represent significant progressions in the field of mathematics.