Applications on TFN-valued shannon entropy and TGC-integrals

Abstract

This study introduces a novel approach to the triangular fuzzy number (TFN)-valued generalized Choquet integral, which is based on a rigorously defined TFN-valued Choquet capacity. The paper establishes the fundamental properties of this capacity, offering a solid theoretical foundation. Building on these properties, the study extends its application to the construction of the TFN-valued Shannon entropy, and explores its key characteristics in detail. To clarify the concept, illustrative examples are provided, highlighting the TFN-valued Shannon entropy and its connection with the TFN-valued generalized Choquet expected utility (TG-CEU). These theoretical developments are further linked to practical applications, with a specific focus on the semiconductor industry. Through this, the study establishes the relevance of the entropy in trade analysis and decision-making processes under uncertainty. © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2026.