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Applications on TFN-valued shannon entropy and TGC-integrals

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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.

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Acknowledgements

The authors express their sincere gratitude to the anonymous referees for their careful reading of the manuscript and valuable comments.

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This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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Correspondence to Dojin Kim.

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Appendix

Appendix

The customs data used in the study are from the UN Comtrade database (WTO 2020) that indicates the national trade volumes in the semiconductor field: China (CHN), Germany (DEU), France (FRA), the United Kingdom (GBR), Israel (ISR), Japan (JPN), the Republic of Korea (KOR), the Netherlands (NLD), the United States (USA), and other Asia, not elsewhere specified (OAN). Tables 6 and 7 show the national annual export values in US dollars divided into five categories under the Harmonized System (HS) commodity code heading 8456, 8486, 8504, 8514, 8541 or 8542 for import and export trade in the semiconductor field (US$) over 10 years (2013–2022).

Table 6 Annual export values (US$) of the selected categories of semiconductors for 2013–2017
Table 7 Annual export values (US$) of the selected categories of semiconductors for 2018–2022

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Kim, D., Choi, J. & Jang, LC. Applications on TFN-valued shannon entropy and TGC-integrals. Comp. Appl. Math. 45, 251 (2026). https://doi.org/10.1007/s40314-025-03600-5

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  • DOI: https://doi.org/10.1007/s40314-025-03600-5

Keywords

Mathematics Subject Classification 2020