Applying Shannon’s Function to Entropy Differences of Arithmetic Operations with Triangular Fuzzy Numbers

Authors

  • Tien-Chin Wang Ho Chi Minh City University of Industry and Trade

DOI:

https://doi.org/10.53893/fms.v3i2.514

Keywords:

Entropy, Triangular Fuzzy Numbers, Fuzzy Sets, Measure of Fuzziness, Arithmetic Operations, Shannon’s Function

Abstract

The main purposes of this paper are to probe for the entropy differences between arithmetically manipulated triangular fuzzy numbers (TFNs) using Shannon’s function and to study the relationships between any two TFNs. Simultaneously, we expand on Wang and Chiu’s article [9]. The entropy differences between two TFNs subjected to different arithmetic operations are classified as fifteen theorems, and fifteen examples are used to prove the accuracy of these theorems. This paper finds that with the application of Shannon’s function on triangular fuzzy numbers, the grades of fuzziness are changed after arithmetic operations.

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References

[1] D. Dumitrescu, Entropy of a fuzzy process, Fuzzy Sets and Systems 55 (1993) 169-177.

[2] D. Dumitrescu, Entropy of fuzzy dynamical systems, Fuzzy Sets and Systems 70 (1995) 45-57.

[3] A. Kaufmann, Introduction to the theory and fuzzy subsets, Academic Press, NY, 1975.

[4] A. Kaufmann and Madan M. GUPTA, Fuzzy mathematical models in engineering and management science, ELSEVIER Science Publishers B.V., 1988.

[5] A. De Luca and S. Termini, A definition of non-probabilistic entropy in the setting fuzzy sets theory, Information and Control, 20 (1972) 301-312.

[6] W. Pedrycz, Why triangular membership functions, Fuzzy Sets and Systems, 64 (1994) 21-30.

[7] Tien-Chin Wang and Hsiao-Lan Chu, The entropy differences of triangular fuzzy numbers through arithmetic, The 9th World Multi-Conference on Systemics, Cybernetics and Informatics (WMSCI 2005), July 10-13, 2005 - Orlando, Florida, USA.

[8] T.-C. Wang, “A Comprehensive Examination of Entropy Differences in Triangular Fuzzy Numbers under Arithmetic Operations”, FMS, vol. 2, no. 2, pp. 17–34, Apr. 2025.

[9] Wen-June Wang and Chih-Hui Chiu, The entropy change of fuzzy numbers with arithmetic operations, Fuzzy Sets and Systems, 111(2000) 357-366.

[10] R. R. Yager, On the measure of fuzziness and negation, Part I: membership in unit interval, Int. Journal of General Systems, (5)1979 221-229.

[11] H.-J. Zimmermann, Fuzzy Set Theory and Its Applications, Kluwer-Nijhoff, Boston, 1996.

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Published

2026-04-22

How to Cite

Wang, T.-C. (2026). Applying Shannon’s Function to Entropy Differences of Arithmetic Operations with Triangular Fuzzy Numbers. Frontier Management Science, 3(2), 01–20. https://doi.org/10.53893/fms.v3i2.514

Issue

Vol. 3 No. 2 (2026): FMS - April

Section

Articles

License

Copyright (c) 2026 Tien-Chin Wang

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