Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Articles

THE LINEARITY OF THE EXPECTED VALUE OF A FUZZY VARIABLE

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  • Uvi Dwian Kencono,
  • Indarsih - Indarsih
Uvi Dwian Kencono
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Indonesia
Indarsih - Indarsih
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Indonesia
DOI: https://doi.org/10.30598/barekengvol19iss4pp2621-2632
Published September 1, 2025
Keywords
  • Credibility,
  • Expected Value,
  • Fuzzy Variable,
  • Membership Function
How to Cite
[1]
U. D. Kencono and I. Indarsih, “THE LINEARITY OF THE EXPECTED VALUE OF A FUZZY VARIABLE”, BAREKENG: J. Math. & App., vol. 19, no. 4, pp. 2621-2632, Sep. 2025.

Copyright (c) 2025 Uvi Dwian Kencono, Indarsih - Indarsih

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Abstract

In this research, we introduce a novel credibility measure defined as a non-empty set satisfying the axioms of normality, monotonicity, self-duality, and maximality. Based on this credibility measure, a credibility space is constructed, upon which a fuzzy variable can be defined. Similar to fuzzy numbers, fuzzy variables are characterized by membership functions. The membership function of this fuzzy variable is directly derived from the credibility measure. Subsequently, by integrating the credibility measure, the expected value of the fuzzy variable is obtained. The linearity property of fuzzy expected value on fuzzy variables will be proven. This linearity property is highly useful in solving various problems involving fuzzy variables. Therefore, the proposed credibility measure provides a new framework in fuzzy variable theory. This credibility measure not only offers a more formal approach to measuring uncertainty but also opens up possibilities for the development of more complex and applicable fuzzy models.

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