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Indarsih, Indarsih -
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THE LINEARITY OF THE EXPECTED VALUE OF A FUZZY VARIABLE Kencono, Uvi Dwian; Indarsih, Indarsih -
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2621-2632

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.
Co-Authors Kencono, Uvi Dwian