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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Sebatik
Kencono, Uvi Dwian
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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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.
Dynamical System Modeling of Dynastic Cycle with Optimal Control Mahardika, Dhimas; Ariyani, Rizki Chika Audita; Kencono, Uvi Dwian; Wanditra, Lucky Cahya; Rahmasari, Shafira Meiria
Sebatik Vol. 29 No. 2 (2025): December 2025
Publisher : STMIK Widya Cipta Dharma

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46984/sebatik.v29i2.2692

Abstract

In ancient China there are three model of society which is farmers, bandits and ruler. When the authority (rulers) is not there, the dynamics system of farmers and bandits become predator-prey interactions system. In here rulers play role on taxing the farmers and catching the bandits and then punish them. Thus, farmers are a sort of renewable resource which is exploited both by bandits and by rulers. In this paper, optimal control is applied to reduce the bandit’s population, by reducing it, the ruler population can also be reduced because the existing bandits can be conquered, so that the cost of running a government is more efficient because it can reduce the need for eradicating bandits from ruler. The type of the optimal control here is fixed time and free end point.
Co-Authors Ariyani, Rizki Chika Audita Indarsih, Indarsih - Mahardika, Dhimas Rahmasari, Shafira Meiria Wanditra, Lucky Cahya