Dan A. Ralescu

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In this paper we define the fuzzy integral of a positive, measurable function, with respect to a fuzzy measure. We show that the monotone convergence theorem and Fatou’s lemma are still true in this new setting. We study some of the properties of this integral, and show that it coincides with another fuzzy integral defmed in the literature. Our main result(More)
Liu’s inference is a process of deriving consequences from uncertain knowledge or evidence via the tool of conditional uncertainty. Using identification functions, this paper derives some expressions of Liu’s inference rule for uncertain systems. This paper also discusses Liu’s inference rule with multiple antecedents and with multiple if-then rules.
Uncertainty theory is a branch of mathematics for modeling uncertainty in human reasoning, and uncertain statistics is a methodology for collecting and interpreting experts’ experimental data by uncertainty theory. In this paper, we will first discuss how to collect experts’ data. We apply this method to a model for estimating the distance between Beijing(More)
Liu process is a new tool to deal with the noise process based on uncertainty theory. In this paper, we view the foreign exchange rate as an uncertain process, described by an uncertain differential equation driven by Liu process, and build an uncertain currency model. Then the uncertain currency option processes are discussed. Moreover, European and(More)
Uncertain logic is a generalization of classical logic for dealing with uncertain knowledge via uncertainty theory. The truth value is defined as the uncertain measure that a proposition is true. In this paper, a numerical method for calculating the truth value of uncertain formulas is proposed and some examples are presented. 2011 Elsevier Ltd. All rights(More)