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.
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)
1 Liu's Stock Model Let X t be the bond price, and Y t the stock price. Assume that stock price follows a geometric canonical process. Then Liu characterized the uncertain price dynamics as follows, dX t = rX t dt dY t = eY t dt + σY t dC t (1) where r is the riskless interst rate, e is the stock drift, and σ is the stock diffusion, and C t is the… (More)
In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t Uncertain logic is a generalization of classical logic for dealing… (More)
Keywords: Uncertain variable Cross-entropy Minimum cross-entropy principle a b s t r a c t ross-entropy is a measure of the difference between two distribution functions. In order to deal with the divergence of uncertain variables via uncertainty distributions, this paper aims at introducing the concept of cross-entropy for uncertain variables based on… (More)