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Content available Decision theory under general uncertainty
EN
The exposure of Toyota management’s cover-up of its faulty car component problems raises a fundamental question: did Toyota management make an appropriate decision taking all uncertainties into account? Statistical decision theory is a framework with a probabilistic foundation, which admits random uncertainty about the real world and human thinking. In general, the uncertainty of the real world is diversified and therefore the effort of trying to deal with different forms of uncertainty with one special form of uncertainty, namely random uncertainty, may be oversimplified. In this paper, we introduce an axiomatic uncertain measure theoretical framework and explore the essential mechanism in formulating a general uncertainty decision theory. We expect that a new understanding of uncertainty and development of a corresponding new uncertainty decision-making approach may assist intelligence communities to survive and deal with the extremely tough and diverse aspects of an uncertain reality.
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Content available Random fuzzy continuous-time Markov chains
EN
Continuous-time Markov chains is an important subclass in stochastic processes, which have facilitated many applications in business decisions, investment risk analysis, insurance policy making and reliability modeling. It should be fully aware that the existing continuous-time Markov chains theory is merely an ideology under which the random uncertainty governs the phenomena. However, the real world phenomena are often revealing the randomness and vagueness co-existence reality and thus the probabilistic continuous-time Markov chains modeling practices may be not adequate. In this paper, we define the random fuzzy continuous-time Markov chains, explore the related average chance distributions, and propose a scheme for the parameter estimation and a simulation scheme as well. It is expecting that a foundational work can be established for reliability modeling and risk analysis, particularly, repairable system modeling.
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