In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d<sup>∞</sup><sub>H</sub> . The results are based on the result ...In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d<sup>∞</sup><sub>H</sub> . The results are based on the result of single-valued random variables obtained by Taylor [1] and set-valued random variables obtained by Li Guan [2].展开更多
A new prioritization method in the analytic hierarchy process (AHP), which improves the group fuzzy preference programming (GFPP) method, is proposed. The fuzzy random theory is applied in the new prioritization m...A new prioritization method in the analytic hierarchy process (AHP), which improves the group fuzzy preference programming (GFPP) method, is proposed. The fuzzy random theory is applied in the new prioritization method. By modifying the principle of decision making implied in the GFPP method, the improved group fuzzy preference programming (IGFPP) method is formulated as a fuzzy linear programming problem to maximize the average degree of the group satisfaction with all possible group priority vectors. The IGFPP method inherits the advantages of the GFPP method, and solves the weighting trouble existed in the GFPP method. Numerical tests indicate that the IGFPP method performs more effectively than the GFPP method in the case of very contradictive comparison judgments from decision makers.展开更多
The primary goal of this paper is to price European options in the Merton's frame- work with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial mar...The primary goal of this paper is to price European options in the Merton's frame- work with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial market, the average jump rate and jump sizes cannot be recorded or collected accurately. So the main idea of this paper is to model the rate as a triangular fuzzy number and jump sizes as fuzzy random variables and use the property of fuzzy set to deduce two different jump-diffusion models underlying principle of rational expectations equilibrium price. Unlike many conventional models, the European option price will now turn into a fuzzy number. One of the major advantages of this model is that it allows investors to choose a reasonable European option price under an acceptable belief degree. The empirical results will serve as useful feedback information for improvements on the proposed model.展开更多
The last three decades ha</span><span style="font-family:"">ve</span><span style="font-family:""> witnessed development of optimization under fuzziness and randomn...The last three decades ha</span><span style="font-family:"">ve</span><span style="font-family:""> witnessed development of optimization under fuzziness and randomness also called Fuzzy Stochastic Optimization. The main objective </span><span style="font-family:"">of </span><span style="font-family:"">this new field is the need for basing many human decisions on information which is both fuzzily imprecise and probabilistically uncertain. Consistency indexes providing a union nexus between possibilities and probabilities of uncertain events exist in the literature. Nevertheless, there are no reliable transformations between them. This calls for new paradigms for coping with mathematical models involving both fuzziness and randomness. Fuzzy Stochastic Optimization (FSO) is an attempt to fulfill this need. In this paper, we present a panoramic view of Fuzzy Stochastic Optimization emphasizing the methodological aspects. The merits of existing methods are also briefly discussed along with some related theoretical aspects.展开更多
In this paper, a data-driven prognostic model capable to deal with different sources of uncertainty is proposed. The main novelty factor is the application of a mathematical framework, namely a Random Fuzzy Variable (...In this paper, a data-driven prognostic model capable to deal with different sources of uncertainty is proposed. The main novelty factor is the application of a mathematical framework, namely a Random Fuzzy Variable (RFV) approach, for the representation and propagation of the different uncertainty sources affecting </span><span style="font-family:Verdana;">Prognostic Health Management (PHM) applications: measurement, future and model uncertainty. </span><span style="font-family:Verdana;">In this way, it is possible to deal not only with measurement noise and model parameters uncertainty due to the stochastic nature of the degradation process, but also with systematic effects, such as systematic errors in the measurement process, incomplete knowledge of the degradation process, subjective belief about model parameters. Furthermore, the low analytical complexity of the employed prognostic model allows to easily propagate the measurement and parameters uncertainty into the RUL forecast, with no need of extensive Monte Carlo loops, so that low requirements in terms of computation power are needed. The model has been applied to two real application cases, showing high accuracy output, resulting in a potential</span></span><span style="font-family:Verdana;">ly</span><span style="font-family:Verdana;"> effective tool for predictive maintenance in different industrial sectors.展开更多
For random vibration of airborne platform, the accurate evaluation is a key indicator to ensure normal operation of airborne equipment in flight. However, only limited power spectral density(PSD) data can be obtaine...For random vibration of airborne platform, the accurate evaluation is a key indicator to ensure normal operation of airborne equipment in flight. However, only limited power spectral density(PSD) data can be obtained at the stage of flight test. Thus, those conventional evaluation methods cannot be employed when the distribution characteristics and priori information are unknown. In this paper, the fuzzy norm method(FNM) is proposed which combines the advantages of fuzzy theory and norm theory. The proposed method can deeply dig system information from limited data, which probability distribution is not taken into account. Firstly, the FNM is employed to evaluate variable interval and expanded uncertainty from limited PSD data, and the performance of FNM is demonstrated by confidence level, reliability and computing accuracy of expanded uncertainty. In addition, the optimal fuzzy parameters are discussed to meet the requirements of aviation standards and metrological practice. Finally, computer simulation is used to prove the adaptability of FNM. Compared with statistical methods, FNM has superiority for evaluating expanded uncertainty from limited data. The results show that the reliability of calculation and evaluation is superior to 95%.展开更多
文摘In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d<sup>∞</sup><sub>H</sub> . The results are based on the result of single-valued random variables obtained by Taylor [1] and set-valued random variables obtained by Li Guan [2].
基金Sponsored by the National Natural Science Foundation of China (70471063)
文摘A new prioritization method in the analytic hierarchy process (AHP), which improves the group fuzzy preference programming (GFPP) method, is proposed. The fuzzy random theory is applied in the new prioritization method. By modifying the principle of decision making implied in the GFPP method, the improved group fuzzy preference programming (IGFPP) method is formulated as a fuzzy linear programming problem to maximize the average degree of the group satisfaction with all possible group priority vectors. The IGFPP method inherits the advantages of the GFPP method, and solves the weighting trouble existed in the GFPP method. Numerical tests indicate that the IGFPP method performs more effectively than the GFPP method in the case of very contradictive comparison judgments from decision makers.
基金Supported by the Key Grant Project of Chinese Ministry of Education(309018)National Natural Science Foundation of China(70973104 and 11171304)the Zhejiang Natural Science Foundation of China(Y6110023)
文摘The primary goal of this paper is to price European options in the Merton's frame- work with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial market, the average jump rate and jump sizes cannot be recorded or collected accurately. So the main idea of this paper is to model the rate as a triangular fuzzy number and jump sizes as fuzzy random variables and use the property of fuzzy set to deduce two different jump-diffusion models underlying principle of rational expectations equilibrium price. Unlike many conventional models, the European option price will now turn into a fuzzy number. One of the major advantages of this model is that it allows investors to choose a reasonable European option price under an acceptable belief degree. The empirical results will serve as useful feedback information for improvements on the proposed model.
文摘The last three decades ha</span><span style="font-family:"">ve</span><span style="font-family:""> witnessed development of optimization under fuzziness and randomness also called Fuzzy Stochastic Optimization. The main objective </span><span style="font-family:"">of </span><span style="font-family:"">this new field is the need for basing many human decisions on information which is both fuzzily imprecise and probabilistically uncertain. Consistency indexes providing a union nexus between possibilities and probabilities of uncertain events exist in the literature. Nevertheless, there are no reliable transformations between them. This calls for new paradigms for coping with mathematical models involving both fuzziness and randomness. Fuzzy Stochastic Optimization (FSO) is an attempt to fulfill this need. In this paper, we present a panoramic view of Fuzzy Stochastic Optimization emphasizing the methodological aspects. The merits of existing methods are also briefly discussed along with some related theoretical aspects.
文摘In this paper, a data-driven prognostic model capable to deal with different sources of uncertainty is proposed. The main novelty factor is the application of a mathematical framework, namely a Random Fuzzy Variable (RFV) approach, for the representation and propagation of the different uncertainty sources affecting </span><span style="font-family:Verdana;">Prognostic Health Management (PHM) applications: measurement, future and model uncertainty. </span><span style="font-family:Verdana;">In this way, it is possible to deal not only with measurement noise and model parameters uncertainty due to the stochastic nature of the degradation process, but also with systematic effects, such as systematic errors in the measurement process, incomplete knowledge of the degradation process, subjective belief about model parameters. Furthermore, the low analytical complexity of the employed prognostic model allows to easily propagate the measurement and parameters uncertainty into the RUL forecast, with no need of extensive Monte Carlo loops, so that low requirements in terms of computation power are needed. The model has been applied to two real application cases, showing high accuracy output, resulting in a potential</span></span><span style="font-family:Verdana;">ly</span><span style="font-family:Verdana;"> effective tool for predictive maintenance in different industrial sectors.
基金supported by Aeronautical Science Foundation of China (No. 20100251006)Technological Foundation Project of China (No. J132012C001)
文摘For random vibration of airborne platform, the accurate evaluation is a key indicator to ensure normal operation of airborne equipment in flight. However, only limited power spectral density(PSD) data can be obtained at the stage of flight test. Thus, those conventional evaluation methods cannot be employed when the distribution characteristics and priori information are unknown. In this paper, the fuzzy norm method(FNM) is proposed which combines the advantages of fuzzy theory and norm theory. The proposed method can deeply dig system information from limited data, which probability distribution is not taken into account. Firstly, the FNM is employed to evaluate variable interval and expanded uncertainty from limited PSD data, and the performance of FNM is demonstrated by confidence level, reliability and computing accuracy of expanded uncertainty. In addition, the optimal fuzzy parameters are discussed to meet the requirements of aviation standards and metrological practice. Finally, computer simulation is used to prove the adaptability of FNM. Compared with statistical methods, FNM has superiority for evaluating expanded uncertainty from limited data. The results show that the reliability of calculation and evaluation is superior to 95%.