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Cautious reliability analysis of multistate and continuumstate systems based on the imprecise Dirichlet model, International Journal of Reliability, Quality and Safety Engineering 13
 in: Computational Intelligence in Reliability Engineering, Volume 2: New Metaheuristics, Neural and Fuzzy Techniques in Reliability
, 2007
"... Cautious reliability estimates of multistate and continuumstate systems are studied in the paper under condition that initial data about reliability of components are given in the form of intervalvalued observations, measurements or expert judgments. The intervalvalued information is processed b ..."
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Cautious reliability estimates of multistate and continuumstate systems are studied in the paper under condition that initial data about reliability of components are given in the form of intervalvalued observations, measurements or expert judgments. The intervalvalued information is processed by means of a set of the imprecise Dirichlet model which can be regarded as a set of Dirichlet distributions. The developed model of reliability provides cautious reliability measures when the number of observations or measurements is rather small. It can be viewed as an extension of models based on random set theory and robust statistical models. A numerical example illustrates the proposed model and an algorithm for computing the system reliability.
Ranking procedures by pairwise comparison using random sets and the imprecise Dirichlet model
"... Methods for ranking of alternatives or objects by pairwise comparisons using random set theory are proposed in the paper. Efficient algorithms weekly depending on the number of independent sources of data are considered. Methods using the imprecise Dirichlet model are used for obtaining cautious com ..."
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Methods for ranking of alternatives or objects by pairwise comparisons using random set theory are proposed in the paper. Efficient algorithms weekly depending on the number of independent sources of data are considered. Methods using the imprecise Dirichlet model are used for obtaining cautious comparison measures when the number of expert judgments is rather small and standard methods of random set theory may give risky results. The methods allow us to overcome some difficulties concerning the conflicting or contradictory sources of data. Various numerical examples illustrate the proposed algorithms and methods.
The Apparent Arbitrariness of SecondOrder Probability Distributions The Apparent Arbitrariness of SecondOrder Probability Distributions
"... DeÀn dà kllios C os _ an aÍtän kaÈ t ndoÔmena íti mlia C en poi¬ Pltwn, {TÐmaios} Abstract Adequate representation of imprecise probabilities is a crucial and nontrivial problem in decision analysis. Secondorder probability distributions is the model for imprecise probabilities whose merits are d ..."
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DeÀn dà kllios C os _ an aÍtän kaÈ t ndoÔmena íti mlia C en poi¬ Pltwn, {TÐmaios} Abstract Adequate representation of imprecise probabilities is a crucial and nontrivial problem in decision analysis. Secondorder probability distributions is the model for imprecise probabilities whose merits are discussed in this thesis. That imprecise probabilities may be represented by secondorder probability distributions is well known but there has been little attention to specific distributions. Since different probability distributions have different properties, the study of the desired properties of models of imprecise probabilities with respect to secondorder models require analysis of particular secondorder distributions. An often held objection to secondorder probabilities is the apparent arbitrariness in the choice of distribution. We find some evidence that the structure of secondorder distributions is an important factor that prohibits arbitrary choice of distributions. In particular, the properties of two secondorder distributions are investigated; the uniform joint distribution and a variant of the Dirichlet distribution that has the property of being the normalised product of its own marginal distributions. The joint uniform distribution is in this thesis shown to have marginal distributions that belie the supposed noninformativeness of a uniform distribution. On the other hand, the modified Dirichlet distribution discovered here has its information content evenly divided among the joint and marginal distributions in that the total correlation of the variables is minimal. It is also argued in the thesis that discrete distributions, as opposed to the continuous distributions mentioned above, would have the advantage of providing a natural setting for updating of lower bounds, and computation of expected utility is made more efficient. Summarium In placitorum scrutatione maxima et mehercle minime levis difficultas eo spectat, quomodo probabilitates dubiae bene ostendantur. In hac thesi de utilitate distributionum probabilitatum secundi ordinis disseremus, in quantum ad probabilitates dubias ostendendas valeant. Omnibus fere notum est probabilitates dubias ostendi posse per distributiones probabilitatum secundi ordinis, sed pauci operam distributionibus singulis operam contulerunt. Cum tamen distributiones probabilitatum valde inter se diversae sint, si quis proprietatibus desideratis probabilitatum dubiarum secundi ordinis studium conferre vult, primum debet quasdam praescriptas distributiones secundi ordinis investigare. Sed fortasse, quod saepenumero fieri solet, quispiam dixerit probabilitates secundi ordinis nulla, ut videtur, ratione habita quasi vagari quoad delectum distributionis. Nos tamen nonnulla indicia comperimus quibus freti confirmare audemus ipsam formam distributionum secundi ordinis multum valere ad praedictum distributionum secundi ordinis delectum rationabiliter peragendum. Imprimis proprietates duarum distributionum secundi ordinis investigabimus, nimirum distributionis uniformis coniunctae et alterius cuiusdam speciei distributionis quae 'Dirichleti' vocatur, quae ex ipsius distributionibus marginalibus ad normam correcta oritur. In hac thesi probamus illam coniunctam uniformem distributionem continere distributiones marginales eius modi quae illos refellant qui negant distributionem uniformem quicquam alicuius momenti afferre. Attamen in illa distributione Dirichleti paulo mutata, quam hoc loco patefacimus, omnia aequaliter inter coniunctas et marginales distributiones divisa sunt, in quantum tota ratio quae inter variantia intercessit ad minimum reducitur. Insuper in hac thesi confirmamus distributiones discretas potius quam antedictas distributiones continuas in hoc utiliores esse, quod per eas limites inferiores in melius mutare licet, et beneficia exspectata accuratius computari possunt.
Secondorder uncertainty calculations by using the imprecise Dirichlet model
"... Natural extension is a powerful tool for combining the expert judgments in the framework of imprecise probability theory. However, it assumes that every judgment is “true ” and this fact leads to some difficulties in many applications. Therefore, a secondorder uncertainty model is considered in the ..."
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Natural extension is a powerful tool for combining the expert judgments in the framework of imprecise probability theory. However, it assumes that every judgment is “true ” and this fact leads to some difficulties in many applications. Therefore, a secondorder uncertainty model is considered in the paper where probabilities on the secondorder level are taken by using the imprecise Dirichlet model. The approach proposed in the paper is illustrated by application and auxiliary examples.
Research Article A Ranking Procedure by Incomplete Pairwise Comparisons Using Information Entropy and DempsterShafer Evidence Theory
"... which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Decisionmaking, as a way to discover the preference of ranking, has been used in various fields. However, owing to the uncertainty in group decisionmaking, how to rank altern ..."
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which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Decisionmaking, as a way to discover the preference of ranking, has been used in various fields. However, owing to the uncertainty in group decisionmaking, how to rank alternatives by incomplete pairwise comparisons has become an open issue. In this paper, an improved method is proposed for ranking of alternatives by incomplete pairwise comparisons using DempsterShafer evidence theory and information entropy. Firstly, taking the probability assignment of the chosen preference into consideration, the comparison of alternatives to each group is addressed. Experiments verified that the information entropy of the data itself can determine the different weight of each group’s choices objectively. Numerical examples in group decisionmaking environments are used to test the effectiveness of the proposed method. Moreover, the divergence of ranking mechanism is analyzed briefly in conclusion section. 1.
CAUTIOUS ANALYSIS OF PROJECT RISKS BY INTERVALVALUED INITIAL DATA
, 2005
"... One of the most common performance measures in selection and management of projects is the Net Present Value (NPV). In the paper, we study a case when initial data about the NPV parameters (cash flows and the discount rate) are represented in the form of intervals supplied by experts. A method for c ..."
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One of the most common performance measures in selection and management of projects is the Net Present Value (NPV). In the paper, we study a case when initial data about the NPV parameters (cash flows and the discount rate) are represented in the form of intervals supplied by experts. A method for computing the NPV based on using random set theory is proposed and three conditions of independence of the parameters are taken into account. Moreover, the imprecise Dirichlet model for obtaining more cautious bounds for the NPV is considered. Numerical examples illustrate the proposed approach for computing the NPV.