Transformation Of Probability Distributions Research Articles

Possibilistic Uncertainty Quantification in One-Dimensional Consolidation Problems

Abstract In this study, we use possibility distribution as a basis for parameter uncertainty quantification in one-dimensional (1D) consolidation problems. A possibility distribution is the one-point coverage function of a random set and is viewed as containing both partial ignorance and uncertainty. Vagueness and scarcity of information needed for characterizing the coefficient of consolidation in clay can be handled using possibility distributions. Possibility distributions can be constructed from existing data, or based on the transformation of probability distributions. An attempt is made to set a systematic approach for estimating uncertainty propagation during the consolidation process. The measure of uncertainty is based on Klir's definition (1995). We make comparisons with results obtained from other approaches (probabilistic…) and discuss the importance of using possibility distributions in this type of problem.

Fuzzy partitioning for clinical DSSs using statistical information transformed into possibility-based knowledge

Fuzzy logic has gained much importance for its applications in Decision Support Systems (DSSs), especially in fields like medicine, where the final user has to handle uncertain data and vague concepts, and needs an intelligible system based on clear rule bases. In medical applications, physicians are often skilled to reason using statistical approaches, since this type of information is often known, or can be extracted from data. However, since decisions have to be applied to single patients, clinical data items have to be classified in order to obtain the plausibility of conclusions, rather than their probability. Therefore, statistical information can be used, in order to define fuzzy sets and rules for constructing DSSs based on fuzzy logic. While the transformation of probability distributions is well known in literature, here, an approach is presented for transforming likelihood functions into fuzzy sets, based on possibility theory, which is actually instanced into four different new methods for knowledge representation. A comparison among different methods is shown, as well as the analysis of transformation properties and resulting fuzzy sets characteristics are considered, by using synthetic and real data. Finally, some considerations about the most suitable method to be used in the context of clinical DSSs are given.

On transformations of probability distributions by read-once quasigroup formulae

- We investigate distributions of values of read-once quasigroup formulae when the variables are replaced by random independent identically distributed elements of the quasigroup. For general read-once formulae of increasing complexity or depth conditions under which of the distributions of values of the formulae converge to the uniform distribution are put forward, and weaker conditions for the convergence ‘in the mean’ is proved also. This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 11-01-00508) and by the Programme of the Division of Mathematics Sciences of the Russian Academy of Sciences “Algebraic and Combinatorial Methods of Mathematical and New Generation of Information Systems” (the project “Problems of Optimal Synthesis of Control Systems”).