Uncertainty and Fuzzy Sets: Classifying the Situation

The so called “Plural Uncertainty Model” is considered, in which statistical, maxmin, interval and Fuzzy model of uncertainty are embedded. For the last case external and internal contradictions of the theory are investigated and the modified definition of the Fuzzy Sets is proposed to overcome the troubles of the classical variant of Fuzzy Subsets by L. Zadeh. The general variants of logit- and probit- regression are the model of the modified Fuzzy Sets. It is possible to say about observations within the modification of the theory. The conception of the “situation” is proposed within modified Fuzzy Theory and the classifying problem is considered. The algorithm of the classification for the situation is proposed being the analogue of the statistical MLM(maximum likelihood method). The example related possible observing the distribution from the collection of distribution is considered.

Em Algorithm for MLE of a Probit Model for Multiple Ordinal Outcomes

The correlated probit model is frequently used for multiple ordered data since it allows to incorporate seamlessly different correlation structures. The estimation of the probit model parameters based on direct maximization of the limited information maximum likelihood is a numerically intensive procedure. We propose an extension of the EM algorithm for obtaining maximum likelihood estimates for a correlated probit model for multiple ordinal outcomes. The algorithm is implemented in the free software environment for statistical computing and graphics R. We present two simulation studies to examine the performance of the developed algorithm. We apply the model to data on 121 women with cervical or endometrial cancer. Patients developed normal tissue reactions as a result of post-operative external beam pelvic radiotherapy. In this work we focused on modeling the effects of a genetic factor on early skin and early urogenital tissue reactions and on assessing the strength of association between the two types of reactions. We established that there was an association between skin reactions and polymorphism XRCC3 codon 241 (C>T) (rs861539) and that skin and urogenital reactions were positively correlated. ACM Computing Classification System (1998): G.3.