By Vladik Kreinovich
This booklet commemorates the sixty fifth birthday of Dr. Boris Kovalerchuk, and displays a few of the study components coated by way of his paintings. It makes a speciality of facts processing lower than uncertainty, particularly fuzzy information processing, while uncertainty comes from the imprecision of specialist reviews. The booklet comprises 17 authoritative contributions via best experts.
Read or Download Uncertainty Modeling: Dedicated to Professor Boris Kovalerchuk on his Anniversary PDF
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Extra info for Uncertainty Modeling: Dedicated to Professor Boris Kovalerchuk on his Anniversary
This data set consists of 20000 messages taken from 20 newsgroups. Each group contains one thousand Usenet articles. Approximately 4% of the articles are crossposted. Our only preprocessing was removing words with length ≤ 2. For defining meaningful words we use NFAT and consider each group as separate container. In Fig. 5, group lengths (total number of words) in tens of words is shown by blue line and number of different words in each group is shown by green line. misc’. After creating meaningful words for each group based on NFAT with = 1 and removing non-meaningful words from each group, the news group lengths (total number of meaningful words) in tens of words is shown my blue line in Fig.
19. Let us introduce the simplest possible classifier C from messages to the set of 20 Newsgroups. For a message M let us denote by set(M) the set of all different words in M. Then C(M) is a group with largest number of words in set(M) MW [i]. If there are several groups with the same largest number of words in set(M) MW [i], then we select as C(M) a group with smallest index. In the case when all intersections set(M) MW [i] are empty, we will mark a message M as “unclassifiable”. The results of applying this classifier to the remaining 90% of 20Newsgroups can be represented by the classification confusion matrix CCM Fig.
Return f (node(m − 1, N, K, x), node(m − 1, N, K, x)). function f _n(w, x, L) 1. create the array N := (k1 , k2 ) by using k1 := w1 2L + 21 , and k2 := 2L − k1 ; 2. K := 1; 3. return node(L, N, K, x). In this algorithm, the array N serves as a counter of how many copies of each of x[K] remains. If there are more than 2m copies, they belong to a branch that can be pruned, so the function node just returns x[K] and never visits the nodes of that branch. If N[K] = 1 then the last remaining copy of x[K] is returned and the value of K is incremented.