Nonlinear integrals and their applications in data mining leung kwong sak wang zhenyuan yang rong
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In this paper the Choquet integrals on L-fuzzy sets is introduced, and some elementary properties of this kind of Choquet integrals are studied. In the definitions of the upper and the lower integrals, the efficiency measure can be replaced by a signed efficiency measure. In this case, one genetic approach which is dedicated to the optimization of unknown parameters is involved. Each zkj can be calculated from the given data set 8. From the above discussion, we may see that, replacing the linear function of the feature attributes, the weighted Choquet integral can be used for classification.

Molecules, 20 6 :10947-10962, 2015. As for the integers in the sixth and twelfth column in Table 6. Identification of signed efficiency measures by a genetic algorithm. Some newly introduced soft computing techniques, such as the genetic algorithm and the pseudo gradient search, which are presented in Chapter 7 of this monograph, must be adopted. It outperforms AutoDock Vina by at least 8.

The pseudo gradient search and a penalty technique used in classifications, Proc. It is pointed out that a fuzzy measure on a set X expresses the interaction between the subsets of X and can be represented by an additive measure. Sequences of Functions and Convergence Theorems. We should notice that, even the Choquet integral is chosen as the nonlinear integral in this identification problem, the algebraic method shown in Section 8. That is to say, when the values of input attributes x1, X2,. The classification problems come down to properly specifying the fuzzy measure on which the Choquet integral s are defined and the classifying boundaries by which the different classes are separated. Inspired by the marginal interaction of the multiple decision criteria, which is a core notion of the probabilistic interaction indices, we define the extremely positive and negative interaction cases of the multiple decision criteria, and find interestingly that the monotone measure sum see Definitions 6 and 7 can be taken as an index to measure the kind and degree of the interaction of the multiple decision criteria.

As it gives an predictive interval without missing the accuracy, this method is powerful, especially to data sets for which the classical linear multiregression fails by leaving a large residual. To improve the flexibility of the inference process, Yang et al. Parameters Estimated Values µ {x1} 0. The contribution rate of each combination of the feature attributes, including each singleton, toward the classification is represented by a fuzzy measure. Efficiency measures and signed efficiency measures -- ch. The algorithm is developed to simulate the inference process from the starting propositions to the goal propositions.

Semi-lattice isomorphism of the extensions of possibility measure and the solutions of fuzzy relation equation, Proc. So, we have to take a relatively complex soft computing technique to obtain an approximately optimal solution for this identification problem. The results show that the classification methods have more than 70 percent accuracy and 80 percent sensitivity for most data sets, which are considered high as an initial scanning method for liver cancer diagnosis. They are denoted by x1 , x2 , and x3 respectively. It is cautioned that if the maps are used for pattern recognition and decision processes, it is necessary to fine-tune the reference vectors such that they directly define the decision borders. They are 5 credits, 3 credits, and 4 credits courses respectively.

Thus, a data set consisting of 4 attributes and 150 records is obtained see columns 2-5 and 8-11 of Table 6. The differences between other algorithms are also presented. Then, at the multidimensional variation of the parameters, stable motion dynamics regularities are mapped in the form of the multileveled fractal structure. Distribution Functions, Measurability and Comonotonicity of Functions. In data mining, when the number of attributes, n, increases, the number of unknown parameters increases exponentially. A compromised way with this contradiction is to consider only a relatively small number of most common and interesting lower-order interactions but omit the higher-order interactions to reduce the complexity.

Results are given on synthetic and real data sets, the latter obtained from a landmine detection problem. The experimental results show that the new model has better performance compared with the classical algorithm and the classical Nonlinear Integral. It can be seen from Figure 10. In order to modeling the interactions among attributes for classification, the non-additive measures are studied in this chapter. Each of them corresponds to a class. These integrals can be applied as aggregation tools in information fusion and data mining, such as synthetic evaluation,. This procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties.

In this study, a new classification model - Multiple Nonlinear Integral with Multiple projections is proposed, which includes Double Nonlinear Integral extending to new variants for adapting for complicated data distribution and enhancing classification accuracy. We may consider them as single-symptom diagnosis certainties, i. Here, the nonlinear integral is used as an aggregation tool. Fuzzy Sets and Systems: Theory and Applications. Her address in China is: 23-606 East China Metallurgical Institute Ma An Shan, An Hui P. Thus, to extend the advantages of Choquet integral to fuzzy domain such that it can manage fuzzy information, the original Choquet integral needs to be generalized or say, fuzzified such that it can be used to deal with fuzzy or linguistic data.