Strengthening Links Between Data Analysis and Soft Computing
This book gathers contributions presented at the 7th International Conference on Soft Methods in Probability and Statistics SMPS 2014, held in Warsaw (Poland) on September 22-24, 2014. Its aim is to present recent results illustrating new trends in intelligent data analysis. It gives a comprehensive overview of current research into the fusion of soft computing methods with probability and statistics.
Synergies of both fields might improve intelligent data analysis methods in terms of robustness to noise and applicability to larger datasets, while being able to efficiently obtain understandable solutions of real-world problems.
There are many tasks where the comparison of histograms (distributions, fuzzy numbers) is required with help of relationship of type ”more-less”. There are many approaches to solving this problem. But the histograms may be distorted. Then we have to find the conditions on the distortions under which the comparison of the two histograms is not changed. The solution of the problem is searched via three popular probabilistic methods of comparison.
The paper presents a new fuzzy set based description which helps to distinguish the expected values of the statistical experiment from the outliers. Since the Neyman-Pearson criterion is not adequate in some real applications for such purpose, we propose to use triangular norms for conjuction of two propositions about typical and non-typical values and describe both of them as a fuzzy set that is called the typical transform. We also investigate such a property of the typical transform as stability.