By Leszek Rutkowski, Marcin Korytkowski, Rafal Scherer, Ryszard Tadeusiewicz, Lotfi A. Zadeh, Jacek M. Zurada
The two-volume set LNAI 9692 and LNAI 9693 constitutes the refereed court cases of the fifteenth foreign convention on synthetic Intelligence and smooth Computing, ICAISC 2016, held in Zakopane, Poland in June 2016.
The 134 revised complete papers awarded have been conscientiously reviewed and chosen from 343 submissions. The papers integrated within the first quantity are geared up within the following topical sections: neural networks and their functions; fuzzy structures and their functions; evolutionary algorithms and their functions; agent platforms, robotics and keep watch over; and development category. the second one quantity is split within the following elements: bioinformatics, biometrics and clinical functions; facts mining; man made intelligence in modeling and simulation; visible details coding meets laptop studying; and numerous difficulties of synthetic intelligence.
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Additional resources for Artificial Intelligence and Soft Computing: 15th International Conference, ICAISC 2016, Zakopane, Poland, June 12-16, 2016, Proceedings, Part II
Keywords: Unsupervised learning · Clustering · Consensus clustering · Ensemble clustering · Frequent closed patterns 1 Introduction Clustering is the process of partitioning a dataset into groups, so that the instances in the same group are more similar to each other than to instances in any other group. This partitioning may lead to discover meaningful patterns in the dataset. ). Thus the question is: How to choose a clustering for a dataset from these many possibilities? The most common solution is to use validation measure(s) to compare the results and select the one that gets the higher score [4,7].
5. Number of rules for the lymphography data set Fig. 6. Number of rules for the wine recognition data set Fig. 7. Total number of conditions for the breast cancer data set Fig. 8. Total number of conditions for the echocardiogram data set Fig. 9. Total number of conditions for the hepatitis data set Fig. 10. Total number of conditions for the image data set 3 Probabilistic Approximations In this section deﬁnitions of singleton, subset and concept approximations are extended to the corresponding probabilistic approximations.
A decision table Case Attributes Decision Wind Temperature Humidity Trip 1 low ? low 2 ? high − yes yes 3 high − low yes 4 − high ? yes 5 high low − no 6 low high ? no 7 ? high no One of the most important ideas of rough set theory  is an indiscernibility relation, deﬁned for complete data sets. Let B be a nonempty subset of A. The indiscernibility relation R(B) is a relation on U deﬁned for x, y ∈ U as deﬁned by (x, y) ∈ R(B) if and only if ∀a ∈ B (a(x) = a(y)) The indiscernibility relation R(B) is an equivalence relation.