By Witold Pedrycz (auth.), Jacek Koronacki, Zbigniew W. Raś, Sławomir T. Wierzchoń, Janusz Kacprzyk (eds.)

This is the second one quantity of a big two-volume editorial venture we want to devote to the reminiscence of the overdue Professor Ryszard S. Michalski who gave up the ghost in 2007. He was once one of many fathers of laptop studying, an exhilarating and proper, either from the sensible and theoretical issues of view, zone in glossy laptop technological know-how and data expertise. His learn profession all started within the mid-1960s in Poland, within the Institute of Automation, Polish Academy of Sciences in Warsaw, Poland. He left for america in 1970, and because then had labored there at numerous universities, significantly, on the collage of Illinois at Urbana – Champaign and at last, till his premature demise, at George Mason college. We, the editors, have been fortunate as a way to meet and collaborate with Ryszard for years, certainly a few of us knew him while he was once nonetheless in Poland. After he got to work within the united states, he used to be a common customer to Poland, collaborating at many meetings till his loss of life. We had additionally witnessed with a very good own excitement honors and awards he had bought through the years, significantly whilst a few years in the past he used to be elected international Member of the Polish Academy of Sciences between a few most sensible scientists and students from worldwide, together with Nobel prize winners.

Professor Michalski’s study effects stimulated very strongly the advance of desktop studying, info mining, and similar components. additionally, he encouraged many verified and more youthful students and scientists all around the world.

We believe more than pleased that such a lot of most sensible scientists from world wide agreed to pay the final tribute to Professor Michalski by way of writing papers of their components of study. those papers will represent the main acceptable tribute to Professor Michalski, a loyal pupil and researcher. additionally, we think that they're going to encourage many newbies and more youthful researchers within the sector of greatly perceived computing device studying, info research and knowledge mining.

The papers incorporated within the volumes, computer studying I and computer studying II, disguise various issues, and diverse elements of the fields concerned. For comfort of the aptitude readers, we are going to now in brief summarize the contents of the actual chapters.

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The upper approximation of a set X with respect to the approximation space AS#,$ is the set of all objects which can be possibly classified as objects of X with respect to AS#,$ . , references in [44]). For more specific details regarding approximation spaces, the reader is referred to [6], [35], and [47]. The key to granular computing is the information granulation process that leads to the formation of information aggregates (with inherent patterns) from a set of available objects. A corresponding methodological and algorithmic issue is the formation of transparent (understandable) information granules, inasmuch as they should provide a clear and understandable description of patterns present in the sample of objects [2,36].

V c p [1] with the number of clusters equal to cp with the number of clusters equal to c2 Note that the number of clusters (prototypes) could vary between data sets. The obtained prototypes are considered together and viewed as a more synthetic data set which is again clustered at the higher level producing generalized prototypes, say z1, z2, …,zc. The crucial phase is to associate each of these prototypes with the prototypes we started with at the lower processing level. The assignment mechanism exploits the maximum association between the given zj and the prototype in each D[1], D[2[, …, D[p] which is linked with one of the prototypes to the highest extent.

Artificial Intelligence 20, 111–161 (1983) 15. : Machine Learning and Data Mining: Methods and Applications. J. Wiley, London (1998) 16. : Interval analysis. Prentice-Hall, Englewood Cliffs (1966) 17. : P-FCM: a proximity-based fuzzy clustering for usercentered web applications. Int. J. of Approximate Reasoning 34, 121–144 (2003) 18. : A privacy-sensitive approach to distributed clustering. Pattern Recognition Letters 26, 399–410 (2005) 19. : Neuro-fuzzy rule generation: survey in soft computing framework.

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