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On exactness, definability and vagueness in partial approximation spaces

Ciucci D., Mihálydeák T., Csajbók Z. E.

Technical Sciences / University of Warmia and Mazury in Olsztyn

2015

nr 18(3)

203--212

In this paper, lower/upper, boundary, and negative regions of set approximations, the fundamental concepts of classical rough set theory, have been considered as primitive ones. Assuming that they are independent of each other, a generalized framework for their investigations is outlined. Its main building blocks are base sets and definable sets. Lower/upper approximations, boundaries and negative sets are all considered as definable sets and their mutual interactions are studied. Lastly exact/rough sets are discussed. In generalized framework, four groups of formulae are defined for representing different variants of rough sets. They emphasize distinct features of roughness, and so it may be of highly importance which one is used in practical applications. Some possible choices appeared in authors’ publications are mentioned.

Frobenius-Perron operator description of Markov chains

Kowalski Z. S.

Probability and Mathematical Statistics

2015

Vol. 35, Fasc. 2

325--341

We consider canonical shift space representation of discretetime Markov chain given by transition kernels. Markov shifts and eigenfunctions of skew products above them are characterized by terms of Frobenius-Perron operator. The results are applied to the exactness property of Markov chains. We introduce also the notion of quasi-Markov chain and apply it to Gauss endomorphisms.

Badania docierania powierzchni płasko-równoległych na docierarkach

Barylski A.

Inżynieria Maszyn

2013

R. 18, z. 2

76--83

Zamieszczono wyniki badań powierzchni docieranych na docierarkach dwutarczowych o obiegowym układzie kinematycznym. Określono wpływ nacisku jednostkowego i czasu obróbki na jakość powierzchni w aspekcie współzależności dokładności kształtu powierzchni czynnych tarcz docierających i powierzchni obrabianych.

This paper contains experimental results of surface lapped by double-plate lapping machine with eiroular drive. The influence of unit pressure and machining time on processing quality is determined regarding interdependence of shape exactness of active surfaces of laps and lapped surfaces.