Search results for "Rough set"
showing 5 items of 25 documents
Calculus of Contextual Rough Sets in Contextual Spaces
1998
ABSTRACT The palier explains the methods of approximation of set which were earlier put forth by the authors (1995a, 1995b) and by W. Marek and H. Rasiowa (1986). An essential part of this paper is devoted to the presentation of a certain calculus of rough sets and contextual rough sets in contextual spaces.
Rough Sets and Vague Sets
2007
The subject-matter of the consideration touches the problem of vagueness. The notion of the rough set, originated by Zdzislaw Pawlak, was constructed under the influence of vague information and methods of shaping systems of notions leading to conceptualization and representation of vague knowledge, so also systems of their scopes as some vague sets. This paper outlines some direction of searching for a solution to this problem. In the paper, in connection to the notion of the rough set, the notion of a vague set is introduced. Some operations on these sets and their properties are discussed. The considerations intend to take into account a classical approach to reasoning, based on vague pr…
Unit Operations in Approximation Spaces
2010
Unit operations are some special functions on sets. The concept of the unit operation originates from researches of U. Wybraniec-Skardowska. The paper is concerned with the general properties of such functions. The isomorphism between binary relations and unit operations is proved. Algebraic structures of families of unit operations corresponding to certain classes of binary relations are considered. Unit operations are useful in Pawlak's Rough Set Theory. It is shown that unit operations are upper approximations in approximation space. We prove, that in the approximation space (U, R) generated by a reflexive relation R the corresponding unit operation is the least definable approximation i…
Thriving Rough Sets: 10th Anniversary - Honoring Professor Zdzisław Pawlak's Life and Legacy & 35 Years of Rough Sets
2017
This special book is dedicated to the memory of Professor Zdzisław Pawlak, the father of rough set theory, in order to commemorate both the 10th anniversary of his passing and 35 years of rough set theory. The book consists of 20 chapters distributed into four sections, which focus in turn on a historical review of Professor Zdzisław Pawlak and rough set theory; a review of the theory of rough sets; the state of the art of rough set theory; and major developments in rough set based data mining approaches. Apart from Professor Pawlak’s contributions to rough set theory, other areas he was interested in are also included. Moreover, recent theoretical studies and advances in applications are a…
Innovation dynamics in space. Local actors and local factors
1997
This paper addresses the issue of technogenesis and its geographical pattern. It aims to offer both a general analysis framework and a test on innovation data from several European cities. This framework is mainly built on the product life-cycle and the incubation approach. On the basis of this framework, it is argued that the phases of an industrial life-cycle have several firm-specific effects. First, these phases influence innovativeness and thus profit levels, output and employment of firms in a spatially distinct way. Second, the phases of the life-cycle mirror the importance of local factors for innovations, and third, they affect strategic decisions of firms, inter alia by influencin…