@INCOLLECTION { Rsds2931,
author = {Polkowski, Lech T. and Skowron, Andrzej},
title = {Rough Mereology in Information Systems. A Case Study: Qualitative Spatial Reasoning},
booktitle = {Rough set methods and applications: new developments in knowledge discovery in information systems},
series = = {Studies in Fuzziness and Soft Computing},
pages = {89--136},
publisher = {Physica-Verlag},
address = {Heidelberg, Germany},
year = 2000,
note = {This volume is dedicated to the memory of Professor Adam Mrozek},
editor = {Polkowski, Lech and Tsumoto, Shusaku and Lin, Tsau Young},
issn = {1434-9922},
isbn = {3-7908-1328-1},
abstract = {Rough Mereology has been proposed as a paradigm for approximate reasoning in complex information systems [65], [66], [67], [68], [76]. Its primitive notion is that of a rough inclusion functor which gives for any two entities of discourse the degree in witch one of them is a part of the other. Rough Mereology may be regarded as an extension of Rough Set Theory as it proposes to argue in terms of similarity relations induced from a rough inclusion instead of reasoning in term of similarity relations induced from a rough inclusion instead of reasoning in terms of indiscernibility relations (cf. Chapter 1); its also proposes an extension of Mereology as it replaces the mereological primitive functor of being a part with a more general functor of being a part in a degree. Rough Mereology has deep relations to Fuzzy Set Theory as it proposes to study the properties of partial containment which is also the fundamental subject of study for Fuzzy Set Theory. Rough Mereology is also a generalization of Mereology i.e. a theory of reasoning based on the notion of a part. Classical language of mathematics are of twofold kind: the language of set theory (naive or normal) expressing classes of objects as sets consisting of "elements", "points" etc. suitable for objects perceived as built of "atoms" and the language of part relations suitable for e.g. continuous objects like solids, regions, etc. where two objects are related to each other by saying that on of them is a part of the other. In the sequel, we will rely on Mereology proposed by Stanislaw Lesniewski. In the schema envisioned by Lesniewski, Mereology is constructed on the basis of Ontology i.e. Theory of Names (Concepts). Ontology plays here the role of set theory: objects are represented by their names: some objects are perceived as atomic and given individual names while other are perceived as (distributive) classes i.e. collections of objects and given general names. Once the taxonomy of names is established, relations like part may be introduced (via their names formed in agreement with ontological principles). This course is adopted by contemporary theory of Spatial Reasoning: in application-oriented spatial reasoning systems, ontology appears as typology of concepts and their successive taxonomy cf. e.g. [57] (to quote a small excerpt: edge is frontier, barrier, dam, cliff, shoreline). This may be interpreted as statement that a general name (concept) i.e. edge is a class (a set) of individual concepts (names): frontier, barrier etc. Let us remark in passing that ontological usage of is, about which below, is opposite to the usage quoted in the last sentence i.e. is syntactically acts like the esti symbol "e" (to be) in set theoretical notation (thus, e.g. frontier is edge). The copula is used informally above is formalized in Ontology and given a precise meaning proposing thus an alternative language to set theory in which it is convenient to express properties of objects in particular their mereological structure. In this Chapter we take this course. We regard this approach as particularly suited for Rough Set Theory which is also primarily concerned with Concept Approximation in Information Systems. In this Chapter, we give a description of Rough Mereology in Information Systems along the lines outlined above: we given an introduction to Ontology and Mereology according to Lesniewski and we show one may introduce them in Information Systems on the basis of Rough Sets Theory. In this framework, we introduce Rough Mereology and we present some ways for defining rough inclusions. We demonstrate applications of Rough Mereology to approximate reasoning taking as the case subject Qualitative Spatial Reasoning. This topic seems to be especially suitable for rough mereological approach as it relies very essentially on Ontology and Mereology; we address its mereo-topological as well as mereo-geometrical aspect.},
keywords = {rough sets, information systems/tables, ontology, mereology, rough mereology, spatial reasoning, },
}