A topological constraint language is a formal language whose variables range over certain subsets of topological spaces, and whose nonlogical primitives are interpreted as topological relations and functions taking these subsets as arguments. Thus, topological constraint languages typically allow us to make assertions such as “region V1 touches the boundary of region V2”, “region V3 is connecte...

In this work, we present an account of our recent results on applications of rough mereology to problems of 1) knowledge granulation; 2) granular preprocessing in knowledge discovery by means of decision rules; 3) spatial reasoning in multi-agent systems in exemplary case of intelligent mobile robotics.

In this paper, we discuss rough inclusions defined in Rough Mereology – a paradigm for approximate reasoning introduced by Polkowski and Skowron – as a basis for common models for rough as well as fuzzy set theories. We justify the point of view that tolerance (or, similarity) is the motif common to both theories. To this end, we demonstrate in Sect. 6 that rough inclusions (which represent a h...

Lattice-theoretic ideals have been used to define and generate non granular rough approximations over general approximation spaces over the last few years by few authors. The goal of these studies, in relation based rough sets, have been to obtain nice properties comparable to those of classical rough approximations. In this research paper, these ideas are generalized in a severe way by the pre...

We discuss problems related to information granule calculus (com-Our approach to information granule construction and general scheme of approximate reasoning on granules is based on rough mereology 14, 15, 16]. The schemes are constructed by agents. Our approach may be applied in the problems of approximate synthesis of complex objects (solutions) in distributed systems of intelligent agents.

Worldwide, there has been a rapid growth in interest in rough set theory and its applications in recent years. Evidence of this can be found in the increasing number of high-quality articles on rough sets and related topics that have been published in a variety of international journals, symposia, workshops, and international conferences in recent years. In addition, many international workshop...

We consider a synthesis of complex objects by multi-agent system based on rough mereology theory 12]. Any agent can produce complex objects from parts obtained from his sub-agents using some composition rules. Agents are equipped with decision tables describing partial speciications of their synthesis tasks. We investigate some problems of searching for optimal task speciications for sub-agents...

The problem of imperfect knowledge under uncertain environments has been tackled for a long time by philosophers, logicians and mathematicians. Rough set theory proposed by Zdzislaw Pawlak [1] has attracted attention of many researchers and practitioners all over the world, and has a fast growing group of researchers interested in this methodology. Fuzzy set theory proposed by Lotfi Zadeh [2] h...

Classification systems working on large feature spaces, despite extensive learning, often perform poorly on a group of atypical samples. The problem can be dealt with by incorporating domain knowledge about samples being recognized into the learning process. We present a method that allows to perform this task using a rough approximation framework. We show how human expert’s domain knowledge ex...

We propose a new approach to tasks of Distributed Artiicial Intelligence (DAI). This approach is based on a novel idea of rough mereology which ooers a framework for a rigorous (numerical) treatment of relations of being a part in degree and allows for approximate reasoning about complex objects in particular for organizing systems of intelligent agents into schemes (assembling teams) for the p...