Fuzzy Sets and Systems - Special issue: fuzzy sets: where do we stand? Where do we go?
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Mathematical Foundations
Rough Sets: Mathematical Foundations
Rough mereology: a rough set paradigm for unifying rough set theory and fuzzy set theory
Fundamenta Informaticae
A note on 3-valued rough logic accepting decision rules
Fundamenta Informaticae
Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
Feature Selection Based on the Rough Set Theory and Expectation-Maximization Clustering Algorithm
RSCTC '08 Proceedings of the 6th International Conference on Rough Sets and Current Trends in Computing
A Study in Granular Computing: On Classifiers Induced from Granular Reflections of Data
Transactions on Rough Sets IX
Transactions on rough sets VI
Reasoning about concepts by rough mereological logics
RSKT'08 Proceedings of the 3rd international conference on Rough sets and knowledge technology
Mereological theories of concepts in granular computing
Transactions on computational science II
Transactions on rough sets XII
Rough mereological reasoning in rough set theory: recent results and problems
RSKT'06 Proceedings of the First international conference on Rough Sets and Knowledge Technology
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In this paper, dedicated to Professor Solomon Marcus on the occasion of His 80th birthday, we discuss the idea of intensional many-valued logic reflecting the logical content of rough set approach to analysis and treatment of uncertainty. In constructing the variety of logics presented in the paper, we make use of a certain kind of tolerance (similarity) relations called rough mereological tolerances. A study of tolerance relations that arise in rough set environments was initiated in 1994, with the paper [23], in which basic ideas pertaining to tolerance relations in the rough set framework were pointed to. The analysis of the role tolerance relations may play in machine learning based on rough set-theoretic ideas was carried out by Professor Solomon Marcus in His seminal paper, written during His stay in Warsaw in December of the year 1994. At the same time the first author had first ideas related to the applicability of ideas of mereology in the rough set analysis of uncertainty. In a later analysis it has turned out that mereological approach has led to a development of a new paradigm in reasoning under uncertainty, called rough mereology, proposed by Lech Polkowski and Andrzej Skowron. Within this paradigm, one is able to construct a variety of tolerance relations. Those tolerance relations, induced by rough mereological constructs called rough inclusions, serve as a basis for constructing a variety of logics, called rough mereological logics, that are related to the inherent structure of any rough set universe. In this paper, we introduce gradually all essential and necessary notions from the area of rough set theory, mereology and rough mereology, and then we discuss tolerance relations induced by rough inclusions along with some methods for inducing rough inclusions with desired properties. The paper culminates with a discussion of intensional logics based on rough mereological tolerance relations. In this way, we explore one of so many paths in scientific research, that have been either pointed to or threaded by Professor Solomon Marcus.