Two views of the theory of rough sets in finite universes
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This paper presents and compares two views of the theory of rough sets: the operator-oriented and set-oriented views, which interprets rough set theory as an extension of set theory with two additional unary operators.About:
This article is published in International Journal of Approximate Reasoning.The article was published on 1996-11-01 and is currently open access. It has received 562 citations till now. The article focuses on the topics: Dominance-based rough set approach & Rough set.read more
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Theory and practice of uncertain programming
TL;DR: This book provides a self-contained, comprehensive and up-to-date presentation of uncertain programming theory, including numerous modeling ideas, hybrid intelligent algorithms, and applications in system reliability design, project scheduling problem, vehicle routing problem, facility location problem, and machine scheduling problem.
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Relational interpretations of neighborhood operators and rough set approximation operators
TL;DR: This paper presents a framework for the formulation, interpretation, and comparison of neighborhood systems and rough set approximations using the more familiar notion of binary relations, and introduces a special class of neighborhood system, called 1-neighborhood systems.
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Constructive and algebraic methods of the theory of rough sets
TL;DR: This paper reviews and compares constructive and algebraic approaches in the study of rough set algebras and states axioms that must be satisfied by the operators.
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Topological approaches to covering rough sets
TL;DR: This paper explores the topological properties of covering-based rough sets, studies the interdependency between the lower and the upper approximation operations, and establishes the conditions under which two coverings generate the same lower approximation operation and the same upper approximation operation.
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Probabilistic rough set approximations
TL;DR: Based on rough membership functions and rough inclusion functions, the Bayesian decision-theoretic analysis is adopted to provide a systematic method for determining the precision parameters by using more familiar notions of costs and risks.
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Fuzzy sets
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Journal ArticleDOI
Rough fuzzy sets and fuzzy rough sets
Didier Dubois,Henri Prade +1 more
TL;DR: It is argued that both notions of a rough set and a fuzzy set aim to different purposes, and it is more natural to try to combine the two models of uncertainty (vagueness and coarseness) rather than to have them compete on the same problems.
Book
An Introduction to Modal Logic
Max J. Cresswell,G. E. Hughes +1 more
TL;DR: This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic with all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing clarity of exposition and approachability.
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Modal Logic: An Introduction
TL;DR: This chapter discusses standard models for modal logics, classical systems of modal logic, and Determination and decidability for classical systems.