A robust logic for rule-based reasoning under uncertainty

2008

Since the present Part has a certain complexity, it is worth introducing, with some details, the intuitive motivations of the entire picture and their connections with the mathematical machinery which will be used.

2012

The paper presents a logic for reasoning about coveringbased rough sets using three logical values: the value t corresponding to the positive region of a set, the value f — to the negative region, and the undefined value u — to the boundary region of that set. Atomic formulas of the logic represent membership of objects of the universe in rough sets, and complex formulas are built out of the atomic ones using three-valued Kleene connectives. In the paper we provide a strongly sound and complete Gentzen-style sequent calculus for the logic.

Transactions on Rough Sets IV, 2005

Rough sets framework has two appealing aspects. First, it is a mathematical approach to deal with vague concepts. Second, rough set techniques can be used in data analysis to find patterns hidden in the data. The number of applications of rough sets to practical problems in different fields demonstrates the increasing interest in this framework and its applicability. Most of the current rough sets techniques and software systems based on them only consider rough sets defined explicitly by concrete examples given in tabular form. The previous research mostly disregards the following two problems. The first problem is related with how to define rough sets in terms of other rough sets. The second problem is related with how to incorporate domain or expert knowledge. This thesis 1 proposes a language that caters for implicit definitions of rough sets obtained by combining different regions of other rough sets. In this way, concept approximations can be derived by taking into account domain knowledge. A declarative semantics for the language is also discussed. It is then shown that programs in the proposed language can be compiled to extended logic programs under the paraconsistent stable model semantics. The equivalence between the declarative semantics of the language and the declarative semantics of the compiled programs is proved. This transformation provides the computational basis for implementing our ideas. A query language for retrieving information about the concepts represented through the defined rough sets is also defined. Several motivating applications are described. Finally, an extension of the proposed language with numerical measures is discussed. This extension is motivated by the fact that numerical measures are an important aspect in data mining applications. I would like to express my sincere gratitude towards my supervisor, Jan Ma luszynski, for his invaluable guidance and constant support. At the department of Computer Science, at New University of Lisbon, my thanks goes to Carlos Viegas Damásio for his suggestions and the time taken to discuss many aspects of this work with me. I also would like to thank the following people for their comments and support:

Studies in Fuzziness and Soft Computing, 2000

Basic ideas of rough set theory were proposed by Zdzis law Pawlak in the early 1980's. In the ensuing years, we have witnessed a systematic, world-wide growth of interest in rough sets and their applications.

The objective of this paper is to present a new approach to reasoning under uncertainty, based on the use of Bayesian belief networks (BBN’s) enhanced with rough sets. The role of rough sets is to provide additional reasoning to assist a BBN in the inference process, in cases of missing data or difficulties with assessing the values of related probabilities. The basic concepts of both theories, BBN’s and rough sets, are briefly introduced, with examples showing how they have been traditionally used to reason under uncertainty. Two case studies from the authors’ own research are discussed: one based on the evaluation of software tool quality for use in real-time safety-critical applications, and another based on assisting the decision maker in taking the right course of action, in real time, in the naval military exercise. The use of corresponding public domain software packages based on BBN’s and rough sets is outlined, and their application for real-time reasoning in processes unde...

Information Processing and Management of Uncertainty in Knowledge-Based Systems, 2014

Rough approximations, which consist of lower and upper approximations, are described under objects characterized by possibilistic information that is expressed by a normal possibility distribution. Concepts of not only possibility but also certainty are used to construct an indiscernibility relation. First, rough approximations are shown for a set of discernible objects by using the indiscernibility relation. Next, a set of objects characterized by possibilistic information is approximated. Consequently, rough approximations consist of objects with a degree expressed by an interval value where lower and upper degrees mean the lower and the upper bounds of the actual degree. This leads to the complementarity property linked with lower and upper approximations in the case of a set of discernible objects, as is valid under complete information. Furthermore, a criterion is introduced to judge whether or not an object is regarded as supporting rules. By using the criterion, we can select only objects that are regarded as inducing rules.

Journal of Advanced Computational Intelligence and Intelligent Informatics, 2020

Rough set theory is studied to manage uncertain and inconsistent information. Because Pawlak’s decision logic for rough sets is based on the classical two-valued logic, it is inconvenient for handling inconsistent information. We propose a bilattice logic as the deduction basis for the decision logic of rough sets to address inconsistent and ambiguous information. To enhance the decision logic to bilattice semantics, we introduce Variable Precision Rough Set (VPRS). As a deductive basis for bilattice decision logic, we define a consequence relation for Belnap’s four-valued semantics and provide a bilattice semantic tableau TB4 for a deduction system. We demonstrate the soundness and completeness of TB4 and enhance it with weak negation.

Knowledge acquisition under uncertainty using rough set theory was first stated as a concept and was introduced by Z.Pawlak in1981. A collection of rules is acquired, on the basis of information stored in a data base-like system, called an information system. Uncertainty implies inconsistencies, which are taken into account, so that the produced are categorized into certain and possible with the help of rough set theory. The approach presented belongs to the class of methods of learning from examples. The taxonomy of all possible expert classifications, based on rough set theory, is also established. It is shown that some classifications are theoretically (and, therefore, in practice) forbidden. For a set of conditions of the information system, and a given action of an expert, lower and upper approximations of a classification, generated are computed in a straightforward way, using their simple definitions. Such approximations are the basis of rough set theory. From these approximations, certain and possible rules may be determined. Certain rules have been propagated separately during the inference process, producing new certain rules. Similarly, possible rules are likely to propagate in a parallel way. Example on the basic of knowledge Acquisition has been discussed in brief.

Information Sciences, 2007

In this article, we discuss methods based on the combination of rough sets and Boolean reasoning with applications in pattern recognition, machine learning, data mining and conflict analysis.

2011

The paper deals with the decision rules synthesis i n the domain of expert systems and knowledge based systems. These systems incorporate expert knowledge which is often expressed in the If Then form. As i t is very hard for experts to formally articulate their knowledge, automated decision rule composing algorithms have been used. The rule composing algorithms are often based on the rough sets theory. Originally, ru les are composed from data table by equivalence relation, while in this paper we investigate the rules based o n dominance relation. The main goal of this paper is to single out possible benefits and advantages of dominance relation based rules over equivalence rel ation based rules.