A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators

Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed in a generalized approximation space. Main properties of these operators are discussed under different interval-valued fuzzy binary relations, and the illustrative examples are given to demonstrate the main features of the proposed operators

LearnFCA: A Fuzzy FCA and Probability Based Approach for Learning and Classification

Formal concept analysis(FCA) is a mathematical theory based on lattice and order theory used for data analysis and knowledge representation. Over the past several years, many of its extensions have been proposed and applied in several domains including data mining, machine learning, knowledge management, semantic web, software development, chemistry ,biology, medicine, data analytics, biology and ontology engineering. This thesis reviews the state-of-the-art of theory of Formal Concept Analysis(FCA) and its various extensions that have been developed and well-studied in the past several years. We discuss their historical roots, reproduce the original definitions and derivations with illustrative examples. Further, we provide a literature review of it’s applications and various approaches adopted by researchers in the areas of dataanalysis, knowledge management with emphasis to data-learning and classification problems. We propose LearnFCA, a novel approach based on FuzzyFCA and probability theory for learning and classification problems. LearnFCA uses an enhanced version of FuzzyLattice which has been developed to store class labels and probability vectors and has the capability to be used for classifying instances with encoded and unlabelled features. We evaluate LearnFCA on encodings from three datasets - mnist, omniglot and cancer images with interesting results and varying degrees of success. Adviser: Dr Jitender Deogu

Solutions to decision-making problems in management engineering using molecular computational algorithms and experimentations

制度:新 ; 報告番号:甲3368号 ; 学位の種類:博士(工学) ; 授与年月日:2011/5/23 ; 早大学位記番号:新568

Matroidal approaches to rough sets via closure operators

AbstractThis paper studies rough sets from the operator-oriented view by matroidal approaches. We firstly investigate some kinds of closure operators and conclude that the Pawlak upper approximation operator is just a topological and matroidal closure operator. Then we characterize the Pawlak upper approximation operator in terms of the closure operator in Pawlak matroids, which are first defined in this paper, and are generalized to fundamental matroids when partitions are generalized to coverings. A new covering-based rough set model is then proposed based on fundamental matroids and properties of this model are studied. Lastly, we refer to the abstract approximation space, whose original definition is modified to get a one-to-one correspondence between closure systems (operators) and concrete models of abstract approximation spaces. We finally examine the relations of four kinds of abstract approximation spaces, which correspond exactly to the relations of closure systems

The semantics of N-soft sets, their applications, and a coda about three-way decision

This paper presents the first detailed analysis of the semantics of N-soft sets. The two benchmark semantics associated with soft sets are perfect fits for N-soft sets. We argue that N-soft sets allow for an utterly new interpretation in logical terms, whereby N-soft sets can be interpreted as a generalized form of incomplete soft sets. Applications include aggregation strategies for these settings. Finally, three-way decision models are designed with both a qualitative and a quantitative character. The first is based on the concepts of V-kernel, V-core and V-support. The second uses an extended form of cardinality that is reminiscent of the idea of scalar sigma-count as a proxy of the cardinality of a fuzzy set

Generation of Exhaustive Set of Rules within Dominance-based Rough Set Approach

AbstractThe rough sets theory has proved to be a useful mathematical tool for the analysis of a vague description of objects. One of extensions of the classic theory is the Dominance-based Set Approach (DRSA) that allows analysing preference-ordered data. The analysis ends with a set of decision rules induced from rough approximations of decision classes. The role of the decision rules is to explain the analysed phenomena, but they may also be applied in classifying new, unseen objects. There are several strategies of decision rule induction. One of them consists in generating the exhaustive set of minimal rules. In this paper we present an algorithm based on Boolean reasoning techniques that follows this strategy with in DRSA

LEARNFCA: A FUZZY FCA AND PROBABILITY BASED APPROACH FOR LEARNING AND CLASSIFICATION

Formal concept analysis(FCA) is a mathematical theory based on lattice and order theory used for data analysis and knowledge representation. Over the past several years, many of its extensions have been proposed and applied in several domains including data mining, machine learning, knowledge management, semantic web, software development, chemistry ,biology, medicine, data analytics, biology and ontology engineering. This thesis reviews the state-of-the-art of theory of Formal Concept Analysis(FCA) and its various extensions that have been developed and well-studied in the past several years. We discuss their historical roots, reproduce the original definitions and derivations with illustrative examples. Further, we provide a literature review of it’s applications and various approaches adopted by researchers in the areas of dataanalysis, knowledge management with emphasis to data-learning and classification problems. We propose LearnFCA, a novel approach based on FuzzyFCA and probability theory for learning and classification problems. LearnFCA uses an enhanced version of FuzzyLattice which has been developed to store class labels and probability vectors and has the capability to be used for classifying instances with encoded and unlabelled features. We evaluate LearnFCA on encodings from three datasets - mnist, omniglot and cancer images with interesting results and varying degrees of success. Adviser: Jitender Deogu