Yiyu Yao

University of Regina, Regina, Saskatchewan, Canada

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Publications (82)5.52 Total impact

  • Yiyu Yao, Xiaofei Deng
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    ABSTRACT: Subsethood measures, also known as set-inclusion measures, inclusion degrees, rough inclusions, and rough-inclusion functions, are generalizations of the set-inclusion relation for representing graded inclusion. This paper proposes a framework of quantitative rough sets based on subsethood measures. A specific quantitative rough set model is defined by a particular class of subsethood measures satisfying a set of axioms. Consequently, the framework enables us to classify and unify existing generalized rough set models (e.g., decision-theoretic rough sets, probabilistic rough sets, and variable precision rough sets), to investigate limitations of existing models, and to develop new models. Various models of quantitative rough sets are constructed from different classes of subsethood measures. Since subsethood measures play a fundamental role in the proposed framework, we review existing methods and introduce new methods for constructing and interpreting subsethood measures.
    Information Sciences 05/2014; 267:306-322. · 3.64 Impact Factor
  • Xiaofei Deng, Yiyu Yao
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    ABSTRACT: The model of decision-theoretic shadowed sets provides a cost-sensitive approach to three-valued approximation of a fuzzy set on a finite universe. We introduce a semantic meaningful objective function for modeling shadowed sets using the decision theory. This paper is an extension and generalization of the decision-theoretic shadowed sets. We improve the cost-sensitive approach by generalizing the three-valued shadowed sets approximation using mean values. In particular, a mean value of the membership grades that are neither 1 nor 0 is used to represent the shadow. As a result, we have a more general and practical decision-theoretic shadowed set model, in which the optimal pair of thresholds is related to the membership structures of objects.
    IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013 Joint; 01/2013
  • Developments in Natural Intelligence Research and Knowledge Engineering: Advancing Applications. 12/2012; 4:1-24.
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    Yiyu Yao
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    ABSTRACT: Granular computing concerns a particular human-centric paradigm of problem solving by means of multiple levels of granularity and its applications in machines. It is closely related to Artificial Intelligence (AI) that aims at understanding human intelligence and its implementations in machines. Basic ideas of granular computing have appeared in AI under various names, including abstraction and reformulation, granularity, rough set theory, quotient space theory of problem solving, hierarchical problem solving, hierarchical planning, learning, etc. However, artificial intelligence perspectives on granular computing have not been fully explored. This chapter will serve the purpose of filling in such a gap. The results will have bidirectional benefits. A synthesis of results from artificial intelligence will enrich granular computing; granular computing philosophy, methodology, and tools may help in facing the grand challenge of reverse-engineering the brain, which has significant implications to artificial machine intelligence.
    04/2011: pages 17-34;
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    Yiyu Yao
    Fundam. Inform. 01/2011; 108:249-265.
  • Yiyu Yao
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    ABSTRACT: Three-way decisions provide a means for trading off different types of classification error in order to obtain a minimum cost ternary classifier. This paper compares probabilistic three-way decisions, probabilistic two-way decisions, and qualitative three-way decisions of the standard rough set model. It is shown that, under certain conditions when considering the costs of different types of miss-classifications, probabilistic three-way decisions are superior to the other two.
    Inf. Sci. 01/2011; 181:1080-1096.
  • Yiyu Yao, Xiaofei Deng
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    ABSTRACT: When approximating a concept, probabilistic rough set models use probabilistic positive, boundary and negative regions. Rules obtained from the three regions are recently interpreted as making three-way decisions, consisting of acceptance, deferment, and rejection. A particular decision is made by minimizing the cost of correct and incorrect classifications. This framework is further extended into sequential three-way decision-making, in which the cost of obtaining required evidence or information is also considered.
    Proceedings of the 10th IEEE International Conference on Cognitive Informatics and Cognitive Computing, ICCI*CC 2011, 18-20 August 2011, Banff, Alberta, Canada; 01/2011
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    Conference Proceeding: Top-Down Progressive Computing.
    Yiyu Yao, Jigang Luo
    Rough Sets and Knowledge Technology - 6th International Conference, RSKT 2011, Banff, Canada, October 9-12, 2011. Proceedings; 01/2011
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    Conference Proceeding: Granular State Space Search.
    Jigang Luo, Yiyu Yao
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    ABSTRACT: Hierarchical problem solving, in terms of abstraction hierarchies or granular state spaces, is an effective way to structure state space for speeding up a search process. However, the problem of constructing and interpreting an abstraction hierarchy is still not fully addressed. In this paper, we propose a framework for constructing granular state spaces by applying results from granular computing and rough set theory. The framework is based on an addition of an information table to the original state space graph so that all the states grouped into the same abstract state are graphically and semantically close to each other.
    Advances in Artificial Intelligence - 24th Canadian Conference on Artificial Intelligence, Canadian AI 2011, St. John's, Canada, May 25-27, 2011. Proceedings; 01/2011
  • Yiyu Yao, Rong Fu
    Rough Sets and Knowledge Technology - 6th International Conference, RSKT 2011, Banff, Canada, October 9-12, 2011. Proceedings; 01/2011
  • Int. J. Intell. Syst. 01/2011; 26:518-539.
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    ABSTRACT: The original rough set model was developed by Pawlak, which is mainly concerned with the approximation of sets described by a single binary relation on the universe. In the view of granular computing, the classical rough set theory is established through a single granulation. This paper extends Pawlak’s rough set model to a multi-granulation rough set model (MGRS), where the set approximations are defined by using multi equivalence relations on the universe. A number of important properties of MGRS are obtained. It is shown that some of the properties of Pawlak’s rough set theory are special instances of those of MGRS.Moreover, several important measures, such as accuracy measureα, quality of approximationγ and precision of approximationπ, are presented, which are re-interpreted in terms of a classic measure based on sets, the Marczewski–Steinhaus metric and the inclusion degree measure. A concept of approximation reduct is introduced to describe the smallest attribute subset that preserves the lower approximation and upper approximation of all decision classes in MGRS as well. Finally, we discuss how to extract decision rules using MGRS. Unlike the decision rules (“AND” rules) from Pawlak’s rough set model, the form of decision rules in MGRS is “OR”. Several pivotal algorithms are also designed, which are helpful for applying this theory to practical issues. The multi-granulation rough set model provides an effective approach for problem solving in the context of multi granulations.
    Information Sciences. 03/2010;
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    Yiyu Yao
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    ABSTRACT: The rough set theory approximates a concept by three regions, namely, the positive, boundary and negative regions. Rules constructed from the three regions are associated with different actions and decisions, which immediately leads to the notion of three-way decision rules. A positive rule makes a decision of acceptance, a negative rule makes a decision of rejection, and a boundary rule makes a decision of abstaining. This paper provides an analysis of three-way decision rules in the classical rough set model and the decision-theoretic rough set model. The results enrich the rough set theory by ideas from Bayesian decision theory and hypothesis testing in statistics. The connections established between the levels of tolerance for errors and costs of incorrect decisions make the rough set theory practical in applications.
    Information Sciences. 02/2010;
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    Xiaohong Zhang, Yiyu Yao, Hong Yu
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    ABSTRACT: The role of topological De Morgan algebra in the theory of rough sets is investigated. The rough implication operator is introduced in strong topological rough algebra that is a generalization of classical rough algebra and a topological De Morgan algebra. Several related issues are discussed. First, the two application directions of topological De Morgan algebras in rough set theory are described, a uniform algebraic depiction of various rough set models are given. Secondly, based on interior and closure operators of a strong topological rough algebra, an implication operator (called rough implication) is introduced, and its important properties are proved. Thirdly, a rough set interpretation of classical logic is analyzed, and a new semantic interpretation of Łukasiewicz continuous-valued logic system Łuk is constructed based on rough implication. Finally, strong topological rough implication algebra (STRI-algebra for short) is introduced. The connections among STRI-algebras, regular double Stone algebras and RSL-algebras are established, and the completeness theorem of rough logic system RSL is discussed based on STRI-algebras.
    Inf. Sci. 01/2010; 180:3764-3780.
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    ABSTRACT: Fuzzy C-means (FCM) and Rough K-means (RKM) algorithms are two popular soft clustering algorithms that allow for overlapping clusters. The overlapping clusters can be useful in applications where restrictions imposed by crisp clustering that force assignment of every object to a unique cluster may not be practical. Likewise RKM and FCM, interval set representation of clusters would also generate overlapping clusters. We present and discuss the interval set K-means algorithm (IKM). This paper applies RKM, FCM and IKM algorithms for clustering web visits to an educational site. The experimental comparison highlights various features of these three soft computing algorithms.
    10th International Conference on Intelligent Systems Design and Applications, ISDA 2010, November 29 - December 1, 2010, Cairo, Egypt; 01/2010
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    ABSTRACT: We explore an extension of rough set theory based on probability theory. Lower and upper approximations, the basic ideas of rough set theory, are generalized by adding two parameters, denoted by alpha and beta. In our experiments, for different pairs of alpha and beta, we induced three types of rules: positive, boundary, and possible. The quality of these rules was evaluated using ten-fold cross validation on five data sets. The main results of our experiments are that there is no significant difference in quality between positive and possible rules and that boundary rules are the worst.
    10th International Conference on Hybrid Intelligent Systems (HIS 2010), Atlanta, GA, USA, August 23-25, 2010; 01/2010
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    ABSTRACT: In this paper we present results of an experimental comparison (in terms of an error rate) of rule sets induced by the LERS data mining system with rule sets induced using the probabilistic rough classification (PRC). As follows from our experiments, the performance of LERS (possible rules) is significantly better than the best rule sets induced by PRC with any threshold (two-tailed test, 5% significance level). Additionally, the LERS possible rule approach to rule induction is significantly better than the LERS certain rule approach (two-tailed test, 5% significance level).
    Rough Sets and Current Trends in Computing - 7th International Conference, RSCTC 2010, Warsaw, Poland, June 28-30,2010. Proceedings; 01/2010
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    ABSTRACT: Cognitive Computing (CC) is an emerging paradigm of intelligent computing theories and technologies based on cognitive informatics that implements computational intelligence by autonomous inferences and perceptions mimicking the mechanisms of the brain. The development of Cognitive Computers (cC) is centric in cognitive computing methodologies. A cC is an intelligent computer for knowledge processing as that of a conventional von Neumann computer for data processing. This paper summarizes the presentations of a set of 9 position papers presented in the ICCI'10 Panel on Cognitive Computing and Applications contributed from invited panelists who are part of the world's renowned researchers and scholars in the field of cognitive informatics and cognitive computing.
    Proceedings of the 9th IEEE International Conference on Cognitive Informatics, ICCI 2010, July 7-9, 2010, Beijing, China; 01/2010
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    Yiyu Yao
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    ABSTRACT: We review and compare two definitions of rough set approximations. One is defined by a pair of sets in the universe and the other by a pair of sets in the quotient universe. The latter definition, although less studied, is semantically superior for interpreting rule induction and is closely re-lated to granularity switching in granular computing. Numerical measures about the accuracy and quality of approximations are examined. Several semantics difficulties are commented.
    01/2010;
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    IJSSCI. 01/2010; 2:32-44.