Yiyu Yao

University of Regina, Regina, Saskatchewan, Canada

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Publications (90)28.71 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
  • Yiyu Yao, Rong Fu
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    ABSTRACT: Rough set approaches to data analysis involve removing redundant attributes, redundant attribute-value pairs, and redundant rules in order to obtain a minimal set of simple and general rules. Pawlak arranges these tasks into a three-step sequential process based on a central notion of reducts. However, reducts used in different steps are defined and formulated differently. Such an inconsistency in formulation may unnecessarily affect the elegancy of the approach. Therefore, this paper introduces a generic definition of reducts of a set, uniformly defines various reducts used in rough set analysis, and examines several mathematically equivalent, but differently formulated, definitions of reducts. Each definition captures a different aspect of a reduct and their integration provides new insights.
    Transactions on Rough Sets XVI; 01/2013
  • 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
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    ABSTRACT: Cognitive informatics is a transdisciplinary enquiry of computer science, information sciences, cognitive science, and intelligence science that investigates the internal information processing mechanisms and processes of the brain and natural intelligence, as well as their engineering applications in cognitive computing. Cognitive computing is an emerging paradigm of intelligent computing methodologies and systems based on cognitive informatics that implements computational intelligence by autonomous inferences and perceptions mimicking the mechanisms of the brain. This article presents a set of collective perspectives on cognitive informatics and cognitive computing, as well as their applications in abstract intelligence, computational intelligence, computational linguistics, knowledge representation, symbiotic computing, granular computing, semantic computing, machine learning, and social computing.
    Developments in Natural Intelligence Research and Knowledge Engineering: Advancing Applications. 12/2012; 4:1-24.
  • Yiyu Yao, Liquan Zhao
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    ABSTRACT: Measurement of granularity is one of the foundational issues in granular computing. This paper investigates a class of measures of granularity of partitions. The granularity of a set is defined by a strictly monotonic increasing transformation of the cardinality of the set. The granularity of a partition is defined as the expected granularity of all blocks of the partition with respect to the probability distribution defined by the partition. Many existing measures of granularity are instances of the proposed class. New measures of granularity of partitions are also introduced.
    Information Sciences 12/2012; 213:1–13. · 3.64 Impact Factor
  • Yiyu Yao, Bingxue Yao
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    ABSTRACT: We propose a framework for the study of covering based rough set approximations. Three equivalent formulations of the classical rough sets are examined by using equivalence relations, partitions, and σ-algebras, respectively. They suggest the element based, the granule based and the subsystem based definitions of approximation operators. Covering based rough sets are systematically investigated by generalizing these formulations and definitions. A covering of universe of objects is used to generate different neighborhood operators, neighborhood systems, coverings, and subsystems of the power set of the universe. They are in turn used to define different types of generalized approximation operators. Within the proposed framework, we review and discuss covering based approximation operators according to the element, granule, and subsystem based definitions.
    Information Sciences 10/2012; 200:91–107. · 3.64 Impact Factor
  • Xiaofei Deng, Yiyu Yao
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    ABSTRACT: In a probabilistic rough set model, the positive, negative and boundary regions are associated with classification errors or uncertainty. The uncertainty is controlled by a pair of thresholds defining the three regions. The problem of searching for optimal thresholds can be formulated as the minimization of uncertainty induced by the three regions. By using Shannon entropy as a measure of uncertainty, we present an information-theoretic approach to the interpretation and determination of thresholds.
    Proceedings of the 7th international conference on Rough Sets and Knowledge Technology; 08/2012
  • Fundamenta Informaticae 01/2012; 115(2). · 0.40 Impact Factor
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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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    Dun Liu, Yiyu Yao, Tianrui Li
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    ABSTRACT: The decision-theoretic rough set model is adopted to derive a profit-based three-way approach to investment decision-making. A three-way decision is made based on a pair of thresholds on conditional probabilities. A positive rule makes a decision of investment, a negative rule makes a decision of noninvestment, and a boundary rule makes a decision of deferment. Both cost functions and revenue functions are used to calculate the required two thresholds by maximizing conditional profit with the Bayesian decision procedure. A case study of oil investment demonstrates the proposed method.
    International Journal of Computational Intelligence Systems 02/2011; 4(1):66-74. · 1.47 Impact Factor
  • 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.
    Information Sciences 01/2011; 181:1080-1096. · 3.64 Impact Factor
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    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
  • Davide Ciucci, Yiyu Yao
    Fundamenta Informaticae 01/2011; 108(3-4). · 0.40 Impact Factor
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    Yiyu Yao
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    ABSTRACT: Probabilistic rough set models are quantitative generalizations of the classical and qualitative Pawlak model by considering degrees of overlap between equivalence classes and a set to be approximated. The extensive studies, however, have not sufficiently addressed some semantic issues in a probabilistic rough set model. This paper examines two fundamental semantics-related questions. One is the interpretation and determination of the required parameters, i.e., thresholds on probabilities, for defining the probabilistic lower and upper approximations. The other is the interpretation of rules derived from the probabilistic positive, boundary and negative regions. We show that the two questions can be answered within the framework of a decision-theoretic rough set model. Parameters for defining probabilistic rough sets are interpreted and determined in terms of loss functions based on the well established Bayesian decision procedure. 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 rules makes a decision of deferment. The three-way decisions are, again, interpreted based on the loss functions. (This work is partially supported by a Discovery Grant from NSERC Canada. The author thanks the reviewers for their constructive comments.)
    Fundamenta Informaticae 01/2011; 108:249-265. · 0.40 Impact Factor
  • Yiyu Yao, Rong Fu
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    ABSTRACT: When applying rough set theory to rule learning, one commonly associates equivalence relations or partitions to a complete information table and tolerance relations or coverings to an incomplete table. Such associations are sometimes misleading.We argue that Pawlak threestep approach for data analysis indeed uses both partitions and coverings for a complete information table. A slightly different formulation of Pawlak approach is given based on the notions of attribute reducts of a classification table, attribute reducts of objects and rule reducts. Variations of Pawlak approach are examined.
    Rough Sets and Knowledge Technology - 6th International Conference, RSKT 2011, Banff, Canada, October 9-12, 2011. Proceedings; 01/2011
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    ABSTRACT: Based on classical rough set approximations, the LERS (Learning from Examples based on Rough Sets) data mining system induces two types of rules, namely, certain rules from lower approximations and possible rules from upper approximations. By relaxing the stringent requirement of the classical rough sets, one can obtain probabilistic approximations. The LERS can be easily applied to induce probabilistic positive and boundary rules from probabilistic positive and boundary regions. This paper discusses several fundamental issues related to probabilistic rule induction with LERS, including rule induction algorithm, quantitative measures associated with rules, and the rule conflict resolution method. © 2011 Wiley Periodicals, Inc. © 2011 Wiley Periodicals, Inc.
    International Journal of Intelligent Systems 01/2011; 26:518-539. · 1.42 Impact Factor
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    Yiyu Yao, Jigang Luo
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    ABSTRACT: A top-down, step-wise progressive computing model is presented as a mode of granular computing. Based on a multilevel granular structure, progressive computing explores a sequence of refinements from coarser information granulation to finer information granulation. A basic progressive computing algorithm is introduced. Examples of progressive computing are provided.
    Rough Sets and Knowledge Technology - 6th International Conference, RSKT 2011, Banff, Canada, October 9-12, 2011. Proceedings; 01/2011
  • Article: Preface.
    Davide Ciucci, Yiyu Yao
    Fundam. Inform. 01/2011; 108.
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    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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    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;