Churn-Jung Liau

Belief, information acquisition, and trust in multi-agent systems: a modal logic formulation

In this paper, we consider the influence of trust on the assimilation of acquired information into an agents belief. By use of modal logic, we semantically and axiomatically characterize the relationship among belief, information acquisition and trust. The belief and information acquisition operators are respectively represented by KD45 and KD normal modalities, whereas trust is denoted by a modal operator with minimal semantics. One characteristic axiom of the basic system is if agent i believes that agent j has told him the truth of p and he trusts the judgement of j on p, then he will also believe p. In addition to the basic system, some variants and further axioms for trust and information acquisition are also presented to show the expressive richness of the logic. The applications of the logic to computer security and database reasoning are also suggested by its connection with some previous works.

Fuzzy Interpolative Reasoning for Sparse Fuzzy-Rule-Based Systems Based on the Areas of Fuzzy Sets

Fuzzy interpolative reasoning is an inference technique for dealing with the sparse rules problem in sparse fuzzy-rule-based systems. In this paper, we present a new fuzzy interpolative reasoning method for sparse fuzzy-rule-based systems based on the areas of fuzzy sets. The proposed method uses the weighted average method to infer the fuzzy interpolative reasoning results and has the following advantages: (1) it holds the normality and the convexity of the fuzzy interpolative reasoning result, (2) it can deal with fuzzy interpolative reasoning with complicated membership functions, (3) it can deal with fuzzy interpolative reasoning when the fuzzy sets of the antecedents and the consequents of the fuzzy rules have different kinds of membership functions, (4) it can handle fuzzy interpolative reasoning with multiple antecedent variables, (5) it can handle fuzzy interpolative reasoning with multiple fuzzy rules, and (6) it can handle fuzzy interpolative reasoning with logically consistent properties with respect to the ratios of fuzziness. We use some examples to compare the fuzzy interpolative reasoning results of the proposed method with those of the existing fuzzy interpolative reasoning methods. In terms of the six evaluation indices, the experimental results show that the proposed method performs more reasonably than the existing methods. The proposed method provides us a useful way to deal with fuzzy interpolative reasoning in sparse fuzzy-rule-based systems.

Privacy-Preserving Collaborative Recommender Systems

Collaborative recommender systems use various types of information to help customers find products of personalized interest. To increase the usefulness of collaborative recommender systems in certain circumstances, it could be desirable to merge recommender system databases between companies, thus expanding the data pool. This can lead to privacy disclosure hazards during the merging process. This paper addresses how to avoid privacy disclosure in collaborative recommender systems by comparing with major cryptology approaches and constructing a more efficient privacy-preserving collaborative recommender system based on the scalar product protocol.

Multicriteria fuzzy decision making based on interval-valued intuitionistic fuzzy sets

In this paper, we present a new method for multicriteria fuzzy decision making based on interval-valued intuitionistic fuzzy sets, where interval-valued intuitionistic fuzzy values are used to represent evaluating values of the decision-maker with respect to alternatives. First, we propose a new method for ranking interval-valued intuitionistic fuzzy values. Based on the proposed fuzzy ranking method of interval-valued intuitionistic fuzzy values, we propose a new method for multicriteria fuzzy decision making. The proposed multicriteria fuzzy decision making method outperforms Yes method (2009) due to the fact that the proposed method can overcome the drawback of Yes method (2009), where the drawback of Yes method is that it can not distinguish the ranking order between alternatives in some situations. The proposed method provides us with a useful way for dealing with multicriteria fuzzy decision making problems based on interval-valued intuitionistic fuzzy sets.

Granular Computing Based on Rough Sets, Quotient Space Theory, and Belief Functions

A model of granular computing (GrC) is proposed by reformulating, re-interpreting, and combining results from rough sets, quotient space theory, and belief functions. Two operations, called zooming-in and zooming-out operations, are used to study connections between the elements of a universe and the elements of a granulated universe, as well as connections between computations in the two universes. The operations are studied with respect to multi-level granulation structures.

Dominance-based fuzzy rough set analysis of uncertain and possibilistic data tables

In this paper, we propose a dominance-based fuzzy rough set approach for the decision analysis of a preference-ordered uncertain or possibilistic data table, which is comprised of a finite set of objects described by a finite set of criteria. The domains of the criteria may have ordinal properties that express preference scales. In the proposed approach, we first compute the degree of dominance between any two objects based on their imprecise evaluations with respect to each criterion. This results in a valued dominance relation on the universe. Then, we define the degree of adherence to the dominance principle by every pair of objects and the degree of consistency of each object. The consistency degrees of all objects are aggregated to derive the quality of the classification, which we use to define the reducts of a data table. In addition, the upward and downward unions of decision classes are fuzzy subsets of the universe. Thus, the lower and upper approximations of the decision classes based on the valued dominance relation are fuzzy rough sets. By using the lower approximations of the decision classes, we can derive two types of decision rules that can be applied to new decision cases.

Positional Analysis in Fuzzy Social Networks

Social network analysis is a methodology used extensively in social and behavioral sciences, as well as in political science, economics, organization theory, and industrial engineering. Positional analysis of a social network aims to find similarities between actors in the network. One of the the most studied notions in the positional analysis of social networks is regular equivalence. According to Borgatti and Everett, two actors are regularly equivalent if they are equally related to equivalent others. In recent years, fuzzy social networks have also received considerable attention because they can represent both the qualitative relationship and the degrees of interaction between actors. In this paper, we generalize the notion of regular equivalence to fuzzy social networks based on two alternative definitions of regular equivalence. While these two definitions are equivalent for social networks, they induce different generalizations for fuzzy social networks. The first generalization, called regular similarity, is based on the characterization of regular equivalence as an equivalence relation that commutes with the underlying social relations. The regular similarity is then a fuzzy binary relation that specifies the degree of similarity between actors in the social network. The second generalization, called generalized regular equivalence, is based on the definition of role assignment or coloring. A role assignment (resp. coloring) is a mapping from the set of actors to a set of roles (resp. colors). The mapping is regular if actors assigned to the same role have the same roles in their neighborhoods. Consequently, generalized regular equivalence is an equivalence relation that can determine the role partition of the actors in a fuzzy social network.

Possibilistic reasoning—a mini-survey and uniform semantics

Abstract In this paper, we survey some quantitative and qualitative approaches to uncertainty management based on possibility theory and present a logical framework to integrate them. The semantics of the logic is based on the Dempsters rule of conditioning for possibility theory. It is then shown that classical modal logic, conditional logic, possibilistic logic, quantitative modal logic and qualitative possibilistic logic are all sublogics of the presented logical framework. In this way, we can formalize and generalize some well-known results about possibilistic reasoning in a uniform semantics. Moreover, our uniform framework is applicable to nonmonotonic reasoning, approximate consequence relation formulation, and partial consistency handling.

Integration of fuzzy cluster analysis and kernel density estimation for tracking typhoon trajectories in the Taiwan region

Highlights? Offer an alternative way to explore the spatial patterns of typhoon tracks. ? Cluster methodologies show that typhoon centers pass through Taiwan from the south-east to the north-west. ? Provide planners to understand the hotspot areas of typhoon tracks and adjust disaster management efforts. Increasing our understanding of typhoon movements remains a priority in the western North Pacific. In this study, the trajectories of typhoons that affected Taiwan between 1986 and 2010 are used for clustering, where each trajectory consists of 6-hourly latitude-longitude positions over two days. We compare the performance of four statistical clustering methods, namely, k-means clustering, fuzzy c-means (FCM) clustering, hierarchical clustering, and normalized cut techniques. The results show that the FCM technique provides sufficient cluster efficiency with a relatively high degree of goodness of fit. FCM identifies six clusters according to the minimum coefficients of variation (CV). The hotspots of the typhoon centers in each cluster are determined by kernel density estimation (KDE). Moreover, the typhoon track belongs to six clusters with different membership degrees in FCM. The typhoon track density map is estimated by combining the KDE hotspot maps associated with the FCM weights. The information could be used in planning for disaster management.

Data Mining: Foundations and Practice

This book contains valuable studies in data mining from both foundational and practical perspectives. The foundational studies of data mining may help to lay a solid foundation for data mining as a scientific discipline, while the practical studies of data mining may lead to new data mining paradigms and algorithms. The foundational studies contained in this book focus on a broad range of subjects, including conceptual framework of data mining, data preprocessing and data mining as generalization, probability theory perspective on fuzzy systems, rough set methodology on missing values, inexact multiple-grained causal complexes, complexity of the privacy problem, logical framework for template creation and information extraction, classes of association rules, pseudo statistical independence in a contingency table, and role of sample size and determinants in granularity of contingency matrix. The practical studies contained in this book cover different fields of data mining, including rule mining, classification, clustering, text mining, Web mining, data stream mining, time series analysis, privacy preservation mining, fuzzy data mining, ensemble approaches, and kernel based approaches. We believe that the works presented in this book will encourage the study of data mining as a scientific field and spark collaboration among researchers and practitioners.