The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

Crime continues to remain a severe threat to all communities and nations across the globe alongside the sophistication in technology and processes that are being exploited to enable highly complex criminal activities. Data mining, the process of uncovering hidden information from Big Data, is now an important tool for investigating, curbing and preventing crime and is exploited by both private and government institutions around the world. The primary aim of this paper is to provide a concise review of the data mining applications in crime. To this end, the paper reviews over 100 applications of data mining in crime, covering a substantial quantity of research to date, presented in chronological order with an overview table of many important data mining applications in the crime domain as a reference directory. The data mining techniques themselves are briefly introduced to the reader and these include entity extraction, clustering, association rule mining, decision trees, support vector machines, naive Bayes rule, neural networks and social network analysis amongst others. © 2016 Wiley Periodicals, Inc. Statistical Analysis and Data Mining: The ASA Data Science Journal, 2016

A review of data mining applications in crime

Fuzzy sets and systems: Theory and applications: Didier DUBOIS and Henri PRADE Academic Press, New York, 1980, xvi + 393 pages, $56.50

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.

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Positional Analysis in Fuzzy Social Networks

The linguistic summarization and the interpretability, scalability of fuzzy representations of multilevel semantic structures of word-domains

In this paper, fuzzy theory has been applied to social network analysis (SNA). Social network analysis models meaningful relations that exist between entities as graph. These entities may be people, events, organizations, symbols in text, sounds in verbalizations, nations of the world and so on. However, the fuzzy graph can be very huge and thus the ability to arrive at meaningful conclusions in a timely fashion may be quite difficult. With this in mind, a method to consolidate the information content of the fuzzy graph is proposed. Since none of the existing fuzzy binary operations meet the requirements, a new fuzzy binary operation called consolidation operation is also introduced.

S.T. Sarasamma

Papers

Data Mining Through Fuzzy Social Network Analysis