Theory of fuzzy integrals and its applications

Most real systems consist of a large number of interacting, multi-typed components, while most contemporary researches model them as homogeneous information networks, without distinguishing different types of objects and links in the networks. Recently, more and more researchers begin to consider these interconnected, multi-typed data as heterogeneous information networks, and develop structural analysis approaches by leveraging the rich semantic meaning of structural types of objects and links in the networks. Compared to widely studied homogeneous information network, the heterogeneous information network contains richer structure and semantic information, which provides plenty of opportunities as well as a lot of challenges for data mining. In this paper, we provide a survey of heterogeneous information network analysis. We will introduce basic concepts of heterogeneous information network analysis, examine its developments on different data mining tasks, discuss some advanced topics, and point out some future research directions.

A Survey of Heterogeneous Information Network Analysis

In this paper, a model for group decision-making is proposed and defined in a linguistic context. A multiperson multicriteria decision problem is considered, in which a group of experts is involved in the evaluation of the performances of a set of alternatives with respect to a predefined set of criteria. The objective is to evaluate a consensual judgement and a consensus degree on each alternative. Both the experts' evaluations of the alternatives and the degree of consensus are expressed linguistically. A "soft" consensus degree referred to a fuzzy majority of the experts is proposed based on the concept of linguistic quantifier. The entire process is defined in a linguistic domain and modeled within fuzzy set theory by ordered weighted average (OWA) operators.

A linguistic modeling of consensus in group decision making based on OWA operators

Analyzing Social Media Networks with NodeXL: Insights from a Connected World

Most real systems consist of a large number of interacting, multi-typed components, while most contemporary researches model them as homogeneous networks, without distinguishing different types of objects and links in the networks. Recently, more and more researchers begin to consider these interconnected, multi-typed data as heterogeneous information networks, and develop structural analysis approaches by leveraging the rich semantic meaning of structural types of objects and links in the networks. Compared to widely studied homogeneous network, the heterogeneous information network contains richer structure and semantic information, which provides plenty of opportunities as well as a lot of challenges for data mining. In this paper, we provide a survey of heterogeneous information network analysis. We will introduce basic concepts of heterogeneous information network analysis, examine its developments on different data mining tasks, discuss some advanced topics, and point out some future research directions.

Many propositions to extend database management systems have been made in the last decade. Some of them aim to support a wider range of queries involving fuzzy predicates and this paper focuses on the evaluation of a particular subset of queries, namely those using fuzzy quantified predicates. More precisely, we consider the queries which can be represented by a statement of the type “Q X are A” where Q is a fuzzy quantifier, X a set of items of the database and A a fuzzy predicate. The evaluation of this kind of statement is considered according to the propositions of Zadeh, Prade and Yager. We show that Prade and Yager’s interpretation of “Q X are A”, when Q is a monotonous quantifier, are respectively equivalent to a Sugeno and a Choquet fuzzy integral. Thanks to some properties of an α-cut and of fuzzy integrals, we are able to show that the evaluation of these queries, according to these three propositions, can be significantly improved with respect to a naive strategy based on the exhaustive scan of set X.

Quantified Statements and Database Fuzzy Querying

An evidential influence measure for Twitter was proposed.Many influence aspects were considered in the proposed measure.Two evidential influence maximization models were introduced.The performance of the proposed models compared to existing ones was shown. Influence maximization is the problem of selecting a set of influential users in the social network. Those users could adopt the product and trigger a large cascade of adoptions through the "word of mouth" effect. In this paper, we propose two evidential influence maximization models for Twitter social network. The proposed approach uses the theory of belief functions to estimate users influence. Furthermore, the proposed influence estimation measure fuses many influence aspects in Twitter, like the importance of the user in the network structure and the popularity of user's tweets (messages). In our experiments, we compare the proposed solutions to existing ones and we show the performance of our models.

Two evidential data based models for influence maximization in Twitter

This paper presents an extension of relational algebra suited to the handling of bipolar concepts. The type of queries considered involves two parts: a first one which expresses a (possibly flexible) constraint, and a second one that corresponds to a (possibly flexible) wish. The framework considered is that of bipolar fuzzy relations where each tuple is associated with a pair of degrees in the unit interval.

Extending relational algebra to handle bipolarity

Previously studied fuzzy bipolar conditions of type ”and if possible” are made of a mandatory condition c and an optional condition w. They allow expressing complex preferences of a conjunctive nature. We define in this paper, a new kind of fuzzy bipolar conditions of the form ”or else” which express complex preferences of a disjunctive nature. We show that the ”or else” form can be used as a negation operator of the ”and if possible” form and vice versa. We also show that these both forms are compatible and, therefore, fuzzy bipolar conditions of both types can be used together in the same bipolar query.

https://hal.archives-ouvertes.fr/hal-00655889/document

Fuzzy bipolar conditions of type ”or else”

The expression of user preferences into queries addressed to a relational database management system allows to obtain more appropriate answers. In this context, it is possible to consider fuzzy bipolar conditions which are made of two parts: i) a fuzzy constraint to represent a mandatory requirement, ii) a fuzzy wish to represent an optional requirement. Fuzzy constraints and fuzzy wishes express user preferences and are defined by fuzzy sets. This article is a first attempt to extend the relational algebra and the SQL language to bipolar fuzzy conditions.

Ludovic Liétard

Papers

Quantified Statements and Database Fuzzy Querying

Two evidential data based models for influence maximization in Twitter

Extending relational algebra to handle bipolarity

Fuzzy bipolar conditions of type ”or else”

On the extension of SQL to fuzzy bipolar conditions