Martine De Cock

Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge

: Just like rough set theory, fuzzy set theory addresses the topic of dealing with imperfect knowledge. Recent investigations have shown how both theories can be combined into a more flexible, more expressive framework for modelling and processing incomplete information in information systems. At the same time, intuitionistic fuzzy sets have been proposed as an attractive extension of fuzzy sets, enriching the latter with extra features to represent uncertainty (on top of vagueness). Unfortunately, the various tentative definitions of the concept of an ‘intuitionistic fuzzy rough set’ that were raised in their wake are a far cry from the original objectives of rough set theory. We intend to fill an obvious gap by introducing a new definition of intuitionistic fuzzy rough sets, as the most natural generalization of Pawlaks original concept of rough sets.

Gradual trust and distrust in recommender systems

Trust networks among users of a recommender system (RS) prove beneficial to the quality and amount of the recommendations. Since trust is often a gradual phenomenon, fuzzy relations are the pre-eminent tools for modeling such networks. However, as current trust-enhanced RSs do not work with the notion of distrust, they cannot differentiate unknown users from malicious users, nor represent inconsistency. These are serious drawbacks in large networks where many users are unknown to each other and might provide contradictory information. In this paper, we advocate the use of a trust model in which trust scores are (trust,distrust)-couples, drawn from a bilattice that preserves valuable trust provenance information including gradual trust, distrust, ignorance, and inconsistency. We pay particular attention to deriving trust information through a trusted third party, which becomes especially challenging when also distrust is involved.

Ranking Approaches for Microblog Search

Ranking microblogs, such as tweets, as search results for a query is challenging, among other things because of the sheer amount of microblogs that are being generated in real time, as well as the short length of each individual microblog. In this paper, we describe several new strategies for ranking microblogs in a real-time search engine. Evaluating these ranking strategies is non-trivial due to the lack of a publicly available ground truth validation dataset. We have therefore developed a framework to obtain such validation data, as well as evaluation measures to assess the accuracy of the proposed ranking strategies. Our experiments demonstrate that it is beneficial for microblog search engines to take into account social network properties of the authors of microblogs in addition to properties of the microblog itself.

Trust and Recommendations

Recommendation technologies and trust metrics constitute the two pillars of trust-enhanced recommender systems. We discuss and illustrate the basic trust concepts such as trust and distrust modeling, propagation and aggregation. These concepts are needed to fully grasp the rationale behind the trust-enhanced recommender techniques that are discussed in the central part of the chapter, which focuses on the application of trust metrics and their operators in recommender systems. We explain the benefits of using trust in recommender algorithms and give an overview of state-of-the-art approaches for trust-enhanced recommender systems. Furthermore, we explain the details of three well-known trust-based systems and provide a comparative analysis of their performance. We conclude with a discussion of some recent developments and open challenges, such as visualizing trust relationships in a recommender system, alleviating the cold start problem in a trust network of a recommender system, studying the effect of involving distrust in the recommendation process, and investigating the potential of other types of social relationships.

On (un)suitable fuzzy relations to model approximate equality

In this paper we state that fuzzy equivalence relations in general are not suitable to model approximate equality, since then the notion of transitivity is counter-intuitive. To substantiate this we investigate some of the undesirable results caused by transitivity, among other things in the case of approximate reasoning. We then introduce a new framework to model approximate equality, i.e. the concept of a pseudometric based resemblance relation. We go into the properties of this new kind of fuzzy relation and illustrate it by means of some examples.

Openings and closures of fuzzy preorderings: theoretical basics and applications to fuzzy rule-based systems

The purpose of this paper is two-fold. Firstly, a general concept of closedness of fuzzy sets under fuzzy preorderings is proposed and investigated along with the corresponding opening and closure operators. Secondly, the practical impact of this notion is demonstrated by applying it to the analysis of ordering-based modifiers.

Spatial reasoning in a fuzzy region connection calculus

Although the region connection calculus (RCC) offers an appealing framework for modelling topological relations, its application in real-world scenarios is hampered when spatial phenomena are affected by vagueness. To cope with this, we present a generalization of the RCC based on fuzzy set theory, and discuss how reasoning tasks such as satisfiability and entailment checking can be cast into linear programming problems. We furthermore reveal that reasoning in our fuzzy RCC is NP-complete, thus preserving the computational complexity of reasoning in the RCC, and we identify an important tractable subfragment. Moreover, we show how reasoning tasks in our fuzzy RCC can also be reduced to reasoning tasks in the original RCC. While this link with the RCC could be exploited in practical reasoning algorithms, we mainly focus on the theoretical consequences. In particular, using this link we establish a close relationship with the Egg-Yolk calculus, and we demonstrate that satisfiable knowledge bases can be realized by fuzzy regions in any dimension.

An introduction to fuzzy answer set programming

In this paper we show how the concepts of answer set programming and fuzzy logic can be successfully combined into the single framework of fuzzy answer set programming (FASP). The framework offers the best of both worlds: from the answer set semantics, it inherits the truly declarative non-monotonic reasoning capabilities while, on the other hand, the notions from fuzzy logic in the framework allow it to step away from the sharp principles used in classical logic, e.g., that something is either completely true or completely false. As fuzzy logic gives the user great flexibility regarding the choice for the interpretation of the notions of negation, conjunction, disjunction and implication, the FASP framework is highly configurable and can, e.g., be tailored to any specific area of application. Finally, the presented framework turns out to be a proper extension of classical answer set programming, as we show, in contrast to other proposals in the literature, that there are only minor restrictions one has to demand on the fuzzy operations used, in order to be able to retrieve the classical semantics using FASP.

Trust- and Distrust-Based Recommendations for Controversial Reviews

The paper is discussing well-known trust enhanced information filtering techniques for recommending controversial reviews by the recommender systems.

Temporal reasoning about fuzzy intervals

Traditional approaches to temporal reasoning assume that time periods and time spans of events can be accurately represented as intervals. Real-world time periods and events, on the other hand, are often characterized by vague temporal boundaries, requiring appropriate generalizations of existing formalisms. This paper presents a framework for reasoning about qualitative and metric temporal relations between vague time periods. In particular, we show how several interesting problems, like consistency and entailment checking, can be reduced to reasoning tasks in existing temporal reasoning frameworks. We furthermore demonstrate that all reasoning tasks of interest are NP-complete, which reveals that adding vagueness to temporal reasoning does not increase its computational complexity. To support efficient reasoning, a large tractable subfragment is identified, among others, generalizing the well-known ORD Horn subfragment of the Interval Algebra (extended with metric constraints).