Chris Cornelis

Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application

Abstract With the demand for knowledge-handling systems capable of dealing with and distinguishing between various facets of imprecision ever increasing, a clear and formal characterization of the mathematical models implementing such services is quintessential. In this paper, this task is undertaken simultaneously for the definition of implication within two settings: first, within intuitionistic fuzzy set theory and secondly, within interval-valued fuzzy set theory. By tracing these models back to the underlying lattice that they are defined on, on one hand we keep up with an important tradition of using algebraic structures for developing logical calculi (e.g. residuated lattices and MV algebras), and on the other hand we are able to expose in a clear manner the two models’ formal equivalence. This equivalence, all too often neglected in literature, we exploit to construct operators extending the notions of classical and fuzzy implication on these structures; to initiate a meaningful classification framework for the resulting operators, based on logical and extra-logical criteria imposed on them; and finally, to re(de)fine the intuititive ideas giving rise to both approaches as models of imprecision and apply them in a practical context.

Attribute selection with fuzzy decision reducts

Rough set theory provides a methodology for data analysis based on the approximation of concepts in information systems. It revolves around the notion of discernibility: the ability to distinguish between objects, based on their attribute values. It allows to infer data dependencies that are useful in the fields of feature selection and decision model construction. In many cases, however, it is more natural, and more effective, to consider a gradual notion of discernibility. Therefore, within the context of fuzzy rough set theory, we present a generalization of the classical rough set framework for data-based attribute selection and reduction using fuzzy tolerance relations. The paper unifies existing work in this direction, and introduces the concept of fuzzy decision reducts, dependent on an increasing attribute subset measure. Experimental results demonstrate the potential of fuzzy decision reducts to discover shorter attribute subsets, leading to decision models with a better coverage and with comparable, or even higher accuracy.

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.

Enhancing evolutionary instance selection algorithms by means of fuzzy rough set based feature selection

In recent years, fuzzy rough set theory has emerged as a suitable tool for performing feature selection. Fuzzy rough feature selection enables us to analyze the discernibility of the attributes, highlighting the most attractive features in the construction of classifiers. However, its results can be enhanced even more if other data reduction techniques, such as instance selection, are considered. In this work, a hybrid evolutionary algorithm for data reduction, using both instance and feature selection, is presented. A global process of instance selection, carried out by a steady-state genetic algorithm, is combined with a fuzzy rough set based feature selection process, which searches for the most interesting features to enhance both the evolutionary search process and the final preprocessed data set. The experimental study, the results of which have been contrasted through nonparametric statistical tests, shows that our proposal obtains high reduction rates on training sets which greatly enhance the behavior of the nearest neighbor classifier.

Sinha-Dougherty approach to the fuzzification of set inclusion revisited

Inclusion for fuzzy sets was first introduced by Zadeh in his seminal 1965 paper. Since it was found that the definition of inclusion was not in the true spirit of fuzzy logic, various researchers have set out to define alternative indicators of the inclusion of one fuzzy set into another. Among these alternatives, the indicator proposed by Sinha and Dougherty stands out as an intuitively appealing one, as it is built up with a strong but appropriate collection of axioms in mind. Starting from a very general expression depending on four functional parameters for such an indicator, those authors proposed conditions they claimed to be necessary and sufficient to satisfy the axioms. This paper aims to revisit this material by exposing it in a clearer way, correcting errors along the way while pinpointing some nasty pitfalls that Sinha and Dougherty overlooked. This results in a new, easier to handle and more consistent framework for the axiomatic characterization of inclusion grades for fuzzy sets, advantageous to the further development of practical applications. In the end, a link is established with Kitainiks results on the fuzzification of set inclusion, allowing amongst others the derivation of a sufficient and necessary characterization of the Sinha-Dougherty axioms.

One-and-only item recommendation with fuzzy logic techniques

Abstract Recommender systems anticipate users’ needs by suggesting items that are likely to interest them. Most existing systems employ collaborative filtering (CF) techniques, searching for regularities in the way users have rated items. While in general a successful approach, CF cannot cope well with so-called one-and-only items, that is: items of which there is only one single instance (like an event), and which as such cannot be repetitively “sold”. Typically such items are evaluated only after they have ceased being available, thereby thwarting the classical CF strategy. In this paper, we develop a conceptual framework for recommending one-and-only items. It uses fuzzy logic, which allows to reflect the graded/uncertain information in the domain, and to extend the CF paradigm, overcoming limitations of existing techniques. A possible application in the context of trade exhibition recommendation for e-government is discussed to illustrate the proposed conceptual framework.

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.

Implementing algorithms of rough set theory and fuzzy rough set theory in the R package “RoughSets”

Abstract The package RoughSets , written mainly in the R language, provides implementations of methods from the rough set theory (RST) and fuzzy rough set theory (FRST) for data modeling and analysis. It considers not only fundamental concepts (e.g., indiscernibility relations, lower/upper approximations, etc.), but also their applications in many tasks: discretization, feature selection, instance selection, rule induction, and nearest neighbor-based classifiers. The package architecture and examples are presented in order to introduce it to researchers and practitioners. Researchers can build new models by defining custom functions as parameters, and practitioners are able to perform analysis and prediction of their data using available algorithms. Additionally, we provide a review and comparison of well-known software packages. Overall, our package should be considered as an alternative software library for analyzing data based on RST and FRST.

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.