3,343 research outputs found
A kernel-based framework for learning graded relations from data
Driven by a large number of potential applications in areas like
bioinformatics, information retrieval and social network analysis, the problem
setting of inferring relations between pairs of data objects has recently been
investigated quite intensively in the machine learning community. To this end,
current approaches typically consider datasets containing crisp relations, so
that standard classification methods can be adopted. However, relations between
objects like similarities and preferences are often expressed in a graded
manner in real-world applications. A general kernel-based framework for
learning relations from data is introduced here. It extends existing approaches
because both crisp and graded relations are considered, and it unifies existing
approaches because different types of graded relations can be modeled,
including symmetric and reciprocal relations. This framework establishes
important links between recent developments in fuzzy set theory and machine
learning. Its usefulness is demonstrated through various experiments on
synthetic and real-world data.Comment: This work has been submitted to the IEEE for possible publication.
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A Declarative Semantics for CLP with Qualification and Proximity
Uncertainty in Logic Programming has been investigated during the last
decades, dealing with various extensions of the classical LP paradigm and
different applications. Existing proposals rely on different approaches, such
as clause annotations based on uncertain truth values, qualification values as
a generalization of uncertain truth values, and unification based on proximity
relations. On the other hand, the CLP scheme has established itself as a
powerful extension of LP that supports efficient computation over specialized
domains while keeping a clean declarative semantics. In this paper we propose a
new scheme SQCLP designed as an extension of CLP that supports qualification
values and proximity relations. We show that several previous proposals can be
viewed as particular cases of the new scheme, obtained by partial
instantiation. We present a declarative semantics for SQCLP that is based on
observables, providing fixpoint and proof-theoretical characterizations of
least program models as well as an implementation-independent notion of goal
solutions.Comment: 17 pages, 26th Int'l. Conference on Logic Programming (ICLP'10
Preference Modelling
This paper provides the reader with a presentation of preference modelling fundamental notions as well as some recent results in this field. Preference modelling is an inevitable step in a variety of fields: economy, sociology, psychology, mathematical programming, even medicine, archaeology, and obviously decision analysis. Our notation and some basic definitions, such as those of binary relation, properties and ordered sets, are presented at the beginning of the paper. We start by discussing different reasons for constructing a model or preference. We then go through a number of issues that influence the construction of preference models. Different formalisations besides classical
logic such as fuzzy sets and non-classical logics become necessary. We then present different types of preference structures reflecting the behavior of a decision-maker: classical, extended and valued ones. It is relevant to have a numerical representation of preferences: functional representations,
value functions. The concepts of thresholds and minimal representation are also introduced in this section. In section 7, we briefly explore the concept of deontic logic (logic of preference) and other formalisms associated with "compact representation of preferences" introduced for special purpoes. We end the paper with some concluding remarks
Existence of Order-Preserving Functions for Nontotal Fuzzy Preference Relations under Decisiveness
Looking at decisiveness as crucial, we discuss the existence of an order-preserving function
for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation.
We further present conditions for the existence of an upper semicontinuous order-preserving function
for a fuzzy binary relation on a crisp topological space
Class Association Rules Mining based Rough Set Method
This paper investigates the mining of class association rules with rough set
approach. In data mining, an association occurs between two set of elements
when one element set happen together with another. A class association rule set
(CARs) is a subset of association rules with classes specified as their
consequences. We present an efficient algorithm for mining the finest class
rule set inspired form Apriori algorithm, where the support and confidence are
computed based on the elementary set of lower approximation included in the
property of rough set theory. Our proposed approach has been shown very
effective, where the rough set approach for class association discovery is much
simpler than the classic association method.Comment: 10 pages, 2 figure
A geometric examination of majorities based on difference in support
Reciprocal preferences have been introduced in the literature of social choice theory in order to deal with preference intensities. They allow individuals to show preference intensities in the unit interval among each pair of options. In this framework, majority based on difference in support can be used as a method of aggregation of individual preferences into a collective preference: option a is preferred to option b if the sum of the intensities for a exceeds the aggregated intensity of b in a threshold given by a real number located between 0 and the total number of voters. Based on a three dimensional geometric approach, we provide a geometric analysis of the non transitivity of the collective preference relations obtained by majority rule based on difference in support. This aspect is studied by assuming that each individual reciprocal preference satisfies a g-stochastic transitivity property, which is stronger than the usual notion of transitivit
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