31,603 research outputs found
Novel methods of measuring the similarity and distance between complex fuzzy sets
This thesis develops measures that enable comparisons of subjective information that is represented through fuzzy sets. Many applications rely on information that is subjective and imprecise due to varying contexts and so fuzzy sets were developed as a method of modelling uncertain data. However, making relative comparisons between data-driven fuzzy sets can be challenging. For example, when data sets are ambiguous or contradictory, then the fuzzy set models often become non-normal or non-convex, making them difficult to compare.
This thesis presents methods of comparing data that may be represented by such (complex) non-normal or non-convex fuzzy sets. The developed approaches for calculating relative comparisons also enable fusing methods of measuring similarity and distance between fuzzy sets. By using multiple methods, more meaningful comparisons of fuzzy sets are possible. Whereas if only a single type of measure is used, ambiguous results are more likely to occur.
This thesis provides a series of advances around the measuring of similarity and distance. Based on them, novel applications are possible, such as personalised and crowd-driven product recommendations. To demonstrate the value of the proposed methods, a recommendation system is developed that enables a person to describe their desired product in relation to one or more other known products. Relative comparisons are then used to find and recommend something that matches a person's subjective preferences. Demonstrations illustrate that the proposed method is useful for comparing complex, non-normal and non-convex fuzzy sets. In addition, the recommendation system is effective at using this approach to find products that match a given query
Novel methods of measuring the similarity and distance between complex fuzzy sets
This thesis develops measures that enable comparisons of subjective information that is represented through fuzzy sets. Many applications rely on information that is subjective and imprecise due to varying contexts and so fuzzy sets were developed as a method of modelling uncertain data. However, making relative comparisons between data-driven fuzzy sets can be challenging. For example, when data sets are ambiguous or contradictory, then the fuzzy set models often become non-normal or non-convex, making them difficult to compare.
This thesis presents methods of comparing data that may be represented by such (complex) non-normal or non-convex fuzzy sets. The developed approaches for calculating relative comparisons also enable fusing methods of measuring similarity and distance between fuzzy sets. By using multiple methods, more meaningful comparisons of fuzzy sets are possible. Whereas if only a single type of measure is used, ambiguous results are more likely to occur.
This thesis provides a series of advances around the measuring of similarity and distance. Based on them, novel applications are possible, such as personalised and crowd-driven product recommendations. To demonstrate the value of the proposed methods, a recommendation system is developed that enables a person to describe their desired product in relation to one or more other known products. Relative comparisons are then used to find and recommend something that matches a person's subjective preferences. Demonstrations illustrate that the proposed method is useful for comparing complex, non-normal and non-convex fuzzy sets. In addition, the recommendation system is effective at using this approach to find products that match a given query
Extending Similarity Measures of Interval Type-2 Fuzzy Sets to General Type-2 Fuzzy Sets
Similarity measures provide one of the core tools that enable reasoning about
fuzzy sets. While many types of similarity measures exist for type-1 and
interval type-2 fuzzy sets, there are very few similarity measures that enable
the comparison of general type-2 fuzzy sets. In this paper, we introduce a
general method for extending existing interval type-2 similarity measures to
similarity measures for general type-2 fuzzy sets. Specifically, we show how
similarity measures for interval type-2 fuzzy sets can be employed in
conjunction with the zSlices based general type-2 representation for fuzzy sets
to provide measures of similarity which preserve all the common properties
(i.e. reflexivity, symmetry, transitivity and overlapping) of the original
interval type-2 similarity measure. We demonstrate examples of such extended
fuzzy measures and provide comparisons between (different types of) interval
and general type-2 fuzzy measures.Comment: International Conference on Fuzzy Systems 2013 (Fuzz-IEEE 2013
Distance Measures for Reduced Ordering Based Vector Filters
Reduced ordering based vector filters have proved successful in removing
long-tailed noise from color images while preserving edges and fine image
details. These filters commonly utilize variants of the Minkowski distance to
order the color vectors with the aim of distinguishing between noisy and
noise-free vectors. In this paper, we review various alternative distance
measures and evaluate their performance on a large and diverse set of images
using several effectiveness and efficiency criteria. The results demonstrate
that there are in fact strong alternatives to the popular Minkowski metrics
Computational Approaches to Measuring the Similarity of Short Contexts : A Review of Applications and Methods
Measuring the similarity of short written contexts is a fundamental problem
in Natural Language Processing. This article provides a unifying framework by
which short context problems can be categorized both by their intended
application and proposed solution. The goal is to show that various problems
and methodologies that appear quite different on the surface are in fact very
closely related. The axes by which these categorizations are made include the
format of the contexts (headed versus headless), the way in which the contexts
are to be measured (first-order versus second-order similarity), and the
information used to represent the features in the contexts (micro versus macro
views). The unifying thread that binds together many short context applications
and methods is the fact that similarity decisions must be made between contexts
that share few (if any) words in common.Comment: 23 page
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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