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

Using entropy-based local weighting to improve similarity assessment

This paper enhances and analyses the power of local weighted similarity measures. The paper proposes a new entropy-based local weighting algorithm to be used in similarity assessment to improve the performance of the CBR retrieval task. It has been carried out a comparative analysis of the performance of unweighted similarity measures, global weighted similarity measures, and local weighting similarity measures. The testing has been done using several similarity measures, and some data sets from the UCI Machine Learning Database Repository and other environmental databases.Postprint (published version

Fuzzy audio similarity measures based on spectrum histograms and fluctuation patterns

Spectrum histograms and fluctuation patterns are representations of audio fragments. By comparing these representations, we can determine the similarity between the corresponding fragments. Traditionally, this is done using the Euclidian distance. We propose fuzzy similarity measures as an alternative. First we introduce some well-known fuzzy similarity measures, together with certain properties that can be desirable or useful in practice. In particular we present several forms of restrictability, which allow to reduce the computation time in practical applications. Next, we show that fuzzy similarity measures can be used to compare spectrum histograms and fluctuation patterns. Finally, we describe some experimental observations for this fuzzy approach of constructing audio similarity measures

Similarity measures for mid-surface quality evaluation

Mid-surface models are widely used in engineering analysis to simplify the analysis of thin-walled parts, but it can be difficult to ensure that the mid-surface model is representative of the solid part from which it was generated. This paper proposes two similarity measures that can be used to evaluate the quality of a mid-surface model by comparing it to a solid model of the same part. Two similarity measures are proposed; firstly a geometric similarity evaluation technique based on the Hausdorff distance and secondly a topological similarity evaluation method which uses geometry graph attributes as the basis for comparison. Both measures are able to provide local and global similarity evaluation for the models. The proposed methods have been implemented in a software demonstrator and tested on a selection of representative models. They have been found to be effective for identifying geometric and topological errors in mid-surface models and are applicable to a wide range of practical thin-walled designs

Distance and Similarity Measures for Soft Sets

In [P. Majumdar, S. K. Samanta, Similarity measure of soft sets, New Mathematics and Natural Computation 4(1)(2008) 1-12], the authors use matrix representation based distances of soft sets to introduce matching function and distance based similarity measures. We first give counterexamples to show that their Definition 2.7 and Lemma 3.5(3) contain errors, then improve their Lemma 4.4 making it a corllary of our result. The fundamental assumption of Majumdar et al has been shown to be flawed. This motivates us to introduce set operations based measures. We present a case (Example 28) where Majumdar-Samanta similarity measure produces an erroneous result but the measure proposed herein decides correctly. Several properties of the new measures have been presented and finally the new similarity measures have been applied to the problem of financial diagnosis of firms.Comment: 14 pages, accepted manuscript, to appear in New Mathematics and Natural Computatio

Similarity Measures for Clustering SNP Data

The issue of suitable similarity measures for a particular kind of genetic data – so called SNP data – arises from the GENICA (Interdisciplinary Study Group on Gene Environment Interaction and Breast Cancer in Germany) case-control study of sporadic breast cancer. The GENICA study aims to investigate the influence and interaction of single nucleotide polymorphic (SNP) loci and exogenous risk factors. A single nucleotide polymorphism is a point mutation that is present in at least 1 % of a population. SNPs are the most common form of human genetic variations. In particular, we consider 65 SNP loci and 2 insertions of longer sequences in genes involved in the metabolism of hormones, xenobiotics and drugs as well as in the repair of DNA and signal transduction. Assuming that these single nucleotide changes may lead, for instance, to altered enzymes or to a reduced or enhanced amount of the original enzymes – with each alteration alone having minor effects – we aim to detect combinations of SNPs that under certain environmental conditions increase the risk of sporadic breast cancer. The search for patterns in the present data set may be performed by a variety of clustering and classification approaches. We consider here the problem of suitable measures of proximity of two variables or subjects as an indispensable basis for a further cluster analysis. Generally, clustering approaches are a useful tool to detect structures and to generate hypothesis about potential relationships in complex data situations. Searching for patterns in the data there are two possible objectives: the identification of groups of similar objects or subjects or the identification of groups of similar variables within the whole or within subpopulations. Comparing the individual genetic profiles as well as comparing the genetic information across subpopulations we discuss possible choices of similarity measures, in particular similarity measures based on the counts of matches and mismatches. New matching coefficients are introduced with a more flexible weighting scheme to account for the general problem of the comparison of SNP data: The large proportion of homozygous reference sequences relative to the homo- and heterozygous SNPs is masking the accordances and differences of interest. --GENICA,single nucleotide polymorphism (SNP),sporadic breast cancer,similarity,Matching Coefficient,Flexible Matching Coefficient