A Fast Multilevel Fuzzy Transform Image Compression Method

We present a fast algorithm that improves on the performance of the multilevel fuzzy transform image compression method. The multilevel F-transform (for short, MF-tr) algorithm is an image compression method based on fuzzy transforms that, compared to the classic fuzzy transform (F-transform) image compression method, has the advantage of being able to reconstruct an image with the required quality. However, this method can be computationally expensive in terms of execution time since, based on the compression ratio used, different iterations may be necessary in order to reconstruct the image with the required quality. To solve this problem, we propose a fast variation of the multilevel F-transform algorithm in which the optimal compression ratio is found in order to reconstruct the image in as few iterations as possible. Comparison tests show that our method reconstructs the image in at most half of the CPU time used by the MF-tr algorithm

A New Geospatial Model Integrating a Fuzzy Rule-Based System in a GIS Platform to Partition a Complex Urban System in Homogeneous Urban Contexts

Here, we present a new unsupervised method aimed at obtaining a partition of a complex urbansysteminhomogenousurbanareas,calledurbancontexts.Ourmodelintegratesspatialanalysis processes and a fuzzy rule-based system applied to manage the knowledge of domain experts; it is implemented using a GIS platform. The area of study is initially partitioned in microzones, homogeneous portions of the urban system, which are the atomic reference elements for the census data. With the contribution of domain experts, we identify the physical, morphological, environmental, and socio-economic indicators needed to identify synthetic characteristics of urban contexts and create the fuzzy rule set necessary for determining the type of urban context. We implement the set of spatial analysis processes required to calculate the indicators for the microzones and apply a Mamdani fuzzy rule system to classify the microzones. Finally, the partition of the area of study in urban contexts is obtained by dissolving continuous microzones belonging to the same type of urban context. Tests are performed on the Municipality of Pozzuoli (Naples, Italy); the reliability of the out model is measured by comparing the results with the ones obtained through a detailed analysis

Fuzzy-Based Spatiotemporal Hot Spot Intensity and Propagation—An Application in Crime Analysis

Cluster-based hot spot detection is applied in many disciplines to analyze the locations, concentrations, and evolution over time for a phenomenon occurring in an area of study. The hot spots consist of areas within which the phenomenon is most present; by detecting and monitoring the presence of hot spots in different time steps, it is possible to study their evolution over time. One of the most prominent problems in hot spot analysis occurs when measuring the intensity of a phenomenon in terms of the presence and impact on an area of study and evaluating its evolution over time. In this research, we propose a hot spot analysis method based on a fuzzy cluster hot spot detection algorithm, which allows us to measure the incidence of hot spots in the area of study. We analyze its variation over time, and in order to evaluate its reliability we use a well-known fuzzy entropy measure that was recently applied to measure the reliability of hot spots by executing fuzzy clustering algorithms. We apply this method in crime analysis of the urban area of the City of London, using a dataset of criminal events that have occurred since 2011, published by the City of London Police. The obtained results show a decrease in the frequency of all types of criminal events over the entire area of study in recent years

A Fuzzy Entropy-Based Thematic Classification Method Aimed at Improving the Reliability of Thematic Maps in GIS Environments

Thematic maps of spatial data are constructed by using standard thematic classification methods that do not allow management of the uncertainty of classification and, consequently, eval uation of the reliability of the resulting thematic map. We propose a novel fuzzy-based thematic classification method applied to construct thematic maps in Geographical Information Systems. An initial fuzzy partition of the domain of the features of the spatial dataset is constructed using triangular fuzzy numbers; our method finds an optimal fuzzy partition evaluating the fuzziness of the fuzzy sets by using a fuzzy entropy measure. An assessment of the reliability of the final thematic map is performed according to the fuzziness of the fuzzy sets. We implement our method on a GIS framework, testing it on various vector and image spatial datasets. The results of these tests confirm that our thematic classification method provide thematic maps with a higher reliability with respect to that obtained through fuzzy partitions constructed by expert users

A GIS-Based Fuzzy Multiclassification Framework Applied for Spatiotemporal Analysis of Phenomena in Urban Contexts

In this research, we propose a GIS-based framework implementing a fuzzy-based document classification method aimed at classifying urban areas by the type of criticality inherent or specific problems highlighted by citizens. The urban study area is divided into subzones; for each subzone, the reports of citizens relating to specific criticalities are analyzed and documents are created, and collected by topic and by temporal extension. The framework implements a model applied to the multiclassification of the documents in which the topic to be analyzed is divided into categories and a dictionary of terms connected to each category is built to measure the relevance of the category in the document. The framework produces, for each time frame, thematic maps of the relevance of a category in a time frame in which a subzone of the study area is classified based on the classification of the corresponding document. The framework was experimented on to analyze and monitor over time the relevance of disruptions detected by users in entities that make up urban areas, such as: roads, private buildings, public buildings and transport infrastructures, lighting networks, and public green areas. The study area is the city of Naples (Italy), partitioned in ten municipalities. The results of the tests show that the proposed framework can be a support for decision makers in analyzing the relevance of categories into which a topic is partitioned and their evolution over time

Max-Min Fuzzy Relation Equations for a Problem of Spatial Analysis

We implement an algorithm that uses a system of max-min fuzzy  relation equations (SFRE) for solving a problem of spatial analysis. We integrate this algorithm in a Geographical information Systems (GIS) tool. We apply our  process to determine the symptoms after that an expert sets the SFRE with the values of the impact coefficients related to some parameters of a geographic zone under study. We also define an index of evaluation about the reliability of the results

Attribute dependency data analysis for massive datasets by fuzzy transforms

We present a numerical attribute dependency method for massive datasets based on the concepts of direct and inverse fuzzy transform. In a previous work, we used these concepts for numerical attribute dependency in data analysis: Therein, the multi-dimensional inverse fuzzy transform was useful for approximating a regression function. Here we give an extension of this method in massive datasets because the previous method could not be applied due to the high memory size. Our method is proved on a large dataset formed from 402,678 census sections of the Italian regions provided by the Italian National Statistical Institute (ISTAT) in 2011. The results of comparative tests with the well-known methods of regression, called support vector regression and multilayer perceptron, show that the proposed algorithm has comparable performance with those obtained using these two methods. Moreover, the number of parameters requested in our method is minor with respect to those of the cited in the above two algorithms

Fuzzy Entropy-Based Spatial Hotspot Reliability

Cluster techniques are used in hotspot spatial analysis to detect hotspots as areas on the map; an extension of the Fuzzy C-means that the clustering algorithm has been applied to locate hotspots on the map as circular areas; it represents a good trade-off between the accuracy in the detection of the hotspot shape and the computational complexity. However, this method does not measure the reliability of the detected hotspots and therefore does not allow us to evaluate how reliable the identification of a hotspot of a circular area corresponding to the detected cluster is; a measure of the reliability of hotspots is crucial for the decision maker to assess the need for action on the area circumscribed by the hotspots. We propose a method based on the use of De Luca and Termini’s Fuzzy Entropy that uses this extension of the Fuzzy C-means algorithm and measures the reliability of detected hotspots. We test our method in a disease analysis problem in which hotspots corresponding to areas where most oto-laryngo-pharyngeal patients reside, within a geographical area constituted by the province of Naples, Italy, are detected as circular areas. The results show a dependency between the reliability and fluctuation of the values of the degrees of belonging to the hotspots

A Novel Image Similarity Measure Based on Greatest and Smallest Eigen Fuzzy Sets

A novel image similarity index based on the greatest and smallest fuzzy set solutions of the max–min and min–max compositions of fuzzy relations, respectively, is proposed. The greatest and smallest fuzzy sets are found symmetrically as the min–max and max–min solutions, respectively, to a fuzzy relation equation. The original image is partitioned into squared blocks and the pixels in each block are normalized to [0, 1] in order to have a fuzzy relation. The greatest and smallest fuzzy sets, found for each block, are used to measure the similarity between the original image and the image reconstructed by joining the squared blocks. Comparison tests with other well-known image metrics are then carried out where source images are noised by applying Gaussian filters. The results show that the proposed image similarity measure is more effective and robust to noise than the PSNR and SSIM-based measures