Biplots of fuzzy coded data

A biplot, which is the multivariate generalization of the two-variable scatterplot, can be used to visualize the results of many multivariate techniques, especially those that are based on the singular value decomposition. We consider data sets consisting of continuous-scale measurements, their fuzzy coding and the biplots that visualize them, using a fuzzy version of multiple correspondence analysis. Of special interest is the way quality of fit of the biplot is measured, since it is well-known that regular (i.e., crisp) multiple correspondence analysis seriously under-estimates this measure. We show how the results of fuzzy multiple correspondence analysis can be defuzzified to obtain estimated values of the original data, and prove that this implies an orthogonal decomposition of variance. This permits a measure of fit to be calculated in the familiar form of a percentage of explained variance, which is directly comparable to the corresponding fit measure used in principal component analysis of the original data. The approach is motivated initially by its application to a simulated data set, showing how the fuzzy approach can lead to diagnosing nonlinear relationships, and finally it is applied to a real set of meteorological data.defuzzification, fuzzy coding, indicator matrix, measure of fit, multivariate data, multiple correspondence analysis, principal component analysis.

Possibilistic and fuzzy clustering methods for robust analysis of non-precise data

This work focuses on robust clustering of data affected by imprecision. The imprecision is managed in terms of fuzzy sets. The clustering process is based on the fuzzy and possibilistic approaches. In both approaches the observations are assigned to the clusters by means of membership degrees. In fuzzy clustering the membership degrees express the degrees of sharing of the observations to the clusters. In contrast, in possibilistic clustering the membership degrees are degrees of typicality. These two sources of information are complementary because the former helps to discover the best fuzzy partition of the observations while the latter reflects how well the observations are described by the centroids and, therefore, is helpful to identify outliers. First, a fully possibilistic k-means clustering procedure is suggested. Then, in order to exploit the benefits of both the approaches, a joint possibilistic and fuzzy clustering method for fuzzy data is proposed. A selection procedure for choosing the parameters of the new clustering method is introduced. The effectiveness of the proposal is investigated by means of simulated and real-life data

A possibilistic approach to latent structure analysis for symmetric fuzzy data.

In many situations the available amount of data is huge and can be intractable. When the data set is single valued, latent structure models are recognized techniques, which provide a useful compression of the information. This is done by considering a regression model between observed and unobserved (latent) fuzzy variables. In this paper, an extension of latent structure analysis to deal with fuzzy data is proposed. Our extension follows the possibilistic approach, widely used both in the cluster and regression frameworks. In this case, the possibilistic approach involves the formulation of a latent structure analysis for fuzzy data by optimization. Specifically, a non-linear programming problem in which the fuzziness of the model is minimized is introduced. In order to show how our model works, the results of two applications are given.Latent structure analysis, symmetric fuzzy data set, possibilistic approach.

Fuzzy spectral and spatial feature integration for classification of nonferrous materials in hyperspectral data

Hyperspectral data allows the construction of more elaborate models to sample the properties of the nonferrous materials than the standard RGB color representation. In this paper, the nonferrous waste materials are studied as they cannot be sorted by classical procedures due to their color, weight and shape similarities. The experimental results presented in this paper reveal that factors such as the various levels of oxidization of the waste materials and the slight differences in their chemical composition preclude the use of the spectral features in a simplistic manner for robust material classification. To address these problems, the proposed FUSSER (fuzzy spectral and spatial classifier) algorithm detailed in this paper merges the spectral and spatial features to obtain a combined feature vector that is able to better sample the properties of the nonferrous materials than the single pixel spectral features when applied to the construction of multivariate Gaussian distributions. This approach allows the implementation of statistical region merging techniques in order to increase the performance of the classification process. To achieve an efficient implementation, the dimensionality of the hyperspectral data is reduced by constructing bio-inspired spectral fuzzy sets that minimize the amount of redundant information contained in adjacent hyperspectral bands. The experimental results indicate that the proposed algorithm increased the overall classification rate from 44% using RGB data up to 98% when the spectral-spatial features are used for nonferrous material classification

WHY FUZZY ANALYTIC HIERARCHY PROCESS APPROACH FOR TRANSPORT PROBLEMS?

The evaluation of transport projects has become increasingly complex. Different aspects have to be taken into account and the consequences of the problems are usually far reaching and the different policy alternatives are numerous and difficult to predict. Several pressure or action groups have also emerged causing an even more complex decision making process. The use of multi criteria analysis for the evaluation of transport projects has increased due to this increasing complexity of the problem situation. At the same time, the importance of stakeholders within this evaluation process should have been recognized. Researches on transport projects are generally carried out to provide information to policymakers that have to operate within restrictive parameters (political, economical, social, etc…). Researchers should therefore take greater account of the different priorities of stakeholders such as policymakers, private enterprises and households. These stakeholders should be incorporated explicitly in the evaluation process. The Analytic Hierarchy Process is one of the Fuzzy Multiple Criteria Decision Making methods. It can be applied in a very broad range of applications of decision problems. Logistics, urban planning, public politics, marketing, finance, education, economics are a part of this wide application area. In transport subjects it can be used for the evaluation of transport policy measures or decision making problems. Due to its wide range application area, it has been an exciting research subject for many different field researchers. The aim of this paper is to introduce AHP method and to offer how to benefit it for the preference of urban planners in transport problems. This paper is composed of two main parts. First part consists of the literature survey regarding with the AHP and its application areas. The advantage of methods had been mentioned. Second part focuses on a sample application of AHP technique. The study uses AHP technique to determine the selection criteria in the transhipment port selection decision-making process. Keywords: Analytic Hierarchy Process, Multi criteria analysis, Transshipment port selection.

FUZZY COMPARATIVE CONCORDANCE ANALYSIS. Proposal and evaluation by a case study

In this paper it is proposed a fuzzy multiple attribute analysis, that we have called comparative concordance, as a help instrument to the decision-making process in an environment of lack of precise information as it generally is the decision-making in regional planning. Through an application to the selection of proceeding programs of the Environmental Plan of Andalusia, 1995-2000, it will be compared to other methods.fuzzy sets, multiple attribute decision, environmental planning

APPLICATION OF FUZZY PRINCIPAL COMPONENT ANALYSIS FOR THE BEST ALTERNATIVE TOURIST ATTRACTION IN YOGYAKARTA

One of the regions in Indonesia that depends on the tourism sector is the Special Region of Yogyakarta Province. The Province of the Special Region of Yogyakarta itself every year becomes a tourist destination province for vacations, many tourists do not know which places are the best choices for tourists. Therefore, this research aims to make it easier for tourists to obtain information on the best tourist spots in the Province of the Special Region of Yogyakarta. Based on the data obtained from the results of distributing online questionnaires during June 2022 – July 2022. The results of the study using the Fuzzy Principal Component Analysis method, it was found that the best tourist attraction is the Prambanan Temple tourist attraction with a PCA score of 0.677057 which means that Prambanan Temple becomes a tourist attraction. The most sought after by tourist visitors, followed by the Malioboro Street Area with a PCA score of 0.48146 and Parangtirtis Beach with a PCA score of 0.369162. The results of this study are expected to help tourists determin