Fuzzy Membership Grades Research Articles

Predicting air pollution using fuzzy membership grade Kriging

A practical situation often facing us is that fuzzy spatial data are recorded as crisp real-valued numbers, e.g., a PM 10 record is 15.1, but we do know that it is an imprecise and vague observation. A new spatial analysis technique – fuzzy membership grade Kriging with semi-statistical membership, proposed by Guo has been developed to address fuzzy spatial data recorded as crisp numbers. In this paper, we will explain fuzzy membership grade Kriging, its root, its theory and its implementations. As an illustration, we will use PM 10 data of California, USA. Three sample membership functions are extracted from the data itself: linear, quadratic and hyperbolic tangent and applied to the PM 10 data. The predicted membership grades are also transformed back into PM 10 concentrations by using inverse functions in order to identify areas being dangerous to human health. Finally, we implement our new fuzzy membership grade Kriging in GIS.

A fuzzy logic model to recognise ecological sectors in the lagoon of Venice based on the benthic community

The lagoon of Venice is a mosaic resulting from the interaction of several biotic and abiotic factors. A qualitative scheme of such a mosaic was proposed in literature; it subdivided the lagoon into six ecological sectors (“lagoon mouths”, “vivified lagoon”, “rough eutrophic”, “calm eutrophic”, “urban”, “estuarine”), related with current velocity, salinity, eutrophication and pollution, and expressed by means of the sessile macrobenthos living on wooden piles. In this paper, we present the conversion of that scheme into a fuzzy logic model, which considers four input variables: abundance of marine species; abundance of lagoon species; abundance of oligohaline species and total abundance of the sessile macrozoobenthos. Three fuzzy sets describe abundance levels ( low, medium, high) for each one of the four variables; the 81 (3 4) resulting combinations have been associated to the six ecological sectors, for a total of 486 “if … then” rules. We have used two different interpretations of the inference process, and combined their results with the “crisp weighting” technique to obtain the fuzzy membership grades to the six ecological sectors. The model, built on data from the lagoon of Venice in 1993–1994, has been validated with more recent data from the same stations and from the nearby lagoon of Grado-Marano; the results are in agreement with the literature information.

NOTION OF FUZZY IC-BAGS

In the present paper, the author introduces the notion of fuzzy IC-bags and does some characterizations of them. The concepts of fuzzy base sets, base equivalent fuzzy IC-Bags, cardinally equispaced fuzzy IC-Bags, and cardinally equivalent fuzzy IC-Bags have been developed. The types of peak elements, and the concerned types of peak membership grades have been discussed. It is observed that the collection of any particular type of peak elements together with their membership grades actually form fuzzy bags. A set of operations on fuzzy IC-Bags have been defined and some propositions have been proved. We note that under the conditions of uncertainty, where the counts of objects are not fixed, then the interval counts can occur with different fuzzy membership grades for each particular object in the collection, and the framework for fuzzy IC-Bags provides us with the opportunity to justify and model the organized complexity as a part of the associated intolerance embedded in the subjective patterns.

Fuzzy possibilistic neural network to vector quantizer in frequency domains

The fuzzy possibilistic c-means (FPCM) is embedded into a 2-D Hopfield neural network termed the fuzzy possibilistic Hopfield network (FPHN) to generate an optimal solution for vector quantization (VQ) in the discrete cosine transform (DCT) and the Hadamard transform (HT) domains. The information transformed by DCT or HT is separated into dc and ac coefficients. Then, the ac coefficients are trained using the proposed methods to generate a better codebook based on VQ. The energy function of the FPHN is defined as the fuzzy membership grades and possibilistic typicality degrees between training samples and codevectors. A near global-minimum codebook in the frequency domains can be obtained when the energy function converges to a stable state. Instead of one state in a neuron for the conventional Hopfield nets, each neuron occupies two states called the membership state and the typicality state in the proposed FPHN. The simulated results show that a valid and promising codebook can be generated in the DCT or HT domains using the FPHN.

Antenatal fetal risk assessment using a neurofuzzy technique.

This study defines an intelligent neurofuzzy system for antepartum fetal evaluation, The task is to investigate the Doppler ultrasound measurements of the umbilical artery (UA) and the cerebral artery (CA) to relate the health conditions of fetuses. We thus use the UA blood flow velocity waveforms [pulsality index, resistance index, and systolic/diastolic ratio] and the ratios of cerebral-umbilical resistance indices in terms of weeks. We then make a decision on the basis of a fuzzy-rule-based system combined with data-based learning strategies such as a radial basis function network and a multilayer perceptron for assessing the hypoxia suspicion. A fuzzy grade of membership is used for the evaluation of the seriousness of the situation of the fetus, and the diagnostic interpretations for doctors such as good, suspicious, and alarming conditions of fetus are derived.

Length estimation of digit strings using a neural network with structure-based features

Accurate length estimation is very helpful for the suc- cessful segmentation and recognition of connected digit strings, in particular, for an off-line recognition system. However, little work has been done in this area due to the difficulties involved. A length es- timation approach is presented as a part of our automatic off-line digit recognition system. The kernel of our approach is a neural network estimator with a set of structure-based features as the in- puts. The system outputs are a set of fuzzy membership grades reflecting the degrees of an input digit string of having different lengths. Experimental results on National Institute of Standards and Technology (NIST) Special Database 3 and other derived digit strings shows that our approach can achieve an about 99.4% cor- rect estimation if the best two estimations are considered. © 1998 SPIE and IS&T. (S1017-9909(98)00901-5)

Entropy-based operations on fuzzy sets

By using a fuzzy entropy approach, three sets of new generalized operators are presented. After a general discussion on fuzzy entropy, the concept of an elementary entropy function of a fuzzy set is introduced. Using this mapping, the generalized intersections and unions are defined as mappings that assign the least and the most fuzzy membership grade to each of the elements of the domain of the operators, respectively. It is shown that these operators can be constructed from the conventional min and max operations. Next, two modified sets of operations are introduced. The second part of the paper investigates the applicability of the new operators in fuzzy logic controllers. Simulations have been carried out so as to determine the effects of the operators on the performance of the fuzzy controllers. It is concluded that the first set of operators does not provide stable control, but the performance of the fuzzy controller can be improved by using the modified operations for a class of plants.

Modelling and Handling Uncertainties in Mobile Robotics

This paper introduces a method for modelling a Mobile Robot's environment, with its in-built uncertainties, in the Configuration Space using sonar range finders. The sonar uncertainties are modelled using a possibilistic, rather than probabilistic, measure and are represented by Fuzzy Membership grades. The Resistive Grid path planning method, that maps the Fuzzy Configuration Space Map into a grid of resistors and models goals as voltage sources, is used for planning a path. The near-optimal planned path takes into consideration position and modelling uncertainties, kinematic constraints of the vehicle as well as the uncertainty of the goal. The path is produced incrementally, giving inherent interleaving between planning and execution, thus the method is particularly suited for real time applications.

Fuzzy representation of geographical boundaries in GIS

Abstract Polygon boundaries on thematic maps are conventionally considered to be sharp lines representing abrupt changes of phenomena. However, in reality changes of environmental phenomena may also be partial or gradual. Indiscriminate use of sharp lines to represent different types of change creates a problem of boundary inaccuracy. Specifically, in the context of vector-based GIS, use of sharp lines to represent gradual or partial changes may cause misunderstanding of geographical information and reduce analysis accuracy. In this paper, the expressive inadequacy of the conventional vector boundary representation is examined. A more informative technique—the fuzzy representation of geographical boundaries—is proposed, in which boundaries describe not only the location but also the rate of change of environmental phenomena. Four methods of determining fuzzy boundary membership grades from different kinds of geographical data are described. An example of applying the fuzzy boundary technique to data analysis is presented and the advantages of the technique are discussed.

Multi‐scale classification of remotely sensed data by the maximization of fuzzy membership grades

Abstract Recent studies have shown that the optimal spatial resolution of remotely sensed data for the identification of scene elements is extremely variable depending on several factors. In particular, for the classification of each cover class using satellite sensor imagery there is generally an optimum aggregation level which is mainly related to the average size of the ground plots and to their internal homogeneity. In the present paper a methodology is presented for finding the relative optimum filtering size for the attribution of all pixels to some ground classes based on the maximization of fuzzy membership grades. Since these grades are indicative of the confidence of the pixel attribution to the classes, they can be used to select the best scale among differently filtered images. This hypothesis is investigated by means of a case study concerning a rugged, complex area in Central Italy sensed by bi‐temporal TM scenes. The results testify to the good performance of the approach which also shows p...

Fuzzy classification of spatially degraded Thematic Mapper data for the estimation of sub-pixel components

Abstract Fuzzy classification procedures are hypothesized to provide more class membership information than hard methods as well as specific insights about sub-pixel components. This hypothesis is investigated in the present work using ancillary and spatially degraded Thematic Mapper (TM) data of a wide valley in central Italy. Hard and fuzzy modified maximum likelihood classifications (MLC) were applied to the data set. Fuzzy membership grades were found to be related to class cover proportions for each degraded pixel. Also, fuzzy probabilities were able to provide more precise estimates of class distribution, as measured by Kappa coefficients of agreement, with respect to hard attributions. Further analysis showed that this improvement was chiefly due to a better characterization of mixed, uncertainly attributable pixels. These results are of great interest for definition of the cases for which the fuzzy approach is appropriate.

Estimation of forest parameters through fuzzy classification of TM data

Several studies have investigated the utility of Landsat 5 TM imagery to estimate forest parameters such as stand composition and density. Regression equations have generally been used to relate these parameters to the radiance responses of the TM channels. Such a method is not feasible in highly complex landscapes, where forest mixtures and terrain irregularities may obscure the existence of simple relationships. A fuzzy approach to the problem is presented based on a multi-step procedure. First, some typical forest plots with known features are spectrally identified. A maximum likelihood fuzzy classification with nonparametric priors is then applied to the study images, so as to derive fuzzy membership grades for all pixels with respect to the typical plots. Finally, these grades are used to compute the estimates of the forest parameters by a weighted average strategy. The method was tested on a complex, rugged area in Tuscany mainly covered by deciduous and coniferous forests. Two TM scenes and accurate ground references taken in spring and summer 1991 were utilized for the testing. The first results, statistically evaluated in comparison with those of a more usual multivariate regression procedure, are quite encouraging. The possible application of the fuzzy approach to other cases of environmental monitoring is finally discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A measurement-informational discussion of fuzzy union and intersection

The question of obtaining fuzzy membership grades is discussed. It is then shown that Zadeh's max and min operations are the only possible extension of the classic union and intersection operations which are meaningful in the face of ordinal information on degrees of membership. A discussion of ratio type information-meaningful operations is also presented.