Fuzzy analysis: a vague way of dealing with uncertainty in real estate analysis?

Risk and uncertainty are, to say the least, poorly considered by most individuals involved in real estate analysis - in both development and investment appraisal. Surveyors continue to express 'uncertainty' about the value (risk) of using relatively objective methods of analysis to account for these factors. These methods attempt to identify the risk elements more explicitly. Conventionally this is done by deriving probability distributions for the uncontrolled variables in the system. A suggested 'new' way of "being able to express our uncertainty or slight vagueness about some of the qualitative judgements and not entirely certain data required in the course of the problem..." uses the application of fuzzy logic. This paper discusses and demonstrates the terminology and methodology of fuzzy analysis. In particular it attempts a comparison of the procedures with those used in 'conventional' risk analysis approaches and critically investigates whether a fuzzy approach offers an alternative to the use of probability based analysis for dealing with aspects of risk and uncertainty in real estate analysis

Data-driven fuzzy analysis in quantitative mineral resource assessment

The integration of geo-information from multiple sources and of diverse nature in developing mineral favourability indexes (MFIs) is a well-known problem in mineral exploration and mineral resource assessment. Fuzzy set theory provides a convenient framework to combine and analyse qualitative and quantitative data independently of their source or characteristics. A novel, data-driven formulation for calculating MFIs based on fuzzy analysis is developed in this paper. Different geo-variables are considered fuzzy sets and their appropriate membership functions are defined and modelled. A new weighted average-type aggregation operator is then introduced to generate a new fuzzy set representing mineral favourability. The membership grades of the new fuzzy set are considered as the MFI. The weights for the aggregation operation combine the individual membership functions of the geo-variables, and are derived using information from training areas and L, regression. The technique is demonstrated in a case study of skarn tin deposits and is used to integrate geological, geochemical and magnetic data. The study area covers a total of 22.5 km(2) and is divided into 349 cells, which include nine control cells. Nine geo-variables are considered in this study. Depending on the nature of the various geo-variables, four different types of membership functions are used to model the fuzzy membership of the geo-variables involved. (C) 2002 Elsevier Science Ltd. All rights reserved.

Об одном методе нечеткого анализа в задаче оценки параметров землетрясеня

ნაშრომის ძირითადი ამოცანა მდგომარეობს მათემატიკური მოდელის აგებასა და მიწისძვრის პარამეტრების განსაზღვრასთან დაკავშირებით გადაწყვეტილების მისაღებად რეკომენდაციების ფორმულირებაში. პირველად მონაცემთა წინასწარი ანალიზის დროს დადგენილია, რომ მათი ბუნება არის კომბინირებული ანუ ალბათურ-შესაძლებოთი. ამიტომ მათი დამუშავებისთვის შერჩეულია სპეციალური არამკაფიო ანალიზის მეთოდი-ბმულობათა ანალიზი.

Supervisory control of wastewater treatment plants by combining principal component analysis and fuzzy c-means clustering

In this paper a methodology for integrated multivariate monitoring and control of biological wastewater treatment plants during extreme events is presented. To monitor the process, on-line dynamic principal component analysis (PCA) is performed on the process data to extract the principal components that represent the underlying mechanisms of the process. Fuzzy c-means (FCM) clustering is used to classify the operational state. Performing clustering on scores from PCA solves computational problems as well as increases robustness due to noise attenuation. The class-membership information from FCM is used to derive adequate control set points for the local control loops. The methodology is illustrated by a simulation study of a biological wastewater treatment plant, on which disturbances of various types are imposed. The results show that the methodology can be used to determine and co-ordinate control actions in order to shift the control objective and improve the effluent quality.

Measures of fit in multiple correspondence analysis of crisp and fuzzy coded data

When continuous data are coded to categorical variables, two types of coding are possible: crisp coding in the form of indicator, or dummy, variables with values either 0 or 1; or fuzzy coding where each observation is transformed to a set of "degrees of membership" between 0 and 1, using co-called membership functions. It is well known that the correspondence analysis of crisp coded data, namely multiple correspondence analysis, yields principal inertias (eigenvalues) that considerably underestimate the quality of the solution in a low-dimensional space. Since the crisp data only code the categories to which each individual case belongs, an alternative measure of fit is simply to count how well these categories are predicted by the solution. Another approach is to consider multiple correspondence analysis equivalently as the analysis of the Burt matrix (i.e., the matrix of all two-way cross-tabulations of the categorical variables), and then perform a joint correspondence analysis to fit just the off-diagonal tables of the Burt matrix - the measure of fit is then computed as the quality of explaining these tables only. The correspondence analysis of fuzzy coded data, called "fuzzy multiple correspondence analysis", suffers from the same problem, albeit attenuated. Again, one can count how many correct predictions are made of the categories which have highest degree of membership. But here one can also defuzzify the results of the analysis to obtain estimated values of the original data, and then calculate a measure of fit in the familiar percentage form, thanks to the resultant orthogonal decomposition of variance. Furthermore, if one thinks of fuzzy multiple correspondence analysis as explaining the two-way associations between variables, a fuzzy Burt matrix can be computed and the same strategy as in the crisp case can be applied to analyse the off-diagonal part of this matrix. In this paper these alternative measures of fit are defined and applied to a data set of continuous meteorological variables, which are coded crisply and fuzzily into three categories. Measuring the fit is further discussed when the data set consists of a mixture of discrete and continuous variables.

Fuzzy Principal Components Analysis

Due to the large number of characteristics, there is a need to extract the most relevant characteristicsfrom the input data, so that the amount of information lost in this way is minimal, and the classification realized with the projected data set is relevant with respect to the original data. In order to achieve this feature extraction, different statistical techniques, as well as the principal components analysis (PCA) may be used. This thesis describes an extension of principal components analysis (PCA) allowing the extraction ofa finite number of relevant features from high-dimensional fuzzy data and noisy data. PCA finds linear combinations of the original measurement variables that describe the significant variation in the data. The comparisonof the two proposed methods was produced by using postoperative patient data. Experiment results demonstrate the ability of using the proposed two methods in complex data. Fuzzy PCA was used in the classificationproblem. The classification was applied by using the similarity classifier algorithm where total similarity measures weights are optimized with differential evolution algorithm. This thesis presents the comparison of the classification results based on the obtained data from the fuzzy PCA.

Fuzzy subgroups, algebraic and topological points of view and complex analysis

Fuzzy subsets and fuzzy subgroups are basic concepts in fuzzy mathematics. We shall concentrate on fuzzy subgroups dealing with some of their algebraic, topological and complex analytical properties. Explorations are theoretical belonging to pure mathematics. One of our ideas is to show how widely fuzzy subgroups can be used in mathematics, which brings out the wealth of this concept. In complex analysis we focus on Möbius transformations, combining them with fuzzy subgroups in the algebraic and topological sense. We also survey MV spaces with or without a link to fuzzy subgroups. Spectral space is known in MV algebra. We are interested in its topological properties in MV-semilinear space. Later on, we shall study MV algebras in connection with Riemann surfaces. In fact, the Riemann surface as a concept belongs to complex analysis. On the other hand, Möbius transformations form a part of the theory of Riemann surfaces. In general, this work gives a good understanding how it is possible to fit together different fields of mathematics.

Fuzzy real option analysis in patent related decision making and patent valuation

The shift towards a knowledge-based economy has inevitably prompted the evolution of patent exploitation. Nowadays, patent is more than just a prevention tool for a company to block its competitors from developing rival technologies, but lies at the very heart of its strategy for value creation and is therefore strategically exploited for economic pro t and competitive advantage. Along with the evolution of patent exploitation, the demand for reliable and systematic patent valuation has also reached an unprecedented level. However, most of the quantitative approaches in use to assess patent could arguably fall into four categories and they are based solely on the conventional discounted cash flow analysis, whose usability and reliability in the context of patent valuation are greatly limited by five practical issues: the market illiquidity, the poor data availability, discriminatory cash-flow estimations, and its incapability to account for changing risk and managerial flexibility. This dissertation attempts to overcome these impeding barriers by rationalizing the use of two techniques, namely fuzzy set theory (aiming at the first three issues) and real option analysis (aiming at the last two). It commences with an investigation into the nature of the uncertainties inherent in patent cash flow estimation and claims that two levels of uncertainties must be properly accounted for. Further investigation reveals that both levels of uncertainties fall under the categorization of subjective uncertainty, which differs from objective uncertainty originating from inherent randomness in that uncertainties labelled as subjective are highly related to the behavioural aspects of decision making and are usually witnessed whenever human judgement, evaluation or reasoning is crucial to the system under consideration and there exists a lack of complete knowledge on its variables. Having clarified their nature, the application of fuzzy set theory in modelling patent-related uncertain quantities is effortlessly justified. The application of real option analysis to patent valuation is prompted by the fact that both patent application process and the subsequent patent exploitation (or commercialization) are subject to a wide range of decisions at multiple successive stages. In other words, both patent applicants and patentees are faced with a large variety of courses of action as to how their patent applications and granted patents can be managed. Since they have the right to run their projects actively, this flexibility has value and thus must be properly accounted for. Accordingly, an explicit identification of the types of managerial flexibility inherent in patent-related decision making problems and in patent valuation, and a discussion on how they could be interpreted in terms of real options are provided in this dissertation. Additionally, the use of the proposed techniques in practical applications is demonstrated by three fuzzy real option analysis based models. In particular, the pay-of method and the extended fuzzy Black-Scholes model are employed to investigate the profitability of a patent application project for a new process for the preparation of a gypsum-fibre composite and to justify the subsequent patent commercialization decision, respectively; a fuzzy binomial model is designed to reveal the economic potential of a patent licensing opportunity.

Consequence modelling,vulnerability assessment and fuzzy fault tree analysis of hazardous storages in an industrial area

The hazards associated with major accident hazard (MAH) industries are fire, explosion and toxic gas releases. Of these, toxic gas release is the worst as it has the potential to cause extensive fatalities. Qualitative and quantitative hazard analyses are essential for the identitication and quantification of the hazards associated with chemical industries. This research work presents the results of a consequence analysis carried out to assess the damage potential of the hazardous material storages in an industrial area of central Kerala, India. A survey carried out in the major accident hazard (MAH) units in the industrial belt revealed that the major hazardous chemicals stored by the various industrial units are ammonia, chlorine, benzene, naphtha, cyclohexane, cyclohexanone and LPG. The damage potential of the above chemicals is assessed using consequence modelling. Modelling of pool fires for naphtha, cyclohexane, cyclohexanone, benzene and ammonia are carried out using TNO model. Vapor cloud explosion (VCE) modelling of LPG, cyclohexane and benzene are carried out using TNT equivalent model. Boiling liquid expanding vapor explosion (BLEVE) modelling of LPG is also carried out. Dispersion modelling of toxic chemicals like chlorine, ammonia and benzene is carried out using the ALOHA air quality model. Threat zones for different hazardous storages are estimated based on the consequence modelling. The distance covered by the threat zone was found to be maximum for chlorine release from a chlor-alkali industry located in the area. The results of consequence modelling are useful for the estimation of individual risk and societal risk in the above industrial area.Vulnerability assessment is carried out using probit functions for toxic, thermal and pressure loads. Individual and societal risks are also estimated at different locations. Mapping of threat zones due to different incident outcome cases from different MAH industries is done with the help of Are GIS.Fault Tree Analysis (FTA) is an established technique for hazard evaluation. This technique has the advantage of being both qualitative and quantitative, if the probabilities and frequencies of the basic events are known. However it is often difficult to estimate precisely the failure probability of the components due to insufficient data or vague characteristics of the basic event. It has been reported that availability of the failure probability data pertaining to local conditions is surprisingly limited in India. This thesis outlines the generation of failure probability values of the basic events that lead to the release of chlorine from the storage and filling facility of a major chlor-alkali industry located in the area using expert elicitation and proven fuzzy logic. Sensitivity analysis has been done to evaluate the percentage contribution of each basic event that could lead to chlorine release. Two dimensional fuzzy fault tree analysis (TDFFTA) has been proposed for balancing the hesitation factor invo1ved in expert elicitation .

Fuzzy cluster analysis on Spanish public universities. 'Análisis de agrupaciones difusas en las universidades públicas españolas'.

Resumen basado en el de la publicación

Transient stability analysis of electric energy systems via a fuzzy ART-ARTMAP neural network

This work presents a methodology to analyze transient stability (first oscillation) of electric energy systems, using a neural network based on ART architecture (adaptive resonance theory), named fuzzy ART-ARTMAP neural network for real time applications. The security margin is used as a stability analysis criterion, considering three-phase short circuit faults with a transmission line outage. The neural network operation consists of two fundamental phases: the training and the analysis. The training phase needs a great quantity of processing for the realization, while the analysis phase is effectuated almost without computation effort. This is, therefore the principal purpose to use neural networks for solving complex problems that need fast solutions, as the applications in real time. The ART neural networks have as primordial characteristics the plasticity and the stability, which are essential qualities to the training execution and to an efficient analysis. The fuzzy ART-ARTMAP neural network is proposed seeking a superior performance, in terms of precision and speed, when compared to conventional ARTMAP, and much more when compared to the neural networks that use the training by backpropagation algorithm, which is a benchmark in neural network area. (c) 2005 Elsevier B.V. All rights reserved.

Mapping soil pollution by spatial analysis and fuzzy classification

Spatial analysis and fuzzy classification techniques were used to estimate the spatial distributions of heavy metals in soil. The work was applied to soils in a coastal region that is characterized by intense urban occupation and large numbers of different industries. Concentrations of heavy metals were determined using geostatistical techniques and classes of risk were defined using fuzzy classification. The resulting prediction mappings identify the locations of high concentrations of Pb, Zn, Ni, and Cu in topsoils of the study area. The maps show that areas of high pollution of Ni and Cu are located at the northeast, where there is a predominance of industrial and agricultural activities; Pb and Zn also occur in high concentrations in the northeast, but the maps also show significant concentrations of Pb and Zn in other areas, mainly in the central and southeastern parts, where there are urban leisure activities and trade centers. Maps were also prepared showing levels of pollution risk. These maps show that (1) Cu presents a large pollution risk in the north-northwest, midwest, and southeast sectors, (2) Pb represents a moderate risk in most areas, (3) Zn generally exhibits low risk, and (4) Ni represents either low risk or no risk in the studied area. This study shows that combining geostatistics with fuzzy theory can provide results that offer insight into risk assessment for environmental pollution.

Transient stability analysis of electrical power systems using a neural network based on fuzzy ARTMAP

This work presents a methodology to analyze transient stability for electric energy systems using artificial neural networks based on fuzzy ARTMAP architecture. This architecture seeks exploring similarity with computational concepts on fuzzy set theory and ART (Adaptive Resonance Theory) neural network. The ART architectures show plasticity and stability characteristics, which are essential qualities to provide the training and to execute the analysis. Therefore, it is used a very fast training, when compared to the conventional backpropagation algorithm formulation. Consequently, the analysis becomes more competitive, compared to the principal methods found in the specialized literature. Results considering a system composed of 45 buses, 72 transmission lines and 10 synchronous machines are presented. © 2003 IEEE.