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In this paper we propose fuzzy hypothesis testing for a proportion with crisp data as the exact generalized one-tailed hypergeometric test with fuzzy (non-)complementary hypotheses, and incorporate the conventional hypergeometric test with crisp hypotheses into its framework. In particular, we formulate hypotheses as ontic or epistemic (fuzzy) sets, since we assume that presumptions regarding the true population proportion can be expressed in the conjunctive or disjunctive reading. Further, we suggest modeling of membership functions in terms of cost or frequency due to considerations of user's priorities or incomplete knowledge in relation to hypotheses formulation. Considering a hypothesis as union of its crisp and fuzzy areas, we illustrate via real-life examples that in contrast to classical test theory, fuzzy hypothesis testing provides an additional partial and gradual consideration of the indifference zone for both complementary and non-complementary hypotheses. The test concept is introduced for both test methods, a test of significance and an alternative test, and leads to a crisp test decision considering further cost aspects like the sample size. The generalized error criteria are derived and interpreted in relation to both hypotheses. Additionally, a corresponding sensitivity analysis is presented for one of the most promising test types. [ABSTRACT FROM AUTHOR]

Abstract This study investigated policy-driven implementations of internationalization in higher education institutions in Taiwan by evaluating its effects as perceived by students and faculty. For organizing the internationalization indicators, we designed a fuzzy questionnaire in which the review indicators were classified into context (C), input (I), process (P), and outcome (O) dimensions according to the context, input, process, and outcome (CIPO) model. This study used statistical models to interpret valid questionnaire returns from 612 students and faculty members from various universities. The results indicated wider gaps between the importance and feasibility of implementing internationalization in the I dimension and partially in the C dimension. In addition, the perceptions of students and faculty suggested a wide chasm between expected and actual results of the CIPO dimensions. Typically, the students favored implementing internationalization regarding the C, I, P, and O indicators more than did the faculty. The diversity of internationalization, based on implementations in public and private sector universities, is demonstrated in the C and I dimensions, with gender-based perceptions and distinctions between participants in universities and technological universities being exhibited in some indicators. This study provides a method for detecting key stakeholders' perceptions of implementing internationalization policies in higher education institutions. [ABSTRACT FROM AUTHOR]

It is recognized that handling uncertainty is essential to obtain more reliable results in modeling and computer simulation. This paper aims to discuss the logistic equation subject to fuzzy uncertainties in the initial conditions and parameters. Here we consider the population density at a specific time as a fuzzy variable in which the possibility distribution function depends on the possibility distribution functions of the environmental carrying capacity, the initial population density and the intrinsic growth rate. We provide closed-form expressions for the expected value of the fuzzy variables population density and for the time of maximum growth. We also perform some numerical simulations to illustrate our main results. [ABSTRACT FROM AUTHOR]

Three organic fertilizers of manure sheep, sewage sludge and municipal waste were mixed with soil at the rates of 0%, 1.25% and 2.5% (w/w), respectively. In a greenhouse experiment, corn seed were grown on pots of 3 kg treated contaminated soils and irrigated. Sixty days after sowing, the aerial plant parts were harvested and analyzed for Cadmium (Cd) and Lead (Pb) contents. Since all of data in this research are fuzzy, we need an extended version of analysis of variance (ANOVA) to investigate on these fuzzy observations. In this paper, as a method to compare several populations, the fuzzy analysis of variance (FANOVA) has been used where the collected data considered fuzzy rather than crisp numbers and therefore all calculations are based on FANOVA method. Although, ANOVA based on vague data can lead to a fuzzy decision, but measuring the vagueness of this fuzzy decision is one of advantages of proposed method from the applied point of view. [ABSTRACT FROM AUTHOR]

In this study, a developed fuzzy-stochastic method with Hurwicz criterion (FSH) is proposed for planning land utilization in a wetland ecosystem under uncertainty. FSH can not only deal with natural stochastic uncertainties represented as random variables (such as water flow), but also handle subjective impressions expressed as fuzzy sets (such as economic data), even it can reflect the compromise of decision makers’ risk preferences in decision-making processes based on Hurwicz criterion. The proposed method can be applied to a practical land utilization management. Rational land utilization plan (including withdrawing reclamation and wetland recovering (WRWR)) is advocated to relive such contradictions artificially, where WRWR can improve ecological function, leading more intangible ecological benefits to human activities. Meanwhile, trading-oriented mechanism is introduced to increase the economic productivity of land plan. Based on various conjunctive goals of socio-economic development and eco-environmental sustainability, results of ecological effects of wetland ecosystem, land utilization patterns, pollution-mitigation schemes, trading mechanisms and system benefits under varied scenarios are obtained and analyzed. The results indicate that land-indicator-based optimization with trading-oriented mechanism can improve the efficiency of land utilization plan in the mass to satisfy regional water resource/environmental load. Meanwhile, tradeoffs between economic benefit and system-failure risk under optimistic/pessimistic option would support generating a robust plan associated with risk control for land utilization in wetland ecosystem under uncertainties. These detections can avail local policymakers to adjust existing land utilization plan with more efficient and sustainable manners, with aim to harmonize economic development and environmental protection in wetland ecosystem. [ABSTRACT FROM AUTHOR]

Process equipment failures (PEFs) are recognized as one of the leading causes of process accidents. Failure modes and effect analysis (FMEA) as a risk assessment technique, has widely been used in a variety of process industries. The conventional form of FMEA uses three parameters of severity (S), occurrence (O), and detection (D) as risk factors to calculate a risk priority number (R.P.N) and rank the failure modes based on this number. But several shortcomings associated with the FMEA have limited its applicability. This study aims at the development of an extension of FMEA that could efficiently handle the vagueness and uncertainty exists in the experts’ judgments in process of failure modes ranking in conventional FMEA. In this paper we used the concept of the Z number to capture the inherent uncertainty exists in the experts’ judgments. In addition, we used Shannon entropy concept to deploy objective weights to adjust subjective weights assigned by experts. Furthermore, the fuzzy VIKOR technique applied to rank and prioritize the failure modes based on the minimum individual regret and the maxi group utility. A numerical example is presented to illustrate an application of the proposed method in a geothermal power plant (GPP). Results are also compared with the conventional FMEA. A sensitivity analysis was conducted to validate the obtained results. Findings indicate that the application of the proposed approach (subjective-objective ranking) in fuzzy environment can improve the applicability of the conventional FMEA method. [ABSTRACT FROM AUTHOR]

This study investigates the application of fuzzy regression to the viscometric analysis of polymer–polymer miscibility by using experimental viscosity data for polystyrene (PS), poly(styrene-co-acrylonitrile) (PSAN) and PS/PSAN blends in CHCI 3 and DMF at different temperatures. The first stage includes the calculations of the fuzzy thermodynamic interaction parameter based on the results from the fuzzy regression models. In the second stage, the possibility and necessity measure-dependent results of the immiscibility (or miscibility) are presented and compared with the traditional miscibility estimations. This study shows that the fuzzification of traditional regression as well as the decision making on miscibility may have a good potential to be used for viscometric studies. [ABSTRACT FROM AUTHOR]

Control charts are the most popular process monitoring techniques designed to determine whether a process is in a state of statistical control or not. When a process change occurs, the control chart exhibits an out-of-control signal. In most cases, the signal is followed by a substantial amount of delay. To address this drawback, supplementary techniques have been considered to be employed along with the control charts to identify the exact time of the process change. This paper presents a hybrid method for estimating the change point on x ¯ chart when neither the change type nor its magnitude are known. For this purpose, two sets of features with the most discriminatory power between x ¯ chart patterns are selected. Then the feature vectors are extracted from the control chart patterns (CCPs) and served as an input to a classification scheme which is comprised of several support vector machine (SVM) classifiers. After parameters tuning, the classifiers are built and used for classifying the CCPs and identifying the change type. Once the change type is determined, the fuzzy statistical clustering (FSC) and the maximum likelihood (ML) estimators are employed to identify the process change point. The performance of selected features, the classification scheme, and the change point estimators are evaluated by conducting several simulation studies. Empirical results show that in identifying the change types, the proposed classification scheme is more accurate than two recent CCP classification methods. The results also confirm that the proposed hybrid method offers an accurate estimate of the process change point, as compared to the most recent methods developed for the change point estimation. [ABSTRACT FROM AUTHOR]

Fuzzy statistics provides useful techniques for handling real situations which are affected by vagueness and imprecision. Several fuzzy statistical techniques (e.g., fuzzy regression, fuzzy principal component analysis, fuzzy clustering) have been developed over the years. Among these, fuzzy regression can be considered an important tool for modeling the relation between a dependent variable and a set of independent variables in order to evaluate how the independent variables explain the empirical data which are modeled through the regression system. In general, the standard fuzzy least squares method has been used in these situations. However, several applicative contexts, such as for example, analysis with small samples and short and fat matrices, violation of distributional assumptions, matrices affected by multicollinearity (ill-posed problems), may show more complex situations which cannot successfully be solved by the fuzzy least squares. In all these cases, different estimation methods should instead be preferred. In this paper we address the problem of estimating fuzzy regression models characterized by ill-posed features. We introduce a novel fuzzy regression framework based on the Generalized Maximum Entropy (GME) estimation method. Finally, in order to better highlight some characteristics of the proposed method, we perform two Monte Carlo experiments and we analyze a real case study. [ABSTRACT FROM AUTHOR]

An alternative bioinformatics approach based on fuzzy theory statistics and linear discriminant analysis is proposed for the interpretation of MALDI MS spectra in peptide profiling. When applied, the methodology enables the establishment of a reproducible plasma preparation protocol appropriate for the evaluation of small data sets. The samples were collected from pregnant women affected by gestational diabetes mellitus (GDM), n = 18 and control group, n = 13. The following pre-treatment sets were tested: pipette tips with C18 stationary phase (ZipTip, Millipore and Omix, Agilent) and magnetic bead-based weak cation exchange chromatography kit (MB WCX, Bruker Daltonics). The spectra were recorded using a MALDI TOF mass spectrometer (UltrafleXtreme, Bruker Daltonics) for a mass range of m/z from 1000 to 10,000. The significant features were selected using the wrapper selection method, and two classification systems were tested: discriminant analysis (DA) and fuzzy inference system (FIS). ClinProTools software was employed to compare the usefulness of the proposed methodology. The study showed that the optimum results for MS spectra were obtained after the use of the ZipTip as pre-treatment method in plasma preparation. Chemometric analysis allowed the differentiation of the GDM group from the control with a high degree of accuracy: 0.7333 (DA) and 0.8065 (FIS). [ABSTRACT FROM AUTHOR]

Abstract: When constructing the model of a word by collecting interval-valued data from a group of individuals, both interpersonal and intrapersonal uncertainties coexist. Similar to the interval type-2 fuzzy set (IT2 FS) used in the enhanced interval approach (EIA), the Cloud model characterized by only three parameters can manage both uncertainties. Thus, based on the Cloud model, this paper proposes a new representation model for a word from interval-valued data. In our proposed method, firstly, the collected data intervals are preprocessed to remove the bad ones. Secondly, the fuzzy statistical method is used to compute the histogram of the surviving intervals. Then, the generated histogram is fitted by a Gaussian curve function. Finally, the fitted results are mapped into the parameters of a Cloud model to obtain the parametric model for a word. Compared with eight or nine parameters needed by an IT2 FS, only three parameters are needed to represent a Cloud model. Therefore, we develop a much more parsimonious parametric model for a word based on the Cloud model. Generally a simpler representation model with less parameters usually means less computations and memory requirements in applications. Moreover, the comparison experiments with the recent EIA show that, our proposed method can not only obtain much thinner footprints of uncertainty (FOUs) but also capture sufficient uncertainties of words. [Copyright &y& Elsevier]

Highlights: [•] This paper gives a new method ICA applied to water quality evaluation. [•] It makes up a deficiency of negative values in the correlative degree. [•] It settles the evaluation problem of interval criteria and interval samples. [•] Interval weights are introduced to deal with the uncertainty of weights. [•] The method is not restricted to WQE only. [Copyright &y& Elsevier]

Abstract: The integration of water quality monitoring variables is essential in environmental decision making. Nowadays, advanced techniques to manage subjectivity, imprecision, uncertainty, vagueness, and variability are required in such complex evaluation process. We here propose a probabilistic fuzzy hybrid model to assess river water quality. Fuzzy logic reasoning has been used to compute a water quality integrative index. By applying a Monte Carlo technique, based on non-parametric probability distributions, the randomness of model inputs was estimated. Annual histograms of nine water quality variables were built with monitoring data systematically collected in the Colombian Cauca River, and probability density estimations using the kernel smoothing method were applied to fit data. Several years were assessed, and river sectors upstream and downstream the city of Santiago de Cali, a big city with basic wastewater treatment and high industrial activity, were analyzed. The probabilistic fuzzy water quality index was able to explain the reduction in water quality, as the river receives a larger number of agriculture, domestic, and industrial effluents. The results of the hybrid model were compared to traditional water quality indexes. The main advantage of the proposed method is that it considers flexible boundaries between the linguistic qualifiers used to define the water status, being the belongingness of water quality to the diverse output fuzzy sets or classes provided with percentiles and histograms, which allows classify better the real water condition. The results of this study show that fuzzy inference systems integrated to stochastic non-parametric techniques may be used as complementary tools in water quality indexing methodologies. [Copyright &y& Elsevier]

Abstract: Time temperature integrators (TTIs) are indicators of food quality changes based on time–temperature history. The key issue in TTI studies is related to the accuracy of estimating food quality changes using mathematical models based on the color of the TTIs attached to food packages. In the original method, the temperature dependency of the reactions is analyzed in terms of Arrhenius relationships. However, when modeling the Arrhenius relationships, there are some problems regarding insufficient data points or non-linearity, thereby leading to significant errors in the predictions. In this study, therefore, a novel method for modeling temperature dependency was developed based on fuzzy reasoning, which is a versatile tool used to account for experimental data with non-linearity. The volatile basic nitrogen (VBN) of beef as well as the color value of the TTIs attached to the beef package were measured during storage. The individual kinetic equations for each temperature under isothermal conditions were incorporated using fuzzy reasoning rather than an Arrhenius equation in order to predict the VBN for a TTI color value under conditions of unknown time–temperature history. It was found that the new method was more accurate in predicting beef quality from TTI color than the original method. [Copyright &y& Elsevier]

Abstract: Sending man to Mars has been a long-held dream of humankind. NASA plans human planetary explorations using approaches that are technically feasible, have reasonable risks and have relatively low costs. This study presents a novel Multi-Attribute Decision Making (MADM) model for evaluating a range of potential mission scenarios for the human exploration of Mars. The three alternatives identified by the Mission Operations Directorate (MOD) at the Johnson Space Center (JSC) include split mission, combo lander and dual scenarios. The proposed framework subsumes the following key methods: first, the conjunction method is used to minimize the number of alternative mission scenarios; second, the Fuzzy Risk Failure Mode and Effects Analysis (RFMEA) is used to analyze the potential failure of the alternative scenarios; third, the fuzzy group Real Option Analysis (ROA) is used to estimate the expected costs and benefits of the alternative scenarios; and fourth, the fuzzy group permutation approach is used to select the optimal mission scenario. We present the results of a case study at NASA’s Johnson Space center to demonstrate: (1) the complexity of mission scenario selection involving subjective and objective judgments provided by multiple space exploration experts; and (2) a systematic and structured method for aggregating quantitative and qualitative data concerning a large number of competing and conflicting mission events. [Copyright &y& Elsevier]

Abstract: Fuzzy rough sets, generalized from Pawlak''s rough sets, were introduced for dealing with continuous or fuzzy data. This model has been widely discussed and applied these years. It is shown that the model of fuzzy rough sets is sensitive to noisy samples, especially sensitive to mislabeled samples. As data are usually contaminated with noise in practice, a robust model is desirable. We introduce a new model of fuzzy rough set model, called soft fuzzy rough sets, and design a robust classification algorithm based on the model. Experimental results show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In 2011, questions raised in medicine, by the occurrence of the unexpected death of an infant (SUDI), are far from having found definitive answers. Explanations remain fragmented, statistics are fuzzy, research is unsystematic and care protocols are still highly varied in spite of recommendations by the HAS (Haute Autorité de santé, French National Authority for Health) in 2007, which are, in practice, difficult to follow. After 17 years, preventive measures should have given much better results but they continue to come up against strong resistance from the public and certain professionals, a lack of proper resources and numerous contradictory messages from business, advertising and even medicine. [Copyright &y& Elsevier]

Abstract: We review various representations of the median and related aggregation functions. An advantage of the median is that it discards extreme values of the inputs, and hence exhibits a better central tendency than the arithmetic mean. However, the value of the median depends on only one or two central inputs. Our aim is to design median-like aggregation functions whose value depends on several central inputs. Such functions will preserve the stability of the median against extreme values, but will take more inputs into account. A method based on graduation curves is presented. [Copyright &y& Elsevier]

Abstract: This study presents a methodology for solving the sealed bid, multi-attribute reverse auction problem of e-sourcing in which the sales item is defined by several attributes, the buyer is auctioneer, and the suppliers are the bidders. There is only one buyer and a number of suppliers. Both qualitative and quantitative attributes of benefit and cost types are considered for solving the winner determination (WD) problem of reverse auction. Here, the WD problem is considered as multi-criteria decision making problem (MCDM). In order to address the imprecision of suppliers or decision makers in formulating the preference value of various attributes in MCDM, a fuzzy TOPSIS based methodology along with a mechanism for determination of fuzzy linguistic value of each attribute is proposed in this article. Entropy method is utilised to enumerate the weights of various attributes automatically without involvement of decision makers. An illustrative example is presented to demonstrate the applicability of the proposed methodology. [Copyright &y& Elsevier]

Abstract: In this paper, we present a novel decision support system for order acceptance/rejection in a hybrid Make-to-Stock/Make-to-Order production environment. The proposed decision support system is comprised of five steps. At the first step, the customers are prioritized based on a fuzzy TOPSIS method. Rough-cut capacity and rough-cut inventory are calculated in the second step and in case of unavailability in capacity and materials, some undesirable orders are rejected. Also, proper decisions are made about non-rejected orders. At the next step, prices and delivery dates of the non-rejected orders are determined by running a mixed-integer mathematical programming model. At the fourth step, a set of guidelines are proposed to help the organization negotiate over price and due date with the customers. In the next step, if the customer accepts the offered price and delivery date, the order is accepted and later considered in the production schedule of the shop floor, otherwise the order is rejected. Finally, numerical experiments are conducted to show the tractability of the applied mathematical programming model. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a data-driven model-based assessment strategy to investigate the performance of a cooling tower. In order to achieve this objective, the operations of a cooling tower are first characterized using a data-driven method, multiple models, which presents a set of local models in the format of linear equations. Satisfactory fuzzy c-mean clustering algorithm is used to classify operating data into several groups to build local models. The developed models are then applied to predict the performance of the system based on design input parameters provided by the manufacturer. The tower characteristics are also investigated using the proposed models via the effects of the water/air flow ratio. The predicted results tend to agree well with the calculated tower characteristics using actual measured operating data from an industrial plant. By comparison with the design characteristic curve provided by the manufacturer, the effectiveness of cooling tower can be obtained in the end. A case study conducted in a commercial plant demonstrates the validity of proposed approach. It should be noted that this is the first attempt to assess the cooling efficiency which is deviated from the original design value using operating data for an industrial scale process. Moreover, the evaluated process need not interrupt the normal operation of the cooling tower. This should be of particular interest in industrial applications. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present an approach for addressing the problem of dynamic dimension reduction during on-line training, evolution and updating of evolving fuzzy classifiers (EFC). The basic idea of our approach is that, instead of permanently changing the list of most important features with newly loaded data blocks, we generalize the concept of incremental feature selection to an incremental feature weighting approach: features are assigned weights in [0,1] according to their importance level. These weights are permanently updated during on-line mode and guarantee a smooth learning process in the evolving fuzzy classifiers, as they change softly and continuously over time. In some cases, when the weights become (approximately) 0, an automatic switching off of some features and therefore a (soft) dimension reduction is achieved. Two novel incremental feature weighting strategies are proposed in this paper, one based on a leave-one-feature-out, the other based on a feature-wise separability criterion. We will describe the integration concept of the feature weights in the evolving fuzzy classifiers, using single and multi-model architecture, where FLEXFIS-Class SM and FLEXFIS-Class MM serve as training engines. The whole approach of integrated incremental feature weighting in evolving fuzzy classifiers will be evaluated based on high-dimensional on-line real-world classification scenarios and based on data from the Internet. The results will show that incremental feature weighting in EFC in fact helps to reduce curse of dimensionality and therefore guides the evolving fuzzy classifiers to a higher on-line predictive power. [Copyright &y& Elsevier]

Abstract: In this paper, we establish a novel regard towards fuzzy clustering, showing it provides a sound framework for fitting finite mixture models. We propose a novel fuzzy clustering-type methodology for finite mixture model fitting, effected by utilizing a regularized form of the fuzzy c-means (FCM) algorithm, and introducing a proper dissimilarity functional for the algorithm with respect to the probabilistic properties of the model being treated. We apply the proposed methodology in a number of popular finite mixture models, and the corresponding expressions of the fuzzy model fitting algorithm are derived. We examine the efficacy of our novel approach in both clustering and classification applications of benchmark data sets, and we demonstrate the advantages of the proposed approach over maximum-likelihood. [ABSTRACT FROM AUTHOR]

Ostertagia ostertagi is a nematode, predominantly affecting cattle in the Pampean region of Argentina. A mathematical model parametrized using fuzzy rule-based systems of the Takagi-Sugeno-Kant type (FTSK) for estimating the development time from egg to infecting larval stage L3 of the gastrointestinal parasite O. ostertagi is here proposed. The estimation of development time of O. ostertagi is essential for the generation of appropriate control mechanisms, since this provides information about the time when parasites are ready to migrate to pastures. For the purpose of reflecting the natural environmental conditions, the mean daily temperature is taken as the main and only regulator of the development time. Humidity conditions are considered to be sufficient for the normal development of the larvae. Hence the individual's daily growth is a function of its length and the mean temperature recorded on the previous day. It is expressed in terms of a difference equation with fuzzy parameters, which are defined using laboratory data. Model outputs are tested against results of field experiments. Simulation results are very satisfactory, yielding a mean estimation error (MEE) of 0.64 weeks, with variance 0.34, and a determination coefficient R 2 =0.74. The model clearly exhibits an inverse relationship between development time and temperature both in controlled and in field conditions. It also exhibits a very sensitive response both to the order in which the temperature sequence occurs, – reproducing the differences observed between spring and autumn – and to the amplitude of the temperature range. [Copyright &y& Elsevier]

Abstract: All Trend Impact Analysis (TIA) algorithms in literature conduct the analysis based on direct estimates provided by experts for the probability of occurrence of an unprecedented event as an input to the algorithm. In this paper, we propose an advanced mechanism to generate more justifiable estimates to the probability of occurrence of an unprecedented event as a function of time with different degrees of severity using Fuzzy Logic. We postulate that in some cases it is better not to estimate the probability of occurrence of an unprecedented event directly; but rather estimate it indirectly via its attributes, using Fuzzy Logic. The core idea of the paper is to customize the generic process of reasoning with Fuzzy Logic by adding the additional step of attributes simulation, as unprecedented events do not occur all of a sudden but rather their occurrence is affected by change in the values of a set of attributes, especially when they reach certain threshold values. [Copyright &y& Elsevier]

Abstract: The bootstrap is a simple and straightforward method for calculating approximated biases, standard deviations, confidence intervals, testing statistical hypotheses, and so forth, in almost any nonparametric estimation problem. A new approach for bootstrap testing fuzzy hypotheses based on fuzzy test statistic is introduced. In this paper we describe bootstrap method that is designed directly for hypothesis testing for fuzzy data based on Yao–Wu signed distance. [Copyright &y& Elsevier]

Abstract: There is a family of well-known external clustering validity indexes to measure the degree of compatibility or similarity between two hard partitions of a given data set, including partitions with different numbers of categories. A unified, fully equivalent set-theoretic formulation for an important class of such indexes was derived and extended to the fuzzy domain in a previous work by the author [Campello, R.J.G.B., 2007. A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment. Pattern Recognition Lett., 28, 833–841]. However, the proposed fuzzy set-theoretic formulation is not valid as a general approach for comparing two fuzzy partitions of data. Instead, it is an approach for comparing a fuzzy partition against a hard referential partition of the data into mutually disjoint categories. In this paper, generalized external indexes for comparing two data partitions with overlapping categories are introduced. These indexes can be used as general measures for comparing two partitions of the same data set into overlapping categories. An important issue that is seldom touched in the literature is also addressed in the paper, namely, how to compare two partitions of different subsamples of data. A number of pedagogical examples and three simulation experiments are presented and analyzed in details. A review of recent related work compiled from the literature is also provided. [Copyright &y& Elsevier]

Abstract: Various approaches to partitioning of high-dimensional input space have been studied with the intent of developing homogeneous clusters formed over input and output spaces of variables encountered in system modeling. In this study, we propose a new design methodology of a fuzzy model where the input space is partitioned by making use of some classification algorithm, especially, fuzzy K-nearest neighbors (K-NN) classifier being guided by some auxiliary information granules formed in the output space. This classifier being regarded in the context of this design as a supervision mechanism is used to capture the distribution of data over the output space. This type of supervision is beneficial when developing the structure in the input space. It is demonstrated that data involved in a partition constructed by the fuzzy K-NN method realized in the input space show a high level of homogeneity with regard to the data present in the output space. This enhances the performance of the fuzzy rule-based model whose premises in the rules involve partitions formed by the fuzzy K-NN. The design is illustrated with the aid of numeric examples that also provide a detailed insight into the performance of the fuzzy models and quantify several crucial design issues. [Copyright &y& Elsevier]

Abstract: Site uncertainties significantly influence groundwater flow and contaminant transport predictions. Aleatoric and epistemic uncertainty are both identified in site characterization and represented using proper uncertainty theories. When one theory best represents one parameter whereas a different theory may be more suitable for another parameter, the hybrid propagation of aleatoric (random) and epistemic (nonrandom) uncertainties will occur. The computational challenges of joint propagation of aleatoric and epistemic uncertainty through groundwater flow and contaminant transport models are significant. A fuzzy-stochastic nonlinear model was developed in this paper to incorporate these two types of uncertain site information and reduce the computational cost. The results show that (1) the computational cost using the nonlinear model is reduced compared with that of using the sparse grid algorithm and Monte Carlo methods; (2) the uncertainty of hydraulic conductivity (K) significantly influences the water head and solute distribution at the observation wells compared to other uncertain parameters, such as the storage coefficient and the distribution coefficient (K d ); and (3) the combination of multiple uncertain parameters substantially affects the simulation results. Neglecting site uncertainties may lead to unrealistic predictions. [Copyright &y& Elsevier]

Abstract: In this paper we propose a new method for combining simple classifiers through the analogue Hopfield Neural Network (HNN) optimization paradigm for classifying natural textures in images. The base classifiers are the Fuzzy clustering (FC) and the parametric Bayesian estimator (BP). An initial unsupervised training phase determines the number of clusters and estimates the parameters for both FC and BP. Then a decision phase is carried out, where we build as many Hopfield Neural Networks as the available number of clusters. The number of nodes at each network is the number of pixels in the image which is to be classified. Each node at each network is initially loaded with a state value, which is the membership degree (provided by FC) that the node (pixel) belongs to the cluster associated to the network. Each state is later iteratively updated during the HNN optimization process taking into account the previous states and two types of external influences exerted by other nodes in its neighborhood. The external influences are mapped as consistencies. One is embedded in an energy term which considers the states of the node to be updated and the states of its neighbors. The other is mapped as the inter-connection weights between the nodes. From BP, we obtain the probabilities that the nodes (pixels) belong to a cluster (network). We define these weights as a relation between states and probabilities between the nodes in the neighborhood of the node which is being updated. This is the classifier combination, making the main finding of this paper. The proposed combined strategy based on the HNN outperforms the simple classifiers and also classical combination strategies. [Copyright &y& Elsevier]

Abstract: Cluster analysis is one of the most crucial techniques in statistical data analysis. Among the clustering methods, density-based methods have great importance due to their ability to recognize clusters with arbitrary shape. In this paper, robustness of the clustering methods is handled. These methods use distance-based neighborhood relations between points. In particular, DBSCAN (density-based spatial clustering of applications with noise) algorithm and FN-DBSCAN (fuzzy neighborhood DBSCAN) algorithm are analyzed. FN-DBSCAN algorithm uses fuzzy neighborhood relation whereas DBSCAN uses crisp neighborhood relation. The main characteristic of the FN-DBSCAN algorithm is that it combines the speed of the DBSCAN and robustness of the NRFJP (noise robust fuzzy joint points) algorithms. It is observed that the FN-DBSCAN algorithm is more robust than the DBSCAN algorithm to datasets with various shapes and densities. [Copyright &y& Elsevier]

Abstract: Motivated by the authors’ previous work on the control of queueing systems, the assessment of sustainable development, and the measurement of material recyclability, this paper provides sufficient conditions on the parameters of hierarchical fuzzy systems under which the output of the system is monotonic with respect to its inputs. This property could be useful in designing multistage fuzzy inference systems and fuzzy controllers. [Copyright &y& Elsevier]

Abstract: In this study, identification of nonlinear systems via Laguerre network based fuzzy model is introduced. We first describe the proposed modeling approach in detail and suggest a fast learning scheme for its training. The proposed approach is applied in three dynamic system modeling problems including Box–Jenkins gas furnace data and forced Van der Pol oscillator. When we compare the performance of the proposed approach against the classical Sugeno and adaptive network based fuzzy inference system modeling, our approach is found to have superior modeling performance and generalization capability. [Copyright &y& Elsevier]

Abstract: In the face of speedy revolution of high technology, the advanced technology becomes one of the key drivers to enhance productivity in a firm or even in a country. In order to compete in the global environment, the ability and effectiveness of acquiring new technology are essential for firms, especially for the traditional machinery industry. In Taiwan, the societal structure is built on the foundation of Small-Medium Enterprises (SMEs). Thus most new technologies need and depend on the technology transfer (TT) from international firms and research institutes. Due to the complicity of influential factors of TT, such as industrial feature (IF), organizational feature (OF), personnel feature (PF) and technological feature (TF), difficulties are encountered in evaluating the effectiveness of TT. This study develops a rule-based decision support mechanism using fuzzy set theory and the method of Analytic Hierarchy Process (AHP) to evaluate the effectiveness of TT. Also, a statistic analysis (Statistics Package for Social Science, SPSS) is adopted to confirm the results of fuzzy AHP analysis. This study finds that prior successful TT experience, workers’ positive attitude, proper authorization, and more codification exist in a novel technology are highly influential. Those factors are important in concern when a firm launching TT. Furthermore, firms’ age and personnel educational background are regardless. [Copyright &y& Elsevier]

This paper models the dissolved oxygen (DO) dynamics in the Orbetello lagoon as a function of the physico-chemical and ecological system variables, including the submerged vegetation, nutrients, and hydrodynamics. It should be viewed as the concluding sequel to a previous paper describing the dynamics of the lagoon ecosystem [Giusti, E., Marsili-Libelli, S., 2006. An integrated model for the Orbetello lagoon ecosystem, Ecol. Model. 196, 379–394] by introducing the missing DO dynamics. The model considers the oxygen demand originating from the decay of carbonaceous and nitrogenous compounds, as well as photosynthesis and natural reaeration by winds and currents as the oxygen producing processes. With a fixed-parameter set the model could accurately reproduce each single circadian DO cycle, but in the long run it failed to extend this fit and could not accommodate the large DO fluctuations induced by the seasonal variability. In order to enhance the model flexibility, a fuzzy pattern recognition algorithm was designed to classify the circadian DO patterns into four typical behaviours, related to the season, and estimate the corresponding parameters, with the overall model output being a fuzzy combination of these sets. The paper discusses several methods to patch the parameter sets and compares their performance in tracking long-term DO variations. A final assessment of the model validity is obtained by incorporating the whole DO dynamics (model, fuzzy pattern recognition and parameter combination) into the general lagoon model and producing a consistently correct series of DO daily distributions over a yearly cycle. Thus the paper contains both a practical and a methodological aspect. The practical one is the linking of all the lagoon dynamics to the dissolved oxygen kinetics in order to clarify to what extent macroalgae and macrophytes influence the oxygen balance. The methodological aspect consists of extending the validity of short-term models to long time-horizons through a patching technique supported by fuzzy pattern recognition. [Copyright &y& Elsevier]

Abstract: The fuzzy weighted average is widely used to solve hierarchical evaluation problems, including fuzzy consideration for the operations of scoring, weighting and aggregating. Previous works considered the fuzziness of score and weight, and used the additive function to aggregate these weighted scores. This study considers the aggregation operator also as a fuzzy variable, and uses a generalized means function to fuzzify the aggregation operator within a fuzzy weighted average. In practice, the proposed model not only considers both the relative important of the criteria and its achieved performance, but also conveys the influence of the DM’s (Decision Maker’s) evaluation attitude. Thus the proposed model can flexibly reflect any DM’s evaluation attitude, such as open, neutral or rigorous. Thereby, the proposed model can make an objective evaluation that approaches a real decision making situation, and thus has the potential to be a useful management tool for improved resolution of fuzzy hierarchical evaluation problems. [Copyright &y& Elsevier]

Abstract: In this paper, a formula for the expected value of a function of a fuzzy variable is presented, with which the exact expected value of the function of the fuzzy variable can be obtained directly. The proposed formula holds provided that the function is monotonic, on the assumption that the fuzzy variable has a continuous membership function. Furthermore, some examples showing how to apply the formula are given. [Copyright &y& Elsevier]

Abstract: This paper analyzes a single-period inventory model of profit maximization with a reordering strategy in an imprecise environment. The entire period is divided into two slots and the customer demand is considered as a fuzzy number in situations where the demand in each slot is linguistic in nature and characterized as ‘demand is about ’. The reordering is to be done during the mid-season after the early-season demand has been observed. The objective is to determine the optimal order quantity in maximizing the expected resultant profit by considering the fuzzy demand and reordering strategy in the single-period framework. The solution procedure is presented using ordering of fuzzy numbers with respect to their possibilistic mean values. Numerical examples are given to illustrate the efficiency of this strategy. [Copyright &y& Elsevier]

This paper constitutes a first step towards an extension of correspondence analysis with fuzzy data (FCA). At this stage, our main objective is to lay down the algebraic foundations for this fuzzy extension of the usual correspondence analysis. A two-step method is introduced to convert the fuzzy eigenvalue problem to an ordinary one. We consider a fuzzy matrix as the set of its cuts. Each such cut is an interval-valued matrix viewed as a line-segment in the matrix space. In this way, line-segments of cut-matrices are transformed into intervals of eigenvalues. Therefore, the two-step method is essentially a reduction of the fuzzy eigenvalue problem to an ordinary one. We illustrate the FCA-fuzzy eigenvalue problem with a simple numerical example. We hope upon the completion of this project in near future, to be able to supply the necessary tools for the end user of the correspondence analysis with fuzzy data. [Copyright &y& Elsevier]

Abstract: A practical situation often facing us is that fuzzy spatial data are recorded as crisp real-valued numbers, e.g., a PM10 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 PM10 data of California, USA. Three sample membership functions are extracted from the data itself: linear, quadratic and hyperbolic tangent and applied to the PM10 data. The predicted membership grades are also transformed back into PM10 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. [Copyright &y& Elsevier]

In this paper, we introduce a new topology of Fuzzy Polynomial Neural Networks (FPNN) that is based on a genetically optimized multi-layer perceptron with fuzzy polynomial neurons (FPNs) and discuss its comprehensive design methodology involving mechanisms of genetic optimization, especially genetic algorithms (GAs). The development of the ‘conventional’ FPNNs uses an extended Group Method of Data Handling. The network exploits a fixed fuzzy inference type in each FPN of the FPNN as well as considers a fixed number of input nodes at FPNs (or nodes) located in each layer. Here, the proposed FPNN gives rise to a structurally optimized structure and comes with a substantial level of flexibility in comparison to the one we encounter in conventional FPNNs. The structural optimization is realized via GAs whereas in case of the parametric optimization we proceed with a standard least-square method-based learning. The performance of the networks is quantified through experimentation involving two time series dataset already used in fuzzy modeling. The results demonstrate their superiority over the existing fuzzy and neural models. [Copyright &y& Elsevier]

Blackwell sufficiency is an accepted instrument for the comparison of random experiments. In this paper it is shown that Blackwell sufficiency, only in special cases, is well suited for the comparison of fuzzy experiments. This is discussed for two types of fuzzy experiments: random experiments with vague outcomes where we ask for links between fuzziness and Blackwell sufficiency, and experiments which are evaluated by belief and plausibility where we find some connections between specificity and Blackwell sufficiency. [Copyright &y& Elsevier]