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This paper presents a comprehensive study of the signed distance metric for fuzzy numbers. Due to the property of directionality, this measure has been widely used. However, it has a main drawback in handling asymmetry and irregular shapes in fuzzy numbers. To overcome this rather bad feature, we introduce two new distances, the balanced signed distance (BSGD) and the generalised signed distance (GSGD), seen as generalisations of the classical signed distance. The developed distances successfully and effectively take into account the shape, the asymmetry and the overlap of fuzzy numbers. The GSGD is additionally directional, while the BSGD satisfies the requirements for being a metric of fuzzy quantities. Analytical simplifications of both distances in the case of often-used particular types of fuzzy numbers are provided to simplify the computation process, making them as simple as the classical signed distance but more realistic and precise. We empirically analyse the sensitivity of these distances. Considering several scenarios of fuzzy numbers, we also numerically compare these distances against established metrics, highlighting the advantages of the BSGD and the GSGD in capturing the shape properties of fuzzy numbers. One main finding of this research is that the defended distances capture with great precision the distance between fuzzy numbers; additionally, they are theoretically appealing and are computationally easy for traditional fuzzy numbers such as triangular, trapezoidal, Gaussian, etc., making these metrics promising. [ABSTRACT FROM AUTHOR]

Machine learning applied to regression models offers powerful mathematical tools for predicting responses based on one or more predictor variables. This paper extends the concept of multiple linear regression by implementing a learning system and incorporating both fuzzy predictors and fuzzy responses. To estimate the unknown parameters of this soft regression model, the approach involves minimizing the absolute distance between two lines under three constraints related to the absolute error distance between observed data and their respective predicted lines. A thorough comparative analysis is conducted, showcasing the practical applicability and superiority of the proposed soft multiple linear regression model. The effectiveness of the model is demonstrated through a comprehensive examination involving simulation studies and real-life application examples.

The EM algorithm is a powerful tool and generic useful device in a variety of problems for maximum likelihood estimation with incomplete data which usually appears in practice. Here, the term ``incomplete" means a general state and in different situations it can mean different meanings, such as lost data, open source data, censored observations, etc. This paper introduces an application of the EM algorithm in which the meaning of ``incomplete" data is non-precise or fuzzy observations. The proposed approach in this paper for estimating an unknown parameter in the parametric statistical model by maximizing the likelihood function based on fuzzy observations. Meanwhile, this article presents a case study in the electronics industry, which is an extension of a well-known example used in introductions to the EM algorithm and focuses on the applicability of the algorithm in a fuzzy environment. This paper can be useful for graduate students to understand the subject in fuzzy environment and moreover to use the EM algorithm in more complex examples.

The EM algorithm is a powerful tool and generic useful device in a variety of problems for maximum likelihood estimation with incomplete data which usually appears in practice. Here, the term "incomplete" means a general state and in different situations it can mean different meanings, such as lost data, open source data, censored observations, etc. This paper introduces an application of the EM algorithm in which the meaning of "incomplete" data is non-precise or fuzzy observations. The proposed approach in this paper for estimating an unknown parameter in the parametric statistical model by maximizing the likelihood function based on fuzzy observations. Meanwhile, this article presents a case study in the electronics industry, which is an extension of a well-known example used in introductions to the EM algorithm and focuses on the applicability of the algorithm in a fuzzy environment. This paper can be useful for graduate students to understand the subject in fuzzy environment and moreover to use the EM algorithm in more complex examples. [ABSTRACT FROM AUTHOR]

An approach is proposed to construct fuzzy confidence intervals for unknown parameters in statistical models. In this approach, a family of confidence intervals of the unknown crisp parameters is considered. Such confidence intervals are used to obtain a fuzzy confidence interval for the parameter of interest. The proposed approach enjoys a wide range of confidence intervals to obtain a trapezoidal shaped fuzzy set of the parameter space as the fuzzy confidence interval for the parameter of interest. By using the resolution identity, it is shown that the constructed fuzzy confidence intervals are really fuzzy sets of the parameter space. Some numerical examples are provided to explain the functionality of the approach at one-sided and two-sided fuzzy confidence intervals. Moreover, the application of this proposed approach in health sciences is provided for the case of the recovery time of olfactory and gustatory dysfunctions for COVID-19 patients. [ABSTRACT FROM AUTHOR]

In several research areas, ratings data and response times have been successfully used to unfold the stagewise process through which human raters provide their responses to questionnaires and social surveys. A limitation of the standard approach to analyze this type of data is that it requires the use of independent statistical models. Although this provides an effective way to simplify the data analysis, it could potentially involve difficulties with regard to statistical inference and interpretation. In this sense, a joint analysis could be more effective. In this research article, we describe a way to jointly analyze ratings and response times by means of fuzzy numbers. A probabilistic tree model framework has been adopted to fuzzify ratings data and four-parameters triangular fuzzy numbers have been used in order to integrate crisp responses and times. Finally, a real case study on psychometric data is discussed in order to illustrate the proposed methodology. Overall, we provide initial findings to the problem of using fuzzy numbers as abstract models for representing ratings data with additional information (i.e., response times). The results indicate that using fuzzy numbers leads to theoretically sound and more parsimonious data analysis methods, which limit some statistical issues that may occur with standard data analysis procedures. [ABSTRACT FROM AUTHOR]

The failure criterion of structural serviceability is often fuzzy, which has a direct impact on the results of structural reliability analysis. Membership function is a basic mathematical tool to describe the fuzziness of failure criteria. At present, the fuzzy statistical method for generating the fuzzy set membership function is to take the numerical interval of the fuzzy set as a sample, and directly generate the membership function through statistics. However, this kind of sample will cover the uncertainty of the individual's understanding of fuzzy boundaries to a certain extent, and its statistical results are difficult to truly reflect the characteristics of fuzzy sets. The fuzzy boundary is described by the membership density function, and the numerical interval covering the fuzzy boundary is taken as the sample. The fuzzy statistical method for generating the membership density function is proposed, and the indirect statistical method for generating the membership function is established. The comparative analysis results show that the membership functions generated by the two statistical methods are different. The membership function generated by indirect statistical method can fully reflect the uncertainty of the individual's understanding of the fuzzy boundary, more truly reflect the characteristics of the fuzzy set, and provide a more solid foundation for the fuzzy probability analysis of structural serviceability. [ABSTRACT FROM AUTHOR]

In order to reduce the risk of slope stability evaluation due to the fuzziness of calculation parameters, a finite element analysis method of slope stability based on fuzzy statistics is proposed. Based on the principle of quasi-static method and with the help of the finite element software COMSOL multiphysics, this paper studies the stability of the gravel soil accumulation rock slope under the action of different seismic acceleration. By analyzing the displacement, plastic zone and safety factor of the rock soil slope, the stability of the rock soil slope is analyzed. The research results show that the fuzziness of mechanical parameters of rock and soil slope will lead to the fuzziness of position displacement and stress analysis results of rock and soil slope, and the analysis of rock and soil slope with the method of fuzzy finite element analysis can strengthen the comprehensive understanding of position displacement, stress and safety of rock and soil slope by engineers and technicians, and reduce the stability of rock and soil slope due to the fuzziness of calculation parameters to a certain extent Evaluate the risk qualitatively. [ABSTRACT FROM AUTHOR]

In marketing, qualitative data are used in theory development to investigate marketing phenomena in more depth. After qualitative data are collected, the judgment-based classification of items into categories is routinely used to summarize and communicate the information contained in the data. In this article, the authors provide marketing researchers with a method that (1) provides useful substantive information about the proportion and degree to which items belong to several categories and (2) measures the classification accuracy of the judges. The model is called the fuzzy latent class model (FLCM), because it extends Dillon and Mulani's (1984) latent class model by freeing it from the restrictive assumption that all items are crisp for a given categorization. Instead, FLCM allows for items to be either crisp or fuzzy. Crisp items belong exclusively to one category, whereas fuzzy items belong--in varying degree--to multiple categories. This relaxation in the assumption about the nature of qualitative data makes FLCM more widely applicable: Qualitative data in marketing research are often fuzzy, because they involve open-ended descriptions of complex phenomena. The authors also propose a moment-based measure of overall data fuzziness that is bounded by 0 (completely crisp) and 1 (completely fuzzy). [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of defining statistical parameters when the uncertainty is expressed using a fuzzy measure. We extend the concept of monotone expectation in order to define a monotone variance and monotone moments. We also study parameters that allow the joint analysis of two functions defined over the same reference set. Finally, we propose some parameters over product spaces, considering the case in which a function over the product space is available and also the case in which such function is obtained by combining those in the marginal spaces.

The measurement of volatility is of fundamental importance in finance. Standard market practice adopted for volatility estimation from option prices leads to a considerable loss of information and the introduction of an element of arbitrariness in the volatility index computation. We propose to adopt fuzzy regression methods in order to include all the available information from option prices, and to obtain an informative volatility index. In fact, the obtained fuzzy volatility indices not only offer a most possible value, but also a lower and an upper bound for the interval of possible values, providing investors with an additional source of information. We also propose a defuzzification procedure to select a representative value within this interval. Moreover, we investigate the occurrence of truncation and discretization errors in volatility index computation by adopting an interpolation-extrapolation method. We also test the forecasting power of each volatility index on future realized volatility. [ABSTRACT FROM AUTHOR]

Abstract: The efficacies of continuous positive airway pressure (CPAP) are well documented in decreasing the apnoea–hypopnoea index in patients with obstructive sleep apnoea. To guarantee these efficacies, CPAP manufacturers must thoroughly test these devices to ensure the flow of oxygenated air to the patient at various temperatures during a prescribed time frame. The calculation of the percent oxygen in a “bimixture” of gas can be done by measuring the travel time of a sound wave through the gas, and the travel time is proportional to the density of the air. We utilized existing multisensor tubes that were developed to collect and measure oxygen flow, diffusion, speed, temperature, and time metrics. Then these metrics were analysed using a Markov fuzzy, statistical, artificial neural network, nearest‐neighbour predictive approach to determine the interactions between these variables. An improved Kalman filter method was employed to reduce noise, increase viscosity, and obtain correct data from the CPAP system. [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]

Contrast Stretching is an important part in medical image processing applications. Contrast is the difference between two adjacent pixels. Fuzzy statistical values are analyzed and better results are produced in the spatial domain of the input image. The histogram mapping produces the resultant image with less impulsive noise and smooth nature. The probabilities of gray values are generated and the fuzzy set is determined from the position of the input image pixel. The result indicates the good performance of the proposed fuzzy based stretching. The inverse transform of the real values are mapped with the input image to generate the fuzzy statistics. This approach gives a flexible image enhancement for medical images in the presence of noises.

Life time data are mainly used in medicine, public health, and engineering sciences. The classical statistics related to these fields are based on precise measurements. However, according to modern measurement science precise measurement of continuous phenomena is not possible. In addition the observed quantity is more or less precise. In order to obtain realistic results, in addition to classical and Bayesian inference, the most up to date model for this are fuzzy number approaches which are more suitable and realistic. In this study, I consider the classical and Bayesian inference criteria for the Pareto distribution to obtain more realistic results for fuzzy observations of life time. In addition to stochastic variation the proposed generalized estimators cover fuzziness of the life times as well. [ABSTRACT FROM AUTHOR]

Despite the growing number of studies focusing on urban vulnerability to climate change, adaptive capacity, which is a key component of the IPCC definition of vulnerability, is rarely assessed quantitatively. We examine the capacity of adaptation in the Concepción Metropolitan Area, Chile. A flexible methodology based on spatial fuzzy modelling was developed to standardise and aggregate, through a stepwise approach, seventeen indicators derived from widely available census statistical data into an adaptive capacity index. The results indicate that all the municipalities in the CMA increased their level of adaptive capacity between 1992 and 2002. However, the relative differences between municipalities did not change significantly over the studied timeframe. Fuzzy overlay allowed us to standardise and to effectively aggregate indicators with differing ranges and granularities of attribute values into an overall index. It also provided a conceptually sound and reproducible means of exploring the interplay of many indicators that individually influence adaptive capacity. Furthermore, it captured the complex, aggregated and continued nature of the adaptive capacity, favouring to deal with gaps of data and knowledge associated with the concept of adaptive capacity. The resulting maps can help identify municipalities where adaptive capacity is weak and identify which components of adaptive capacity need strengthening. Identification of these capacity conditions can stimulate dialogue amongst policymakers and stakeholders regarding how to manage urban areas and how to prioritise resources for urban development in ways that can also improve adaptive capacity and thus reduce vulnerability to climate change. [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]

Background: The fuzzy rating scale was introduced to cope with the imprecision of human thought and experience in measuring attitudes in many fields of Psychology. The flexibility and expressiveness of this scale allow us to properly describe the answers to many questions involving psychological measurement. Method: Analyzing the responses to a fuzzy rating scale-based questionnaire is indeed a critical problem. Nevertheless, over the last years, a methodology is being developed to analyze statistically fuzzy data in such a way that the information they contain is fully exploited. In this paper, a summary review of the main procedures is given. Results: The methods are illustrated by their application on the dataset obtained from a case study with nine-year-old children. In this study, children replied to some questions from the well-known TIMSS/ PIRLS questionnaire by using a fuzzy rating scale. The form could be filled in either on the computer or by hand. Conclusions: The study indicates that the requirements of background and training underlying the fuzzy rating scale are not too demanding. Moreover, it is clearly shown that statistical conclusions substantially often differ depending on the responses being given in accordance with either a Likert scale or a fuzzy rating scale. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce and study certain new concepts of α-ψ-proximal contractions in an intuitionistic fuzzy metric space. Then we establish certain best proximity point theorems for such proximal contractions in intuitionistic fuzzy metric spaces. As an application, we deduce best proximity and fixed point results in partially ordered intuitionistic fuzzy metric spaces. Several interesting consequences of our obtained results are presented in the form of new fixed point theorems which contain some recent fixed point theorems as special cases. Moreover, we discuss some illustrative examples to highlight the realized improvements. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to use soft computing technique and fuzzy statistical tool to evaluate people's performance on the marketing research and time management. Design/methodology/approach – Through standardized measurement system, the authors come up with real-value data to satisfy not the current needs but data itself. This is when fuzzy classification stands out and highlights the area of in-between and undefined. Findings – The proposed metric system helps the authors to assess the distance among trapezoidal fuzzy data. The index of efficiency between observed time and ideal time is also presented. Originality/value – With the ranking of fuzzy sample, the authors can examine the decision process by non-parametric testing hypothesis. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that the use of probability‐statistic methods, especially at the early stage of diagnosing the technical condition of aviation gas turbine engines (GTE) when the flight information has fuzzy and limitation and uncertainty properties, is unfounded. Hence the efficiency of the use of Soft Computing methods‐fuzzy logic and neural networks at these diagnostic stages is considered. Training with high accuracy of fuzzy multiple linear and non‐linear models (fuzzy regression equations) which received on the statistical fuzzy data basis is made. Thus, for to make a more adequate model of the technical condition of GTE, the dynamics changes of skewness and kurtosis coefficients are analysed. Research of skewness and kurtasis coefficients shows, that the statistical distributions of the work parameters of GTE have a fuzzy character. Hence, consideration of fuzzy skewness and kurtosis coefficients is expedient. Investigation of the basic characteristics of the changes in the dynamics of the work parameters of GTE allows to draw the conclusion that it is necessary to use fuzzy statistical analysis during the preliminary identification of the technical condition of engines. Research of changes in the values of correlation coefficients also demonstrates their fuzzy character. Therefore for models choice the application of the Fuzzy Correlation Analysis results is offered. The fuzzy multiple correlation coefficient of fuzzy multiple regression is considered for checking the adequacy of models. At the information sufficiency is offered to use recurrent algorithm of aviation GTE technical condition identification (hard computing technology is used) on measurements of input and output parameters of the multiple linear and nonlinear generalised models at presence of noise measured (the new recursive Least Squares Method (LSM)). The system that is developed to monitor the condition of GTE provides stage‐by‐stage estimation of the technical condition of an engine. As an application of this technique, an estimation of the new operating aviation engine temperature condition was made. Santrauka Straipsnyje atskleidžiamas tikimybinio-statistinio metodo nepagrįstumas diagnozuojant dujų turbininius variklius, kai informacija yra netiksli, ribota ir neapibrėžta. Parodytas technologijos Soft Computing taikymo efektyvumas. Taikant netikslios statistikos, netikslios logikos ir neuroninių tinklų tikslius metodus dujų turbininių variklių diagnozavimui atliekamas daugiamačių tiesinių ir netiesinių modelių (regresijos lygčių), gautų iš netikslių statistinių duomenų, apmokymas. Taikant aprašytą metodą buvo atlikta pradėto eksploatuoti turbininio variklio šiluminės būsenos analizė. First Published Online: 14 Oct 2010 Reikšminiai žodžiai: aviacinis dujų turbininis variklis, netiksli logika ir neuroniniai tinklai, netiksli statistika, netikslus daugialypės koreliacijos koeficientas.

The usage stage of distributed IT&C applications - DIAs raises specific risks relating to the increased processing and usage strain related to live interactions. The incident categories and impact, as well as associated actors, are shown in order to serve as quantifying factors in the building of models aiming at quantifying their impact on distributed application reliability. A model aiming at extension impact assessment is built and details on the evaluation of the MERICS testing application are detailed. The component obsolescence is evaluated through an additional model and its impact on MERICS is shown alongside difficulties in identifying composing factors. [ABSTRACT FROM AUTHOR]

The testing-development phase has been carried out in a given control environment. However, the product will be used in different operating environment by different end-users, which is unknown to the developer. The operating environment may range from a very clean one up to a harsh environment. These uncertain operating environments will impact to the reliability and performance of the software which may differ from the testing phase reliability. We consider that the effect of environment on reliability has a fuzzy nature. The fuzzy effects of the field environments can be captured by a unit-free environmental factor. To overcome this problem, the fuzzy probabilistic theory may be used in the processing of stochastic parameters, taking into account their fuzzy nature. The proposed model is based on Weibull distribution. The aim of this paper is to introduce a fuzzy field environment (FFE) reliability model that covers both the testing and operating phases in the development cycle. Illustration examples of the proposed model have been validated on data collected from two industries. [ABSTRACT FROM AUTHOR]

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: In order to accurately describe the equipment’ severity caused by voltage sag, the credibility measure which meets the conditions of non-additive is proposed based on their physical properties of responses. This assessment measure can avoid the deficiencies that classical probability measure needs a large number of samples and the non-duality of fuzzy measure. The membership functions of sensitive equipment voltage tolerance capability that corresponding to the characteristic quantities in the status uncertain area was determined by fuzzy statistical method and polynomial fitting method. Then the joint credibility distribution function was deduced based on uncertainty theory. Hence, the assessment model of severity of equipment failure is constructed. Based on practical samples, the PCs were simulated using the proposed method. Comparing the simulation results with methods using classical probability measure and possibility measure prove that the proposed method is proper and credible and can reflect practical condition more objectively. [Copyright &y& Elsevier]

A new approach to stochastic ordering of fuzzy random variables is investigated in this paper. The traditional definitions of stochastic ordering, hazard rate ordering, and also mean residual life ordering were extended and proposed the unified indexes to ranking fuzzy random variables. Finally, we study the stochastic ordering of fuzzy order statistics by using our proposed approach and established some properties. [ABSTRACT FROM AUTHOR]

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]

This paper extends the simple fuzzy linear regression model to multiple fuzzy linear regression model in which response variable is fuzzy variable and part of the covariates are crisp variables. The least squares methods based on D-metric and the idea of stepwise regression are applied in parameter estimation. The significance test of the regression coefficients is considered. The Bootstrap methods are used to compute the standard errors of the estimates and P-values of tests. Fuzzy diagnostics based on D-metric are also developed to detect the outliers. Some simulations are performed to verify the obtained results, which are found to be satisfied. Finally, the early warning of macro-economic index data of China are illustrated our methodology. [ABSTRACT FROM AUTHOR]

These last decades, the Berre lagoon (in southeastern France) has been deeply affected since the 1930s by strong inputs of contaminants associated with industrial development and since 1966 by huge inputs of freshwater and silts due to the installation of a hydroelectric power plant. Surveys of the surface sediment contamination have been sparsely performed since 1964 for management and research purposes. These surveys were performed by various laboratories that investigated different chemicals and sampling areas using different analysis protocols. Therefore, the available data are disconnected in time and space and differ in quality. In order to reconstruct coherent time series of sediment contamination from this heterogeneous datasets and to discuss the influences of industrial and hydroelectric discharges we used a statistical approach. This approach is based on Principal Component Analysis (PCA) and Fuzzy clustering analysis on data from one extensive survey realized on surface sediments in 1976. The PCA allowed identifying two geochemical indexes describing the main surface sediment geochemical characteristics. The fuzzy clustering analysis on these indexes allowed identifying sub-areas under the specific influence of industrial or hydroelectric discharges. This allowed us to reconstruct, for each sub-area, a coherent and interpretable long-term time series of sediment contamination from the available database. Reconstructed temporal trends allowed us to estimate: (i) the overall decrease of sediment contamination since the mid-1970 attributed to industrial discharge regulations enacted at this period and (ii) the dilution of the concentrations of sediment bound contaminants induced by the hydroelectric power plant and its associated particulate matter inputs. [Copyright &y& Elsevier]

Abstract: Fuzzy set theory models situations in which the uncertainty is due to the non-precise (fuzzy) environment. One such case is testing the hypotheses problem where hypotheses are fuzzy rather than crisp and the data are crisp. Pais and Benton (1997) present a suitable amount of cadmium absorption which is more appropriate for modeling by a fuzzy subset. In this paper, on real-world agricultural data generated by Ivani (2007) , the suitableness of the mean absorption cadmium in the plant from the polluted soil is tested at the given significance level. Due to uncertainty in the suitable amount of cadmium absorption, in order to test this amount, we use fuzzy hypotheses testing instead of classical hypotheses testing. The fuzzy -value approach is used for this test to conclude whether or not the mean absorption of cadmium coincides with the proposed amounts by Pais and Benton . As expected, in fuzzy hypotheses testing, the degree of acceptance or rejection of the null fuzzy hypothesis is computed for each treatment of pollution. The data are from two plants: radish and cress, which are experimented on in soil polluted with CdNO3 salt. The results showed that using classical hypotheses testing may lead to contradictory decisions, and the proposed fuzzy hypotheses testing is a rational substitute for classical hypotheses testing when the environment is in a vague status. [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]

Fuzzy regression has been applied to marketing, management, and sales forecasting for many years. In this paper, two types of forecasting methods within the framework of fuzzy regression analysis are discussed. The first type is a conventional forecasting method, which intends to find the value of a dependent variable when the given values of independent variables are beyond the range covered by historical data. The second type considers forecasting in which the necessary values of independent variables are desired when the given value of a dependent variable does not fall within the range of historical data. While the first type can be applied in planning, the second one is useful for control and management. Numerical examples are provided for illustration. [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: 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]

Due to a high number of spectral channels and a large information quantity, multispectral remote-sensing images are difficult to be classified with high accuracy and efficiency by conventional classification methods, particularly when training data are not available and when unsupervised clustering techniques should be considered for data analysis. In this paper, we propose a novel image clustering method [called fuzzy-statistics -based affinity propagation (FS-AP)] which is based on a fuzzy statistical similarity measure (FSS) to extract land-cover information in multispectral imagery. AP is a clustering algorithm proposed recently in the literature, which exhibits a fast execution speed and finds clusters with small error, particularly for large datasets. FSS can get objective estimates of how closely two pixel vectors resemble each other. The proposed method simultaneously considers all data points to be equally suitable as initial exemplars, thus reducing the dependence of the final clustering from the initialization. Results obtained on three kinds of multispectral images (Landsat-7 ETM+, Quickbird, and moderate resolution imaging spectroradiometer) by comparing the proposed technique with K-means, fuzzy K-means, and AP based on Euclidean distance (ED-AP) demonstrate the good efficiency and high accuracy of FS-AP. [ABSTRACT FROM AUTHOR]

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 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]

The classical temporal scan statistic is used to identify disease clusters. In recent years, this method has become a very popular technique and its field of application has been notably increased. Many bioinformatics problems have been solved with this technique. In this paper a new scan method is proposed: fuzzy scan. Three approximations for the distribution of fuzzy scan statistic are presented and the behaviors of the classic and fuzzy scan techniques are studied with simulated data. Finally, ROC curves are calculated and it is demonstrated the superiority of the fuzzy scan technique compared with the classic scan method. [ABSTRACT FROM AUTHOR]