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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]

Purpose: Predicted the explanatory power of core through the application of autoregressive functions and fuzzy time series by archery performance. Can the archery performance of different athletes (high-score group and low-score group) be predicated and evaluated? In this study, purposive sampling was used to recruit the research participants by Chinese Taipei Archery Association (CTAA) were data collected in this study. Method: This study applied fuzzy statistics to the analysis of quadratic regression, autoregressive functions, and transfer functions. Subsequently, these statistics and relevant data were analyzed using Minitab 16.0 and Microsoft Office Excel 2013. Results: The findings of this study are listed as follows: Using autoregressive functions and fuzzy time series can truly reflect the explanatory power of athletes' performance in archery and effectively predict the archery performance of male athletes in the high-score group during the 2013 Asian Games. Suggestion: Fuzzy mode could be used to investigate the academic performance and learning environment of universities because it enhances the authenticity of students learn skill. Further academic learn training programs for student could be planned according to contest goals and contents, and the proportion of male to female student can be determined according to current situations. Contribution: The performance of student predicted using fuzzy time series should be used to design training programs for athletes and to assess students' ability to participate in learn environment. [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]

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 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]

Classifiers based on Gamma statistical distribution can be found in the scientific literature, but they assume the collected data doesn't present any errors. However, in some cases, information precision can not be guaranteed, then the fuzzy approach is convenient. Several methods found in the literature are not able to ponder the specific contribution of each class and/or feature for the classification tasks. This paper presents a proposal of a new classifier named Doubled Weighted Fuzzy Gamma Naive Bayes network (DW-FGamNB). This new classifier uses two types of weights in order to allow users to ponder the real contribution of each class and feature in the classification task. The theoretical development is presented, as well as results of its application on simulated multidimensional data using Gamma statistical distribution. A comparison among DW-FGamNB, Fuzzy Gamma Naive Bayes classifier, classical Gamma Naive Bayes classifier, Naive Bayes classifier, DecionTree-Naive Bayes, Decision Tree C4.5, Logistic Regression, Multilayer Perceptron Neural Network, Adaboost-M1, Radial Basis Function Network and Random Forest was performed. The results obtained showed that the DW-FGamNB produced the best performance, according to the Overall Accuracy Index, Kappa and Tau Coefficients, and diagnostic tests. [ABSTRACT FROM AUTHOR]

The phenomena treated in this paper are classified into the following three cases: (I) Phenomena whose objective variable is quantitative, where such quantitative changes of the objective variable are referred to as quantitative external criterion. (II) Phenomena whose objective variable is qualitative, where the qualitative changes of the objective variable are referred to as qualitative external criterion. (III) Phenomena which are specified without any objective variables. This paper has consisted of three parts corresponding to the above classification of phenomena. The methods for analyzing phenomena with quantitative external criterion are presented in Section 3 as fuzzy time-series analysis and in Section 4 as fuzzy regression qualitative analysis. The methods for analyzing phenomena with qualitative external criterion are described in Section 5 as fuzzy discriminant qualitative analysis and in Section 7 as fuzzy discriminant analysis. In Section 6 the fuzzy discriminant qualification analysis is successively applied to the analysis of purchasing factors in consumer's behavior. The methods for analyzing phenomena without any external criteria are treated in Sections 8 to 11. In Section 8 the heuristic method is proposed in order to find a fuzzy transitive relation. This heuristic method is applied to the hierarchical clustering problem in Section 9 and to the identifying problem of preference ordering in Section 10. In Section 11 the evaluation of alternatives with multiple attributes is analytically discussed in view of the concept of fuzzy sets. In Section 1 the survey of the fuzzy set theory and the into-introductory description of fuzzy multivariate analysis are given. Section 2 briefly describes concepts and definitions of fuzzy sets in preparation for the main parts of this paper. At the end Section 12 summarizes the results of this paper. [ABSTRACT FROM AUTHOR]

In view of the problems existing in the evaluation index selection and whether the evaluation method is too simple to evaluate the coordinated development of regional economy. Based on the comprehensive analysis of the definition of the coordinated development of regional economy, this paper discusses the definition of the scientific connotation of the coordinated development of regional economy and puts forward three evaluation indexes for coordinated development of regional economy (the degree of regional economic integration, the degree of regional economic development gap, and the speed of regional economic development). In view of the diversity of evaluation factors and the fuzziness of the relationship between evaluation indexes, this paper uses the fuzzy classification statistical model to evaluate the coordinated development of regional economy and established a regional economic development coordination management system based on fuzzy hierarchical statistical model to evaluate the degree of regional economic coordinated development. Finally, the eastern region and the central and western regions are taken as the object of study. The analysis results show that the conclusion drawn from the model is basically consistent with the actual situation in China. This model can effectively manage the coordinated development of regional economy in China. [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]

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]

Objectives: This study aims to analyze various psychological propensities with fuzzy questionnaires in physical education. Motivations: Fuzzy questionnaires with fuzzy statistical analysis can better reflect people's psychological thinking. Method: Fuzzy descriptive statistics, fuzzy correlation coefficients and fuzzy regression models. Finding: Comparing among three scales, fuzzy Kaiser-Meyer-Olkin (KMO), Cronbach's a and traditional one: fuzzy Mastery-Avoidance had a positive correlation with self-esteem. Fuzzy positive self-esteem significantly impacted predictive Mastery-Approach (AF_MA) and Mastery-Avoidance (AF_M_a); while traditional positive self-esteem significantly impacted predictive Performance-Avoidance (A_P_a) and Mastery-Avoidance (AF_M_a). Further, fuzzy and traditional negative selfesteem significantly impacted predictive AF_MA, simultaneously fuzzy negative self-esteem significantly impacted predictive AF_MA. Only fuzzy negative self-esteem significantly impacted predictive AF_MA. Innovations: Traditional psychological examination technology has been used for many years, while a new approach with fuzzy statistical analysis on artificial intelligence technology will promote the quality of sampling survey and marketing information. Value: This study offered new examination skill in analyzing psychological propensity in physical education. [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]

In this paper, the classical statistical test based on intuitionistic fuzzy hypotheses in relation to the underlying population parametric is extended. In this approach, the type-I, type-II, power of test, andp-value are extended for intuitionistic fuzzy hypotheses. Throughout the paper, some applied examples are provided for both parametric and non parametric cases to clarify the discussions. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive mutation particle swarm optimization (AMPSO) to realize multi-objective optimization design method through scale-based product platform theory model. The Pareto-optimal solution was obtained via AMPSO, then the fuzzy statistics algorithm is presented to extract the optimal solution of multi-objective optimization problem. The Multi-objective Optimization Method was carried out in two stages. In the first stage, each product is optimized independently via AMPSO and the product platform constant parameter and its value is obtained according to the change ratio of design variables; In the second stage, the scaling variables of each product are solved via AMPSO based on the optimization objectives improving the performance in constraint of restrictions and the best compromise solution is extracted based on fuzzy statistics algorithm. [ABSTRACT FROM AUTHOR]

Purpose Ultrasound ( US) imaging has been widely used in breast tumor diagnosis and treatment intervention. Automatic delineation of the tumor is a crucial first step, especially for the computer-aided diagnosis ( CAD) and US-guided breast procedure. However, the intrinsic properties of US images such as low contrast and blurry boundaries pose challenges to the automatic segmentation of the breast tumor. Therefore, the purpose of this study is to propose a segmentation algorithm that can contour the breast tumor in US images. Methods To utilize the neighbor information of each pixel, a Hausdorff distance based fuzzy c-means ( FCM) method was adopted. The size of the neighbor region was adaptively updated by comparing the mutual information between them. The objective function of the clustering process was updated by a combination of Euclid distance and the adaptively calculated Hausdorff distance. Segmentation results were evaluated by comparing with three experts' manual segmentations. The results were also compared with a kernel-induced distance based FCM with spatial constraints, the method without adaptive region selection, and conventional FCM. Results Results from segmenting 30 patient images showed the adaptive method had a value of sensitivity, specificity, Jaccard similarity, and Dice coefficient of 93.60 [ABSTRACT FROM AUTHOR]

In this paper, we consider the following functional equation af(x + y) + bf(x - y) + cf(y - x) = (a + b)f(x) + cf(-x) + (a + c)f(y) + bf(-y) for a fixed real numbers a; b; c with a = b + c and a ≠ 0. We study the fuzzy version of the generalized Hyers-Ulam stability for it in the sense of Mirmostafaee and Moslehian. [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]

Life time data analysis is regarded as one of the significant out-shoots of statistics. Classical statistical techniques reckon life time observations as precise numbers and solely cover variation among the observations. In fact, there are two types of uncertainty in data: variation among the observations and the fuzziness. To this effect, the analysis techniques, which do not consider fuzziness and are only based on precise life time observations, use incomplete information; hence lead to pseudo results. This study aimed at generalizing parameters estimation, survival functions, and hazard rates for fuzzy life time data. [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]

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]

Transportation facility and automotive service enterprise location is an interesting and important issue. In practice, such factors as customer demand, allocations, even locations of customers and facilities are usually changing, thus making facility location problematic with uncertainty. To account for it, some researchers have addressed stochastic/fuzzy models for locating an automotive service enterprise. However, probabilistic/fuzzy models are not suitable to describe all kinds of uncertainty, but only randomness or fuzziness. In fact, the uncertain environment of locating an automotive service enterprise is a mixed one with both randomness and fuzziness. To handle this issue in a practical manner, this work proposes fuzzy random tradeoff issues for it. Moreover, some regional constraints can greatly influence its location. By taking the vehicle inspection station as a typical example, this work presents new fuzzy random cost-profit tradeoff models of its location problem with regional constraints. A hybrid algorithm integrating fuzzy random simulation and genetic algorithms is adopted to solve the proposed models. Additionally, some risk factors have a great impact on decision making when faced with a location problem. This work thus conducts a risk performance analysis for locating an automotive service enterprise. Some numerical examples are given to illustrate the proposed models. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [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]

The case of nonresponse in multivariate stratified sampling survey was first introduced by Hansen and Hurwitz in 1946 considering the sampling variances and costs to be deterministic. However, in real life situations sampling variance and cost are often random (stochastic) and have probability distributions. In this article, we have formulated the multivariate stratified sampling in the presence of nonresponse with random sampling variances and costs as a multiobjective stochastic programming problem. Here, the sampling variance and costs are considered random and converted into a deterministic NLPP by using chance constraint and modified E-model. A solution procedure using three different approaches are adopted viz. goal programming, fuzzy programming, and D1distance method to obtain the compromise allocation for the formulated problem. An empirical study has also been provided to illustrate the computational details. [ABSTRACT FROM PUBLISHER]

Statistical institutes are focusing on variety of data sources from traditional surveys to big-data. Many of these data and concepts can be expressed as crisp values. But many other data cannot be expressed by precise values. In order to collect, store and manage the fuzziness in data we have adapted the fuzzy meta model as an extension of traditional relational database. Furthermore, experts' knowledge often contains vagueness and subjectivity. If we store this knowledge in a fuzzy database we can build knowledge management systems capable to cope with fuzziness. Statistical institutes cooperate in the data exchange. We have briefly discussed a simple way of extending the SDMX standard to cope with the fuzzy data in a way that does not influence exchanging precise values. Our research was focused on examining promising ways for managing fuzziness of real world because statistical institutes have been starting to analyze variety of promising data sources where not all data are always precise. [ABSTRACT FROM AUTHOR]

The ability of fuzzy logic systems to make use of human interpretable linguistic terms makes them very attractive for many applications. These systems make use of membership functions to represent the linguistic variables. The choice of type of the membership function to use and the associated parameters affect the performance of the system. The current types of membership functions like triangular, trapezoidal, Gaussian functions etc., make use of parameters that are possibilistic in nature thus requiring expert knowledge or other sophisticated methods in order to choose the parameters. In this paper, we propose a newtype of membership function constructed based on fuzzy estimators. This membership function depends entirely on well-known statistical parameters like the mean, standard deviation and confidence intervals and thus the parameters are easier to choose. Another advantage of this membership function is that it is suitable for modeling systems that exhibit both randomness and fuzziness. Furthermore, in contrast to the parameters of other membership functions, in the case where the parameters are tuned and optimized for a particular application, the final parameters of the proposed membership function can have useful statistical interpretations and provide a better understanding of the system. [ABSTRACT FROM AUTHOR]

Anomalies are subsequences that exhibit departures from normal state of operation. In this paper, to solve the problems of unknown data distribution, control limit determination, multiple parameters, training data and fuzziness of 'anomaly', a self-adaptive and unsupervised model is developed for finding anomalies in data streams. A salient feature is a synergistic combination of both statistical and fuzzy set-based techniques. Anomaly detection problem is viewed as a certain statistical hypothesis testing which is realized in an unsupervised mode. At the same time, 'anomaly' is a much more complex concept and as such can be described with fuzzy set theory. Fuzzy sets bring a facet of robustness to the overall scheme and play an important role in the successive step of hypothesis testing. Because of the fuzzification, parameters determination is self-adaptive and no parameter needs to be specified by the user, what's more, there is no need to consider the data distribution in statistical hypothesis testing in this paper. The approach is validated with a number of experiments, which help to quantify the performance of constructed algorithm. [ABSTRACT FROM AUTHOR]

Eigenvalues and eigenvectors are one of the important topics over bipolar fuzzy linear algebra. In order to develop the bipolar fuzzy linear space we introduce in this article, the similarity relations, eigenvalues and eigenvectors of bipolar fuzzy matrices (BFMs). Idempotent, diagonally dominant and spectral radius of BFMs are considered here. Also, some properties and results of eigenvalues and eigenvectors for BFMs are investigated. [ABSTRACT FROM AUTHOR]

Fuzzy modeling and fuzzy statistics provide useful tools for handling empirical situations affected by vagueness and imprecision in the data. Several fuzzy statistical models and methods (e.g., fuzzy regression, fuzzy principal component analysis, fuzzy clustering) have been developed over the years. Generally the standard LR-fuzzy data representation has been used in these methods. However, several empirical contexts, such as human ratings and decision making, may show more complex fuzzy structures which cannot be successfully modeled by the LR representation. In all these cases another type of fuzzy data representation, the so-called LHIR representation, should be preferred instead. In particular, this novel representation allows to handle with fuzzy data which are characterized by non-convex membership functions. In this paper, we address the problem of summarizing large datasets characterized by two-mode non-convex fuzzy data. We introduce a novel dimension reduction technique (NCFCA) based on the framework of Component Analysis and Least squares programming. Finally, to better highlight some important characteristics of the proposed model, we apply NCFCA to three empirical datasets concerning behavioral and socio-economic issues. [ABSTRACT FROM AUTHOR]

In this paper, the author mainly discusses fuzzy statistical theory and its application in economic forecasting and decision making. Firstly, some concepts, classification, rules, methods, procedures, research goal and significance in the economic forecasting are briefly presented, which provide a fundamental for establishment of economic forecasting models. Secondly, economy development is introduced with its algorithm. Fuzzy statistical learning theory and realization of the support vector machine (SVM) are also detailed. In addition, SVM and Fuzzy Algorithm are compared based on training process and network structure. [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]

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]

Using the fixed point method, we prove the Hyers-Ulam stability of the Cauchy additive functional equation and the quadratic functional equation in matrix fuzzy normed spaces. [ABSTRACT FROM AUTHOR]

Process capability analysis has been widely applied in the field of quality control to monitor the performance of industrial processes. In practice, process capability index Cpk is a popular means to assess target-the-best type quality performance. Normal distribution is an important assumption in process capability analysis. In product quality testing experiments, the experimenter may not always be in a position to observe the quality data of all the products (or items) put on test. Therefore, censored samples may arise in practice. Moreover, observations with coarse scales; measurement error that is not quantified accurately. Therefore, imprecise data also may arise in practice. Our study purposes to utilize the process capability index Cpk in assessing the quality performance of products more generally and accurately. A new approach of analyzing normal, censored and imprecise data is proposed in our study. The new approach will apply a fuzzy statistical estimator of Cpk to develop a new fuzzy statistical hypothesis testing procedure under the normal distribution with the type II right censored sample, imprecise data and large sample. The new fuzzy statistical hypothesis testing procedure can handle normal, censored, imprecise and large sample quality data. Moreover, the purchasers can then employ the new fuzzy statistical hypothesis testing procedure to determine whether the quality performance of products adheres to the required level. The manufactures also can utilize the new fuzzy statistical hypothesis testing procedure to enhance product process capability. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new notions, namely, ideal statistical convergence and ideal lacunary statistical convergence for fuzzy numbers, their relationship and also make some observations about these classes. [ABSTRACT FROM AUTHOR]

In this study, we modify the method proposed by Buckley to testing statistical hypothesis for the mean of an inverse Gaussian distribution. In order to obtain fuzzy test statistic, we use confidence intervals by the help of $$\alpha $$ -cuts. Then the method is applied to test the hypothesis for the mean of inverse Gaussian distribution when the scale parameter is known. Also a comparison is made between the fuzzy and non-fuzzy test procedure for the inverse Gaussian distribution. [ABSTRACT FROM AUTHOR]

For statistical diagnosis of fuzzy linear regression model with one variable, via parameter estimation based on data deletion, taken fuzzy nearness as a diagnostic statistics, strongly affecting points or outliers of the fuzzy observed data were tested. Numerical result shows the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Decisions relating to most irrigation-planning problems need to be made in the face of hydrologic uncertainties, which make the irrigation-planning problem more complex. The uncertainties can be tackled by formulating the problem as Fuzzy Linear Programming (FLP). In the present study, Single Objective Fuzzy Linear Programming (SOFLP) irrigation planning model was formulated for deriving the optimal cropping pattern plan with the objective of minimization of cost of cultivation and maximization of net benefits for the case study of Jayakwadi Project Stage-I in Godavari River sub-basin in Maharashtra State, India. The objective function coefficients, technological coefficients, and stipulations/resources under consideration were taken as triangular fuzzy numbers. The interactive approach was used to solve SOFLP model by involving the Decision Maker (DM) in all phases of decision-making process. The SOFLP model gave better results at highest degree of the membership value by keeping balance between feasibility degree of constraints and satisfaction degree of objectives. The minimized cost of cultivation and maximized net benefits for irrigation planning for the SOFLP model proposed, was found at greatest membership degree of 0.406 and 0.331, respectively, with the consideration of balance between the feasibility degree of constraints and satisfaction degree of goal. The DM can be involved in all phases of decision process, which is very essential in real world problems of irrigation planning where the data/information is vague or uncertain. [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]

In real-world applications, sometimes randomness and fuzziness may coexist. In facility-location problems, the data expressed in natural language may contain vague information. We discuss the uncertainty included in demands in facility-location problems. The uncertain demand is called fuzzy demand in this paper. In the facility-location model, the parameters of fuzzy demand are determined by calculating the estimated expected value of the fuzzy demand, which is obtained by using the estimated parameters of the underlying probability distribution function of the fuzzy data. Moreover, we propose a defuzzification formula of the fuzzy demand called the realization of fuzzy demand. The defuzzification formula of fuzzy demand comprises the upper bound and the lower bound of the fuzzy demand. Moreover, the error of the fuzzy demand is assessed as the mean absolute percentage error of the fuzzy demand. Empirical studies show that we can solve real-life location problems by using the defuzzification formula of fuzzy demand and get higher profit in our facility-location model than by using conventional methods. [ABSTRACT FROM AUTHOR]

LR-fuzzy numbers are widely used in Fuzzy Set Theory applications based on the standard definition of convex fuzzy sets. However, in some empirical contexts such as, for example, human decision making and ratings, convex representations might not be capable to capture more complex structures in the data. Moreover, non-convexity seems to arise as a natural property in many applications based on fuzzy systems (e.g., fuzzy scales of measurement). In these contexts, the usage of standard fuzzy statistical techniques could be questionable. A possible way out consists in adopting ad-hoc data manipulation procedures to transform non-convex data into standard convex representations. However, these procedures can artificially mask relevant information carried out by the non-convexity property. To overcome this problem, in this article we introduce a novel computational definition of non-convex fuzzy number which extends the traditional definition of LR-fuzzy number. Moreover, we also present a new fuzzy regression model for crisp input/non-convex fuzzy output data based on the fuzzy least squares approach. In order to better highlight some important characteristics of the model, we applied the fuzzy regression model to some datasets characterized by convex as well as non-convex features. Finally, some critical points are outlined in the final section of the article together with suggestions about future extensions of this work. [ABSTRACT FROM AUTHOR]

Taking into account the intrinsic drawbacks of both classic and fuzzy PERT, the authors present a new approach in an attempt to deal with them. The tools for this approach are fuzzy statistics and fuzzy probabilities. A necessary condition for this approach is the existence of statistical data for the project activity duration. The final findings are the fuzzy activity times (earliest/latest start - earliest/latest finish), the fuzzy float, the Criticality Degree both for each activity and for each path, a fuzzy probability for the activity duration to be in a certain time interval and a fuzzy probability for the project completion time to be in certain time interval. A numerical example is provided for thorough comprehension. [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]

Nonparametric statistical tests are a distribution-free method without any assumption that data are drawn from a particular probability distribution. In this paper, to identify the distribution difference between two populations of fuzzy data, we derive a function that can describe continuous fuzzy data. In particular, the Kolmogorov-Smirnov two-sample test is used for distinguishing two populations of fuzzy data. Empirical studies illustrate that the Kolmogorov-Smirnov two-sample test enables us to judge whether two independent samples of continuous fuzzy data are derived from the same population. The results show that the proposed function is successful in distinguishing two populations of continuous fuzzy data and useful in various applications. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

This paper is concerned with the delay-dependent generalized H2 fuzzy static out feedback control scheme for a class of nonlinear systems with mixed time delays. The nonlinear plant is represented by Takagi-Sugeno (T-S) fuzzy bilinear stochastic systems with time-varying and infinite-distributed delays. Firstly, a novel delay-dependent piecewise Lyapunov-Krasovskii functional (DDPLKF) is proposed, in which both the upper and the lower bound of delays are considered. Then, based on this DDPLKF, a new delay-dependent generalized H2 fuzzy static output feedback controller design approach is first derived for the fuzzy bilinear stochastic system, and two improved delay-dependent stochastic stability conditions are established. The solutions of the problem can be obtained by solving a set of nonlinear minimization problems involving linear matrix inequalities (LMIs) constraints. An iterative algorithm making use of sequential linear programming matrix method (SLPMM) is proposed to solve the nonlinear minimization problem. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approaches in this paper. [ABSTRACT FROM AUTHOR]

The aging of the population in today's society has become a worldwide phenomenon. The elderly population is increasing. Care for the elderly people has become an important issue in the national policy. It is important to pay attention to and then analyze elderly people's leisure lifestyle issues. For different age groups and different residence, exploring the time of outgoing and watching TV, ideal retirement age, and the situation successful aging, etc. Unlike traditional statistical methods, we used fuzzy theory and soft Computing, proposed the counter-fuzzy transformation, and, by using the median test and variance test, established a nonparametric fuzzy statistical model for small-sized samples and for parameters of the fuzzy number or fuzzy interval types. Then, we made recommendations for elderly issues policy to decisions. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a new approach and concept of human capital measurement through sof t computation and statistical analysis with fuzzy data. This integrated evaluation procedure is aimed at yielding appropriate and reasonable rank and value of teacher internationalization capital. We also give empirical examples to illustrate the techniques and how to evaluate the teacher internationalization capital (TIC). Results show that fuzzy statistical analysis with soft computation tends to more realistic and reasonable in the human capital evaluation. [ABSTRACT FROM AUTHOR]