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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]

This paper is concerned with fuzzy hypothesis testing in the framework of the randomized and non-randomized hypergeometric test for a proportion. Moreover, we differentiate between a test of significance and an alternative test to control the type I error or both error types simultaneously. In contrast to classical (non-)randomized hypothesis testing, fuzzy hypothesis testing provides an additional gradual consideration of the indifference zone in compliance with expert opinion or user priorities. In particular, various types of hypotheses with user-specified membership functions can be formulated. Additionally, the proposed test methods are compared via a comprehensive case study, which demonstrates the high flexibility of fuzzy hypothesis testing in practical applications. [ABSTRACT FROM AUTHOR]

The aim of the paper is to examine procedures of descriptive statistics in the case when the values of relevant attribute in a sample are set in the form of fuzzy categories. The paper provides alternative definitions of a fuzzy random variable, and describes corresponding procedures for calculating the analogues of location and spread parameters. The paper also presents some illustrative examples and analyses the results obtained. Based on the result analysis, practical recommendations are given on how to use procedures of fuzzy statistics. [ABSTRACT FROM AUTHOR]

The premise of dealing with uncertainty in this article is to figure out the impact of uncertainties on project performance. This article proposes a framework for quantitative analysis that combines a fuzzy mathematics approach with system dynamics theory. Simulations generated using a model based on the framework show that uncertainties affect project performance by changing project parameters, and the mechanisms involved depend on the sources of the uncertainties. Furthermore, while technical and financial uncertainties mainly influence project costs, uncertainties related to markets, regulations, and organizational structures affect both project duration and cost. Finally, strategies for coping with uncertainties in a resource allocation perspective are presented. [ABSTRACT FROM AUTHOR]

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 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]

The software quality evaluation is still not a fully resolved problem in Software Engineering. It is known that software quality depends upon several quality attributes such as reliability, modifiability, understandability, testability, usability, portability, and so on. Several authors and international standards have tried to reach an agreement on their definition over the years and provide a standard and accurate one. Due to the complexity of software systems, it is often difficult to evaluate the overall quality of their underlying software components. A way for evaluation is to use software metrics as quantitative predictors when evaluating the quality attributes. There are several metrics based on statistical methods, similar to those used for product inspection and quality assurance in manufacturing, that have been investigated during time by Software Engineering. Some authors have started to use Fuzzy Theory in software assessment and evaluation. And it seems that its usage improves the evaluation of the software quality. [ABSTRACT FROM AUTHOR]

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]

Association rule mining is an important data analysis method that can discover associations within data. There are numerous previous studies that focus on finding fuzzy association rules from precise and certain data. Unfortunately, real-world data tends to be uncertain due to human errors, instrument errors, recording errors, and so on. Therefore, a question arising immediately is how we can mine fuzzy association rules from uncertain data. To this end, this paper proposes a representation scheme to represent uncertain data. This representation is based on possibility distributions because the possibility theory establishes a close connection between the concepts of similarity and uncertainty, providing an excellent framework for handling uncertain data. Then, we develop an algorithm to mine fuzzy association rules from uncertain data represented by possibility distributions. Experimental results from the survey data show that the proposed approach can discover interesting and valuable patterns with high certainty. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and characterize α-preirresolute functions between fuzzy topological spaces and also study these functions in relation to some other types of already known fuzzy functions. We speculate that fuzzy α-preirresolute functions may be relevant to the physics of fractal and cantorian spacetime. [ABSTRACT FROM AUTHOR]

The aim of this paper is to extend the concept of inverse of a matrix with fuzzy numbers as its elements, which may be used to model uncertain and imprecise aspects of real-world problems. We pursue two main ideas based on employing real scenarios and arithmetic operators. In each case, exact and inexact strategies are provided. In the first idea, we give some necessary and sufficient conditions for invertibility of fuzzy matrices based on regularity of their scenarios. And then Zadeh's extension principle and interpolation on Rohn's approach for inverting interval matrices are followed to compute fuzzy inverse. In the second idea, Dubois and Prade's arithmetic operators will be employed for the same purpose. But with respect to the inherent difficulties which are derived from the positivity restriction on spreads of fuzzy numbers, the concept of ε-inverse of a fuzzy matrix and its relaxation are generalized and some useful theorems will be revealed. Finally fuzzifying the defuzzified version of the original problem for introducing fuzzy inverse, which can be followed by each idea, will be presented. [ABSTRACT FROM AUTHOR]

Principal component analysis (PCA) is a favorite multivariate statistical method for image enhancement and compression. However, it is well known that the classical PCA is sensitive to outliers and missing data. Fortunately, fuzzy statistics is an effective theory for processing these kinds of data. Fuzziness and randomicity are just the important characteristics of the data of remote-sensing images. Therefore, by introducing fuzzy statistics variables into classical PCA methods, a novel method for multispectral image processing called fuzzy-statistics-based PCA (FS-PCA) is proposed in this paper. To verify our proposed method, both the classical PCA and the FS-PCA are applied to the multispectral Landsat ETM+ data for image enhancement. The experimental results show that the differences among surface characteristics are expanded sufficiently and that the accuracy of surface feature recognition is improved greatly. [ABSTRACT FROM AUTHOR]

Karakuş, Demirci, Duman [Chaos, Solitons and Fractals (2006), doi: 10.1016/j.chaos.2006.05.046.] has recently introduced the notion of statistical convergence on intuitionistic fuzzy normed spaces. Using this notion, we study the concept of statistical limit points, statistical cluster points on intuitionistic fuzzy normed spaces and then we give the relations between these and limit points of sequence on intuitionistic fuzzy normed spaces and also we give some topological properties. [ABSTRACT FROM AUTHOR]

This short paper discusses the modeling of random fuzzy renewal reward processes in which the interarrival times and rewards are represented by nonnegative random fuzzy variables. Based on random fuzzy theory, a random fuzzy variable denotes a measurable function from a credibility space to a collection of random variables. Under this setting, the long-run expected reward per unit time is addressed and the theorem on random fuzzy renewal rewards is established. The utility of this research is demonstrated with a realistic application case. [ABSTRACT FROM AUTHOR]

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

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

The problem of defuzzification is examined in this paper from a broader perspective as a special way of dealing with the general problem of retranslation. The paper includes an overview of different formulations of the problem of defuzzification, as well as an overview of methods that have been suggested in the literature for dealing with the problem. Our own approach to defuzzification, which is described in the paper in more details, is based on relevant measures of uncertainty-based information. This paper is a companion to our recent paper that addresses the general problem of retranslation in computing with perceptions (Martin and Klir 2006). [ABSTRACT FROM AUTHOR]

We introduce the notions of fuzzy ternary subsemiring, fuzzy ideal and quasi-ideal in ternary semirings and study some properties of these two ideals. We also study the properties of fuzzy ideal and fuzzy quasi-ideal of ternary semirings. [ABSTRACT FROM AUTHOR]

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

A novel method (Fuzzy factor method) is presented, which is used in the dynamic response analysis of fuzzy stochastic truss structures under fuzzy stochastic step loads. Considering the fuzzy randomness of structural physical parameters, geometric dimensions and the amplitudes of step loads simultaneously, fuzzy stochastic dynamic response of the truss structures is developed using the mode superposition method and fuzzy factor method. The fuzzy numerical characteristics of dynamic response are then obtained by using the random variable’s moment method and the algebra synthesis method. The influences of the fuzzy randomness of structural physical parameters, geometric dimensions and step load on the fuzzy randomness of the dynamic response are demonstrated via an engineering example, and Monte-Carlo method is used to simulate this example, verifying the feasibility and validity of the modeling and method given in this paper. [ABSTRACT FROM AUTHOR]

This paper proposes an automatic image segmentation algorithm. Our hierarchical algorithm uses recursive segmentation that consists of two major steps. First, local thresholding is carried out by the fuzzy hit-or-miss operator, which allows dynamic separation of a grey-scale image into two classes, based on local intensity distributions. The fuzzy hit-or-miss, being an operator of fuzzy mathematical morphology, plays an important role in performing the dynamic local segmentation. This operator gives a better shape description than global thresholding methods. It also retains small but significant regions in satellite images. Second, the homogeneity index is measured in each class based on the quality of normalized intra-region uniformity. The proposed method has been tested using both synthetic and satellite images successfully; moreover, the algorithm can estimate the number of classes automatically. [ABSTRACT FROM AUTHOR]

In a fuzzy multiple criteria decision-making (MCDM) problem, with a hierarchical structure of more than two levels and involving multiple decision-makers (DMs), to find the exact membership functions of the final aggregation ratings of all feasible alternatives is almost impossible. Thus, ranking methods based on exact membership functions cannot be utilized to rank the feasible alternatives and complete the optimal selection. To resolve the above-mentioned complexity and to incorporate assessments of all DMs' viewpoints, in this paper a fuzzy MCDM method with multiple DMs, based on the concepts of fuzzy set theory and α-cut, is developed. This method incorporates a number of perspectives on how to approach the fuzzy MCDM problem with multiple DMs, as follows: (1) combining quantitative and qualitative criteria as well as negative and positive ones; (2) using the generalized means to develop the aggregation method of multiple DMs' opinions; (3) incorporating the risk attitude index β to convey the total risk attitude of all DMs by using the estimation data obtained at the data input stage; (4) employing the algebraic operations of fuzzy numbers based on the concept of α-cut to calculate the final aggregation ratings and develop a matching ranking method for proposed fuzzy MCDM method with multiple DMs. Furthermore, we use this method to survey the site selection for free port zone (FPZ) in Taiwan as an empirical study to demonstrate the proposed fuzzy MCDM algorithm. The result of this empirical investigation shows that the port of Kaohsiung, the largest international port of Taiwan as well as the sixth container port in the world in 2004, is optimal for the Taiwan government in enacting the plan of FPZ. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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

Abstract: We argue that in some recent papers discussing the completion of fuzzy metric and fuzzy normed spaces proper credit is not given to earlier works on the subject. [Copyright &y& Elsevier]

Based on the SLLN for fuzzy random variables in uniform metric d 8, some asymptotical properties of point estimation with fuzzy random samples are investigated. The results of this paper establish a corresponding version on the consistency and unbiasedness of point estimation with n-dimensional fuzzy samples under considering a kind of fuzzy statistic. [ABSTRACT FROM AUTHOR]