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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]

In this paper, a new class of fuzzy random optimization problem called two-stage fuzzy random programming or fuzzy random programming with recourse (FRPR) problem is first presented; then its deterministic equivalent programming problem is characterized. Because the FRPR problems include fuzzy random variable parameters with an infinite support, they are inherently infinite-dimensional optimization problems that can rarely be solved directly. Therefore, an approximation approach to the fuzzy random variables with infinite supports by finitely supported ones is proposed, which results in finite-dimensional FRPR problems. After that, this paper is devoted to establishing the conditions under which the objective value (optimal objective value, and minimizers) of such finite-dimensional FRPR problem can be shown to converge to the objective value (respectively, optimal objective value and minimizers) of the original infinite-dimensional FRPR problem. [ABSTRACT FROM AUTHOR]

In practice, the lifetimes of unrepairable systems contain both randomness and fuzziness. So it is appropriate to assume the lifetimes of systems to be fuzzy random variables. In this paper, the definitions of reliability and mean time to failure (MTTF) of unrepairable systems with fuzzy random lifetimes are given, respectively. Then basic mathematical models of unrepairable systems with fuzzy random lifetimes are established. Furthermore, the reliability and MTTF of series systems, parallel systems, series-parallel systems, parallel-series systems, and cold standby systems are discussed, respectively. Finally, some numerical examples are presented to illustrate how to calculate the reliability and MTTF of unrepairable systems with fuzzy random lifetimes. [ABSTRACT FROM AUTHOR]

As a fuzzification of the Choquet integral, the defuzzified choquet integral with fuzzy-valued integrand (DCIFI) takes a fuzzy-valued integrand and gives a crisp-valued integration result. In this paper, the DCIFI acts as a projection to project high-dimensional heterogeneous fuzzy data to one-dimensional crisp data to handle the classification problems involving different data forms, such as crisp data, interval values, fuzzy numbers, and linguistic variables, simultaneously. The nonadditivity of the signed fuzzy measure applied in the DCIFI can represent the interaction among the measurements of features towards the discrimination of classes. Values of the signed fuzzy measure in the DCIFI are considered to be unknown parameters which should be learned before the classifier is used to classify new data. We have implemented a genetic algorithm (GA)-based adaptive classifier-learning algorithm to optimally learn the signed fuzzy measure values and the classified boundaries simultaneously. The performance of our algorithm has been tested both on synthetic and real data. The experimental results are satisfactory and outperform those of existing methods, such as the fuzzy decision trees and the fuzzy-neuro networks. [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]

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

Abstract: A practical situation often facing us is that fuzzy spatial data are recorded as crisp real-valued numbers, e.g., a PM10 record is 15.1, but we do know that it is an imprecise and vague observation. A new spatial analysis technique –fuzzy membership grade Kriging with semi-statistical membership, proposed by Guo has been developed to address fuzzy spatial data recorded as crisp numbers. In this paper, we will explain fuzzy membership grade Kriging, its root, its theory and its implementations. As an illustration, we will use PM10 data of California, USA. Three sample membership functions are extracted from the data itself: linear, quadratic and hyperbolic tangent and applied to the PM10 data. The predicted membership grades are also transformed back into PM10 concentrations by using inverse functions in order to identify areas being dangerous to human health. Finally, we implement our new fuzzy membership grade Kriging in GIS. [Copyright &y& Elsevier]

Purpose -- The purpose of this research is to introduce a class of FRC (fuzzy random coefficient) volatility models and to study their moment properties. Fuzzy option values and the superiority of fuzzy forecasts over minimum mean-square forecasts are also discussed in some detail. Design/methodology/approach -- Fuzzy components are assumed to be triangular fuzzy numbers. Buckley's dam-driven method is used to determine the spread of the triangular fuzzy numbers by using standard errors of the estimated parameters. Findings -- The fuzzy kurtosis of various volatility models is obtained in terms of fuzzy coefficients. Fuzzy option values and fuzzy forecasts are illustrated with examples. Fuzzy forecast intervals are narrower than the corresponding MMSE forecast intervals. Originality/value -- This paper will be of value to econometricians and to anyone with an interest in financial volatility models. [ABSTRACT FROM AUTHOR]

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 deals with a novel buffer management scheme based on evolutionary computing for shared-memory asynchronous transfer mode (ATM) switches. The philosophy behind it is adaptation of the threshold for each logical output queue to the real traffic conditions by means of a system of fuzzy inferences. The optimal fuzzy system is achieved using a systematic methodology, based on genetic algorithms (GAs), which allows the fuzzy system parameters to be derived for each switch size, offering a high degree of scalability to the fuzzy control system. Its performance is comparable to that of the push-out (PO) mechanism, which can be considered ideal from a performance viewpoint, and at any rate much better than that of threshold schemes based on conventional logic. In addition, the fuzzy threshold (FT) scheme is simple and cost-effective when implemented using VLSI technology. [ABSTRACT FROM AUTHOR]

In the fuzzy clustering literature, two main types of membership are usually considered: A relative type, termed probabilistic, and an absolute or possibilistic type, indicating the strength of the attribution to any cluster independent from the rest. There are works addressing the unification of the two schemes. Here, we focus on providing a model for the transition from one schema to the other, to exploit the dual information given by the two schemes, and to add flexibility for the interpretation of results. We apply an uncertainty model based on interval values to memberships in the clustering framework, obtaining a framework that we term graded possibility. We outline a basic example of graded possibilistic clustering algorithm and add some practical remarks about its implementation. The experimental demonstrations presented highlight the different properties attainable through appropriate implementation of a suitable graded possibilistic model. An interesting application is found in automated segmentation of diagnostic medical images, where the model provides an interactive visualization tool for this task. [ABSTRACT FROM AUTHOR]

The hydrogeological effectiveness of fracture sets is determined and evaluated by the fuzzy c-mean and hierarchical clustering. These cluster analyses combine the geological spatial attributes and the hydraulic relevant attributes of fractures. Based on the results of the clustering the fracture set volumes are estimated. [ABSTRACT FROM AUTHOR]

Measurement of volume and surface area of the frontal, parietal, temporal and occipital lobes from magnetic resonance (MR) images shows promise as a method for use in diagnosis of dementia. This article presents a novel computer-aided system for automatically segmenting the cerebral lobes from 3T human brain MR images. Until now, the anatomical definition of cerebral lobes on the cerebral cortex is somewhat vague for use in automatic delineation of boundary lines, and there is no definition of cerebral lobes in the interior of the cerebrum. Therefore, we have developed a new method for defining cerebral lobes on the cerebral cortex and in the interior of the cerebrum. The proposed method determines the boundaries between the lobes by deforming initial surfaces. The initial surfaces are automatically determined based on user-given landmarks. They are smoothed and deformed so that the deforming boundaries run along the hourglass portion of the three-dimensional shape of the cerebrum with fuzzy rule-based active contour and surface models. The cerebrum is divided into the cerebral lobes according to the boundaries determined using this method. The reproducibility of our system with a given subject was assessed by examining the variability of volume and surface area in three healthy subjects, with measurements performed by three beginners and one expert user. The experimental results show that our system segments the cerebral lobes with high reproducibility. [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]

Image classification of historical aerial photographs is very useful for the study of medium-to-long term (10–50 years) vegetation changes. To determine the quality of information derived from the classification process, accuracy assessment of the classification is implemented. Error matrix, which is primarily used in remote sensing for accuracy assessment, is typically based on an evaluation of the derived classification against some ‘ground truth’ or reference dataset. Regrettably ‘ground truths’ for some old historical photographs are rarely available. To solve this problem we formulate, in this Part I, methods of classification of aerial photographs and computation of accuracy assessment parameters of classification products in the absence of ground data, using the fuzzy classification technique. In addition, since point estimates of these accuracy parameters require associated standard errors, in order to be useful for statistical analysis, the method of computation of standard errors of accuracy measures using the bootstrap resampling techniques is presented. These methods are tested with historical aerial photographs, of part of Adulam Nature Reserve, Israel, spanning a period of 51 years. Results illustrate the applicability and efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

The notion of coherent systems plays an essential role in conventional reliability theory. A system is said to be coherent if all of its components are relevant and the system reliability is improved as the component reliabilities are improved. However, in many complex systems or networks, not all the components are unconditionally relevant. As a result, in this paper we introduce the notion of variable-structure coherent systems to describe those systems that extensively exist and demonstrate essentially distinct features not observed in conventional coherent systems. A variable-structure coherent system consists of a number of substructures that are each a coherent system in conventional sense themselves. We then analyze the structural properties of variable-structure coherent systems; define the system operational profile, the system reliability, and the system structural profile. We study the system life distribution, the substructure importance, and the component importance. Finally, we deal with phase-cyclic systems in the context of variable-structure coherent systems. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of operators called quasi-triangular norms. They are denoted by H and parameterized by a parameter ν : H(a1, a2, . . . , an; ν). From the construction of function H, it follows that it becomes a t-norm for ν = 0 and a dual t-conorm for ν = 1. For ν close to 0, function H resembles a t-norm and for ν close to 1, it resembles a t-conorm. In the paper, we also propose adjustable quasi-implications and a new class of neuro-fuzzy systems. Most neuro-fuzzy systems pro- posed in the past decade employ ‘engineering implications’ defined by a t-norm as the minimum or product. In our proposition, a quasi-implication I(a, b; ν) varies from an ‘engineering implication’ T(a, b) to corresponding S-implication as ν goes from 0 to 1. Consequently, the structure of neuro-fuzzy systems presented in this paper is determined in the process of learning. Learning procedures are derived and simulation examples are presented. [ABSTRACT FROM AUTHOR]

The goal of the training evaluation in a simulation is to provide feedback about the user performance in the training environment. Approaches to online or offline evaluation of training in simulators based on virtual reality have been proposed. An online evaluator must have low complexity algorithm to not compromise the performance of the simulator. A new approach to quality of training online evaluation in virtual reality worlds is proposed in this work. This approach uses fuzzy hidden Markov models (FHMM) for modeling and classification of trainee in pre-defined classes of training. [ABSTRACT FROM AUTHOR]

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

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]

A number of optimization approaches regarding monitoring network design and sampling optimization procedures have been reported in the literature. Cokriging Estimation Variance (CEV) is a useful optimization tool to determine the influence of the spatial configuration of monitoring networks on parameter estimations. It was used in order to derive a reduced configuration of a nitrate concentration monitoring well network. The reliability of the reduced monitoring configuration suffers from the uncertainties caused by the variographer's choices and several inherent assumptions. These uncertainties can be described considering the variogram parameters as fuzzy numbers and the uncertainties by means of membership functions. Fuzzy and non-fuzzy approaches were used to evaluate differences among well network configurations. Both approaches permitted estimates of acceptable levels of information loss for nitrate concentrations in the monitoring network of the aquifer of the Plain of Modena, Northern Italy. The fuzzy approach was found to require considerably more computational time and numbers of wells at comparable level of information loss. [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]

Some life tests are terminated with few or no failures. In such cases, a recent approach is to obtain degradation measurements of product performance that may contain some useful information about product reliability. Generally degradation paths of products are modeled by a nonlinear regression model with random coefficients. If we can obtain the estimates of parameters under the model, then the time-to-failure distribution can be estimated. In some cases, the patterns of a few degradation paths are different from those of most degradation paths in a test. Therefore, this study develops a weighted method based on fuzzy clustering procedure to robust estimation of the underlying parameters and time-to-failure distribution. The method will be studied on a real data set. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We argue that with the addition of a rule-ranking procedure, our fuzzy expert system FLOPS can correct previous conclusions given new, possibly conflicting, information. [ABSTRACT FROM AUTHOR]