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Fuzzy relation inequalities based on max-F composition are dis- cussed, where F is a binary aggregation on [0,1]. For a fixed fuzzy relation inequalities system A' 0Fx ≤b, we characterize all matrices A' For which the solution set of the system A' 0 F x ≤b is the same as the original solution set. Similarly, for a fixed matrix A, the possible perturbations b 0 of the right-hand side vector b not modifying the original solution set are determined. Several illustrative examples are included to clarify the results of the paper. [ABSTRACT FROM AUTHOR]

A regression method desires to fit the curve on a data set irrespective of outliers. This paper modifies the granular box regression approaches to deal with data sets with outliers. Each approach incorporates a three-stage procedure includes granular box configuration, outlier elimination, and linear regression analysis. The first stage investigates two objective functions each applies different penalty schemes on boxes or instances. The second stage investigates two methods of outlier elimination to, then, perform the linear regression in the third stage. The performance of the proposed granular box regressions are investigated in terms of: volume of boxes, insensitivity of boxes to outliers, elapsed time for box configuration, and error of regression. The proposed approach offers a better linear model, with smaller error, on the given data sets containing varieties of outlier rates. The investigation shows the superiority of applying penalty scheme on instances. [ABSTRACT FROM AUTHOR]

Process capability indices provide numerical measures to compare the output of a process to client's expectations. However, most of the existing researches have used traditional distribution frequency method by using a single sample due to assess process capability. An alternative to this approach is to use the Bayesian method. In this paper, we utilize a Bayesian approach based on subsamples to check process capability via capability index Cpk. As a new suggestion, we used the informative normal prior distribution and the characteristics of sufficient statistic of the parameter to drive the posterior distribution. The capability test is done, and the posterior probability p, for which the process under investigation is capable, is derived both based on the most popular index Cpk. Finally, a numerical example is given to clarify the method. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Analysis of variance (ANOVA) is an important method in exploratory and confirmatory data analysis. The simplest type of ANOVA is one-way ANOVA for comparison among means of several populations. In this article, we extend one-way ANOVA to a case where observed data are fuzzy observations rather than real numbers. Two real-data examples are given to show the performance of this method. [ABSTRACT FROM AUTHOR]

In quality control, we may confront imprecise concepts. One case is a situation in which upper and lower specification limits (SLs) are imprecise. If we introduce vagueness into SLs, we face quite new, reasonable and interesting processes, and the ordinary capability indices are not appropriate for measuring the capability of these processes. In this paper, similar to the traditional process capability indices (PCIs), we develop a fuzzy analogue by a distance defined on a fuzzy limit space and introduce PCIs, where instead of precise SLs we have two membership functions for upper and lower SLs. These indices are necessary when SLs are fuzzy, and they are helpful for comparing manufacturing process with fuzzy SLs. Some interesting relations among these introduced indices are proved. Numerical examples are given to clarify the method. [ABSTRACT FROM AUTHOR]

Process capability indices are used to determine whether a production process is capable of producing items within specification tolerance. In practice these indices are estimated using sample data, often with quite small sample sizes. Thus, it is of interest to obtain confidence limits for capability index given a sample estimate. Most of the traditional methods for assessing the capability of manufacturing processes are dealing with crisp quality. In this paper we obtain 100(1 - α)% fuzzy confidence interval for &Ctilde;_p fuzzy process capability index, where instead of precise quality we have two membership functions for specification limits. We present several interpretations for introduced fuzzy confidence interval. Some numerical examples are given to clarify the method. [ABSTRACT FROM AUTHOR]

This paper presents a method for approximating the nondominated set of a multiobjective linear fractional programming (MOLFP) problem. The resulting approximation set has acceptable quality measures, and is an-approximation to the nondominated set, whereis the tolerance vector and can be controlled by the decision-maker. The distance between every two resulting solutions is greater than or equal to a positive valueand hence there is no redundant information. Also, for a given upper bound the method controls the cardinality of the resulting approximation set. [ABSTRACT FROM PUBLISHER]

Granulation extracts a bundle of similar patterns by decomposing universe. Hyperboxes are granular classifiers to confront the uncertainties in granular computing. This paper proposes a granular classifier to discover hyperboxes in three phases. The first phase of the proposed model uses the set calculus to build the hyperboxes; where, the means of the DBSCAN clustering algorithm constructs the structure. The second phase develops the geometry of hyperboxes to improve the classification rate. It uses the Particle Swarm Optimization (PSO) algorithm to optimize the seed_points and expand the hyperboxes. Finally, the third phase identifies the noise points; where, the patterns in the second phase did not belong to any hyperboxes. We have used the capability of membership function of a fuzzy set to improve the geometry of classifier. The performance of a proposed model is carried out in terms of coverage, misclassification error and accuracy. Experimental results reveal that the proposed model can adaptively choose an appropriate granularity. [ABSTRACT FROM AUTHOR]

Abstract: This paper suggests an iterative parametric approach for solving multiobjective linear fractional programming (MOLFP) problems which only uses linear programming to obtain efficient solutions and always converges to an efficient solution. A numerical example shows that this approach performs better than some existing algorithms. Randomly generated MOLFP problems are also solved to demonstrate the performance of new introduced algorithm. [Copyright &y& Elsevier]

Abstract: In this paper a mathematical problem with linear flexible constraints is considered. In order to solve the problem an approach is proposed based on multiobjective linear programming. Indeed, allowing violations for the constraints, and using multiobjective linear programming to minimize these violations, a subset of solution set which has less violations, namely efficiently feasible set, is obtained. Then, the corresponding objective function is optimized over efficiently feasible set in order to obtain an optimal solution. An application of the proposed approach in pattern classification is introduced. [Copyright &y& Elsevier]

Uncertainty is an inherent part of control systems used in real world applications. Various instruments used in such systems produce uncertainty in their measurements and thus influence the integrity of the data collection. Type-1 fuzzy sets used in conventional fuzzy systems cannot fully handle the uncertainties present but type-2 fuzzy sets that are used in type-2 fuzzy systems can handle such uncertainties in a better way because they provide more parameters and more design degrees of freedom. There are membership functions that can be parameterized by a few variables and when optimized, the membership optimization problem can be reduced to a parameter optimization problem. This paper deals with the parameter optimization of the type-2 fuzzy membership functions using a new proposed reinforcement learning algorithm in automatic voltage regulator. The results of the proposed method referred to as the Extended Discrete Action Reinforcement Learning Automata algorithm are compared with the results obtained by the Discrete Action Reinforcement Learning Automata algorithm and well known genetic algorithm. The performance of the proposed method on initial error reduction and error convergence issues are investigated by computer simulations. [ABSTRACT FROM PUBLISHER]

Abstract: Curve fitting is an interesting and important subject in mathematics and engineering. It has been studied extensively and a number of approaches, mostly based on polynomials and piecewise polynomials, have been employed. In the usual setting, some data points are given and one wants to find a polynomial function with the minimum violations measured by a norm in the given data points. In these approaches, norms are applied to aggregate all violations as a scalar. In this paper, the polynomial curve fitting problem is considered from the viewpoint of decision making. Taking into account some weaknesses of the norm-based approaches, a multiobjective programming model for curve fitting is given in which the violations are minimized simultaneously as a vector. This approach is more flexible for the curve fitting problem. Indeed, using the concept of efficiency in multiobjective programming, it enables us to impose some additional helpful secondary preferences. Especially, this approach can obtain a fitted curve with efficient violations and minimum average curvature or minimum average slope. [ABSTRACT FROM AUTHOR]

Abstract: Finding an efficient or weakly efficient solution in a multiobjective linear programming (MOLP) problem is not a difficult task. The difficulty lies in finding all these solutions and representing their structures. Since there are many convenient approaches that obtain all of the (weakly) efficient extreme points and (weakly) efficient extreme rays in an MOLP, this paper develops an algorithm which effectively finds all of the (weakly) efficient maximal faces in an MOLP using all of the (weakly) efficient extreme points and extreme rays. The proposed algorithm avoids the degeneration problem, which is the major problem of the most of previous algorithms and gives an explicit structure for maximal efficient (weak efficient) faces. Consequently, it gives a convenient representation of efficient (weak efficient) set using maximal efficient (weak efficient) faces. The proposed algorithm is based on two facts. Firstly, the efficiency and weak efficiency property of a face is determined using a relative interior point of it. Secondly, the relative interior point is achieved using some affine independent points. Indeed, the affine independent property enable us to obtain an efficient relative interior point rapidly. [Copyright &y& Elsevier]

Process capability indices (PCIs) provide numerical measures on whether a process conforms to the defined manufacturing capability prerequisite. These have been successfully applied by companies to compete with and to lead high-profit markets by evaluating the quality and productivity performance. The PCICpcompares the output of a process to the specification limits (SLs) by forming the ratio of the width between the process SLs with the width of the natural tolerance limits which is measured by six process standard deviation units. As another common PCI,Cpmincorporates two variation components which are variation to the process mean and deviation of the process mean from the target. A meaningful generalized version of above PCIs is introduced in this paper which is able to handle in a fuzzy environment. These generalized PCIs are able to measure the capability of a fuzzy-valued process in producing products on the basis of a fuzzy quality. Fast computing formulas for the generalized PCIs are computed for normal and symmetric triangular fuzzy observations, where the fuzzy quality is defined by linear and exponential fuzzy SLs. A practical example is presented to show the performance of proposed indices. [ABSTRACT FROM AUTHOR]