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The purpose of this paper is to present a measure method of the uncertainty for rough fuzzy set based on general binary relation.

Rough set and fuzzy set are two different but complementary theories for expressing uncertainty information, and based on the combination of these two uncertainty theories of expressing and handling uncertainty information, the rough fuzzy set model and uncertainty measure based on general relation are discussed.

This paper reveals the intrinsic of the uncertainty for rough fuzzy set based on general relation and presents a new measure method by introducing the Shannon entropy to generalized approximation space.

The paper contributes to the discussion on the research of rough set and fuzzy set. The conclusions are useful in information processing with uncertainty.

This paper seeks to present the use of Rough Sets (RS) theory as a processing method to improve the results in customer satisfaction survey applications.

The research methodology is to apply an innovative tool to discover knowledge on customer behavior patterns instead of using conventional statistical methods. The RS theory was applied to discover the voice of customers in market research. The collected data contained 422 records. Each record included 20 condition attributes as well as two decision attributes. The important attributes that ensured high quality of classification were generated first. Then decision rules for classifying high and low overall satisfaction and loyalty categories were derived.

Three important facts were found: the important product and service attributes that lead to overall satisfaction and loyalty; the percentage of latently dissatisfied customers; and customer decision rules.

The study is limited by the case company and its experience. These rules were presented to the company's sales and marketing managers who believed that they provided them with valuable information for creating strategies to increase customer satisfaction and retention.

RS theory provides a mathematical tool to discover patterns hidden in survey data. The paper describes a new attempt of applying a RS‐based method to analyze overall customer satisfaction and loyalty behavior through regular satisfaction questionnaire surveys.

Practical needs in geographical information systems (GIS) have led to the investigation of formal, sound and computational methods for spatial analysis. Since models based on topology of R² have a serious problem of incapability of being applied directly for practical computations, we have noticed that models developed on the raster space can overcome this problem. Because some models based on vector spaces have been effectively used in practical applications, we then introduce the idea of using the raster space as our platform to study spatial entities of vector spaces. In this paper, we use raster spaces to study not only morphological changes of spatial entities of vector spaces, but also equal relations and connectedness of spatial entities of vector spaces. Based on the discovery that all these concepts contain relativity, we then introduce several new concepts, such as observable equivalence, strong connectedness, and weak connectedness. Additionally, we present a possible method of employing raster spaces to study spatial relations of spatial entities of vector spaces. Since the traditional raster spaces could not be used directly, we first construct a new model, called pansystems model, for the concept of raster spaces, then develop a procedure to convert a representation of a spatial entity in vector spaces to that of the spatial entity in a raster space. Such conversions are called approximation mappings.

Achieves efficient structural optimization of plate structures while the design constraints are multiple frequency constraints. Reduces the computational cost of optimization by approximating the frequencies using the Rayleigh quotient. Uses an optimality criteria method to solve each of the approximate problems. The creation of a high quality approximation is the key to the efficiency of the method. Also, with the great number of design variables, the optimality criteria methods are robust approaches. Thus the combination of approximation concepts and optimality criteria methods forms the basis of an efficient tool for optimum design of plate structures with frequency constraints. Presents examples and compares the results with previous work.

The purpose of this paper is to propose that the grey tolerance rough set (GTRS) and construct the GTRS-based classifiers.

The authors use grey relational analysis to implement a relationship-based similarity measure for tolerance rough sets.

The proposed classification method has been tested on several real-world data sets. Its classification performance is comparable to that of other rough-set-based methods.

The authors design a variant of a similarity measure which can be used to estimate the relationship between any two patterns, such that the closer the relationship, the greater the similarity will be.

Rough set theory is a simple and potential methodology in extracting and minimizing rules from decision tables. Its concepts are core, reduct and discovering knowledge in the form of rules. The decision rules explain the decision state to predict and support the new situation. Initially it was proposed as a useful tool for analysis of decision states. This approach produces a set of decision rules involves two types namely certain and possible rules based on approximation. The prediction may highly be affected if the data size varies in larger numbers. Application of Rough set theory towards this direction has not been considered yet. Hence the main objective of this paper is to study the influence of data size and the number of rules generated by rough set methods. The performance of these methods is presented through the metric like accuracy and quality of classification. The results obtained show the range of performance and first of its kind in current research trend.

Global optimization in electrical engineering using stochastic methods requires usually a large amount of CPU time to locate the optimum, if the objective function is calculated either with the finite element method (FEM) or the boundary element method (BEM). One approach to reduce the number of FEM or BEM calls using neural networks and another one using multiquadric functions have been introduced recently. This paper compares the efficiency of both methods, which are applied to a couple of test problems and the results are discussed.

The analysis of certain structures must be performed with due consideration to non‐linear behavior, such as material and geometric non‐linearities. The existing methods for treating non‐linear structural behavior generally make use of repeated linearization, such as load increment methods. This paper demonstrates that there is an alternative type of linearization that appears to have significant advantages when applied to the analysis of non‐linear structural systems. Briefly stated, this alternative linearization can be thought of as a “monomialization”. This monomial (single‐termed power function) approximation more faithfully models the power function behavior inherent in typical structural systems. Conveniently, it becomes a linear form when transformed into log space. Thus, computational tools based on linear algebra remain useful and effective. Preliminary results indicate that the monomial approximation provides a higher quality approximation to non‐linear phenomena exhibited in structural applications. Consequently, incremental and iterative methods become more effective because larger steps can be taken. The net result is an increase in reliability of the solution process and a significant reduction in computational effort. Two examples are presented to demonstrate the method.

This paper compares three different radial basis function neural networks, as well as the diffuse element method, according to their ability of approximation. This is very useful for the optimization of electromagnetic devices. Tests are done on several analytical functions and on the TEAM workshop problem 25.

Rough set theory (RST) involves techniques for knowledge discovery or data mining. RST is typically applied within decision tables and offers an alternative to more conventional techniques for classification and rule induction. It is based on describing decisions or categories by means of certain approximations. Offers an overview of the basic principle through the use of a small example. Concludes with a marketing case study, dealing with the characteristics of different brands of cereal.