Traditional intuitionistic fuzzy sets and hesitant fuzzy sets will lose some information while representing vague information, to avoid this problem, this paper constructs weighted generalized hesitant fuzzy sets by remaining multiple intuitionistic fuzzy values and giving them corresponding weights. For weighted generalized hesitant fuzzy elements in weighted generalized hesitant fuzzy sets, the paper defines some basic operations and proves their operation properties. On this basis, the paper gives the comparison rules of weighted generalized hesitant fuzzy elements and presents two kinds of aggregation operators. As for weighted generalized hesitant fuzzy preference relation, this paper proposes its definition and computing method of its corresponding consistency index. Furthermore, the paper designs an ensemble learning algorithm based on weighted generalized hesitant fuzzy sets, carries out experiments on 6 datasets in UCI database and compares with various classification algorithms. The experiments show that the ensemble learning algorithm based on weighted generalized hesitant fuzzy sets has better performance in all indicators.

In order to improve the anomaly detection efficiency of network traffic, firstly, the model is established for network flows based on complex networks. Aiming at the uncertainty and fuzziness between network traffic characteristics and network states, the deviation extent is measured from the normal network state using deviation interval uniformly, and the intuitionistic fuzzy sets (IFSs) are established for the various characteristics on the network model that the membership degree, non-membership degree and hesitation margin of the IFSs are used to quantify the ownership of values to be tested and the corresponding network state. Then, the knowledge measure (KM) is introduced into the intuitionistic fuzzy weighted geometry (IFWGω) to weight the results of IFSs corresponding to the same network state with different characteristics together to detect network anomaly comprehensively. Finally, experiments are carried out on different network traffic datasets to analyze the evaluation indicators of network characteristics by our method, and compare with other existing anomaly detection methods. The experimental results demonstrate that the changes of various network characteristics are inconsistent under abnormal attack, and the accuracy of anomaly detection results obtained by our method is higher, verifying our method has a better detection performance.

Multi-slot information extraction, also known as frame extraction, is a task that identify several related entities simultaneously. Most researches on this task are concerned with applying IE patterns (rules) to extract related entities from unstructured documents. An important obstacle for the success in this task is unknowing where text portions containing interested information are. This problem is more complicated when involving languages with sentence boundary ambiguity, e.g. the Thai language. Applying IE rules to all reasonable text portions can degrade the effect of this obstacle, but it raises another problem that is incorrect (unwanted) extractions. This paper aims to present a method for removing these incorrect extractions. In the method, extractions are represented as intuitionistic fuzzy sets, and a similarity measure for IFSs is used to calculate distance between IFS of an unclassified extraction and that of each already-classified extraction. The concept of k nearest neighbor is adopted to design whether the unclassified extraction is correct or not. From the experiment on various domains, the proposed technique improves extraction precision while satisfactorily preserving recall.

This paper focuses mainly on issues related to the pricing of American options under a fuzzy environment by taking into account the clustering of the underlying asset price volatility, leverage effect and stochastic jumps. By treating the volatility as a parabolic fuzzy number, we constructed a Levy-GJR-GARCH model based on an infinite pure jump process and combined the model with fuzzy simulation technology to perform numerical simulations based on the least squares Monte Carlo approach and the fuzzy binomial tree method. An empirical study was performed using American put option data from the Standard & Poor's 100 index. The findings are as follows: under a fuzzy environment, the result of the option valuation is more precise than the result under a clear environment, pricing simulations of short-term options have higher precision than those of medium- and long-term options, the least squares Monte Carlo approach yields more accurate valuation than the fuzzy binomial tree method, and the simulation effects of different Levy processes indicate that the NIG and CGMY models are superior to the VG model. Moreover, the option price increases as the time to expiration of options is extended and the exercise price increases, the membership function curve is asymmetric with an inclined left tendency, and the fuzzy interval narrows as the level set α and the exponent of membership function n increase. In addition, the results demonstrate that the quasi-random number and Brownian Bridge approaches can improve the convergence speed of the least squares Monte Carlo approach.

It is the key concern for service providers that how a web service stands out among functionally similar services. QoS is a distinct and decisive factor in service selection among functionally similar services. Therefore, how to design services to meet customers' QoS requirements is an urgent problem for service providers. This paper proposes an approach using QFD (Quality Function Deployment) which is a quality methodology to transfer services' QoS requirements into services' design attribute characteristics. Fuzzy set is utilized to deal with subjective and vague assessments such as importance of QoS properties. TCI (Technical Competitive Index) is defined to compare the technical competitive capacity of a web service with those of other functionally similar services in the aspect of QoS. Optimization solutions of target values of service design attributes is determined by GA (Genetic Algorithm) in order to make the technical performance of the improved service higher than those of any other rival service products with the lowest improvement efforts. Finally, we evaluate candidate improvement solutions on cost-effectiveness. As the output of QFD process, the optimization targets and order of priority of service design attributes can be used as an important basis for developing and improving service products.

The development of the electricity market enables us to provide electricity of varied quality and price in order to fulfill power consumers' needs. Such customers choices should influence the process of adjusting power generation and spinning reserve, and, as a result, change the structure of a unit commitment optimization problem (UCP). To build a unit commitment model that considers customer choices, we employ fuzzy variables in this study to better characterize customer requirements and forecasted future power loads. To measure system reliability and determine the schedule of real power generation and spinning reserve, fuzzy Value-at-Risk (VaR) is utilized in building the model, which evaluates the peak values of power demands under given confidence levels. Based on the information obtained using fuzzy VaR, we proposed a heuristic algorithm called local convergence-averse binary particle swarm optimization (LCA-PSO) to solve the UCP. The proposed model and algorithm are used to analyze several test systems. Comparisons between the proposed algorithm and the conventional approaches show that the LCA-PSO performs better in finding the optimal solutions.

Several papers have presented measured function to handle multi-criteria fuzzy decision-making problems based on interval-valued intuitionistic fuzzy sets. However, in some cases, the proposed function cannot give sufficient information about alternatives. Consequently, in this paper, we will overcome previous insufficient problem and provide a novel accuracy function to measure the degree of the interval-valued intuitionistic fuzzy information. And a practical example has been provided to demonstrate our proposed approach. In addition, to make computing and ranking results easier and to increase the recruiting productivity, a computer-based interface system has been developed for decision makers to make decisions more efficiently.

We propose a thresholding method based on interval-valued fuzzy sets which are used to define the grade of a gray level belonging to one of the two classes, an object and the background of an image. The effectiveness of the proposed method is demonstrated by comparing our classification results on eight test images to results from the conventional methods.

Yubazaki et al. have proposed "single input rule modules connected type fuzzy reasoning method" (SIRMs method, for short) whose final output is obtained by summarizing the product of the importance degrees and the inference results from single input fuzzy rule module. Another type of single input type fuzzy reasoning method proposed by Hayashi et al. (we call it "Single Input Connected fuzzy reasoning method" (SIC method, for short) in this paper) uses rule modules to each input item as well as SIRMs method. We expect that inference results of SIRMs method and SIC method have monotonicity if the antecedent parts and consequent parts of fuzzy rules in SIRMs rule modules have monotonicity. However, this paper points out that even if fuzzy rules in SIRMs rule modules have monotonicity, the inference results do not necessarily have monotonicity. Moreover, it clarifies the conditions for the monotonicity of inference results by SIRMs method and SIC method.

The fuzzy set framework can be utilized in several different approaches to modeling the diagnostic process. In this paper, we introduce two main relations between symptoms and diseases where the relations are described by intuitionistic fuzzy set data. Also, we suggest four measures for medical diagnosis. We are dealing with the preliminary diagnosis from the information of interview chart. We quantify the qualitative information based on the interview chart by dual scaling. Prototype of fuzzy diagnostic sets and the linear regression methods are established with these quantified data. These methods can be used to classify new patient's tone of diseases with certain degrees of belief and its concerned symptoms.

In 1982, Buckles and Petry proposed fuzzy relational database for incorporating non-ideal or fuzzy information in a relational database. The fuzzy relational database relies on the specification of similarity relation in order to distinguish each scalar domain in the fuzzy database. These relations are reflexive, symmetric, and max-min transitive. In 1989, Shenoi and Melton extended the fuzzy relational database model of Buckles and Petry to deal with proximity relation for scalar domain. Since reflexivity and symmetry are the only constraints placed on proximity relations, proximity relation is considered as a generalization of similarity relation. However, we realized that naturally relation between fuzzy information is not symmetric. Here, we consider using conditional probability relation to represent similarity between two fuzzy data. Related to the properties of conditional probability relation, we introduce an interesting mathematical relation, called weak similarity relation, as generalization of similarity relation as well as proximity relation in which conditional probability relation is regarded as a concrete example of the weak similarity relation. In this paper, we propose design of fuzzy relational database to deal with conditional probability relation for scalar domain. These relations are reflexive and not symmetric. In addition, we define a notion of asymmetric redundant tuple based on two interpretations generalizing the concept of redundancy in classical relational database. In the relation to data querying, we discuss partitioning of domains with the objective of developing similarity class. Finally, we propose a new definition of partial fuzzy functional dependency (PFFD). Fuzzy functional dependency (FFD) as an extension of functional dependency (FD), usually used in design of fuzzy relational database, can be generated by the PFFD. Inference rules that are similar to Armstrong's Axioms for the FFD are both sound and complete.

A fuzzy-like phenomenon in a dynamic neural network is demonstrated and analyzed. The network operates as a dynamic associative memory. Each neuron of the dynamic neural network has an all-or-none output and exponentially decaying refractoriness. When several related patterns are stored in the dynamic neural network and an external stimulus with a property shared by two of the stored patterns is applied to the neural network, the output of the neural network dynamically transits between the two stored patterns. The frequency ratio that the network visits the two stored patterns is dependent on the ratio of the Hamming distances between the external pattern and the two stored patterns. This phenomenon is similar to the human decision-making process, some of which characteristics can be described by fuzzy set theory. A framework for the analysis of this phenomenon is proposed, and is used to derive sufficient conditions which ensure the dynamical transition between the two stored patterns. The properties of the transition in the network are also discussed.

A fuzzy-like phenomenon is observed in a chaotic neural network operating as dynamic autoassociative memory. When an external stimulation with properties shared by two stored patterns is applied to the chaotic neural network, the output of the network transits between the two patterns. The ratio of the network visiting two stored patterns is dependent on the ratio of the Hamming distances between the external stimulation and the two stored patterns. This phenomenon is similar to the human decision-making process, which can be described by fuzzy set theory. Here, we analyze the fuzzy-like phenomenon from the viewpoint of the fuzzy set theory.

Chen et al., have proposed a new estimation method for the membership values in fuzzy sets. The proposed scheme takes input from empirical/experimental data, which reflect the expert's knowledge on the relative degree of belonging of the members, and then searches for the best fit membership values of the element. Through the estimation of the practical case (Sect. 3 in [1]) the algorithm suggests to normalize the estimated membership values if there is any among them more than one and change some condition to guarantee its positiveness. In this paper, we show how to use the same imposed condition to guarantee that the estimated membership values will be within the unit interval without normalization.

A fuzzy Kohonen clustering network was proposed which integrates the Fuzzy c-means (FCM) model into the learning rate and updating strategies of the Kohonen network. This yields an optimization problem related to FCM, and the numerical results show improved convergence as well as reduced labeling error. However, the clusters may be either hyperspherical-shaped or hyperellipsoidal-shaped, we use a generalized objective function involving a collection of linear varieties. In this way the model is distributed and consists of a series of `local' linear-type models (based on the revealed clusters). We propose a method to generalize the fuzzy Kohonen clustering networks. Anderson's IRIS data and the artificial data set are used to illustrate this method; and results are compared with the standard Kohonen approach and the fuzzy Kohonen clustering networks.

Fuzzy value is a Fuzzy set the α-cuts of which are closed intervals. Let [0,1] be the set of Fuzzy values on [0,1]. We introduce two kinds of metric D and D1 in it, and investigate some topological properties.

This paper proposes the concept of information retrieval for fine arts database system on the fuzzy set theory, especially concerning to sensitive impression and location data. The authors have already reported several important formulations about the data structure and information retrieval models based on the fuzzy set theory for multimedia database. The fuzzy models of the information retrieval are implemented in the fine arts database system, which has the following features: (1) The procedure of information retrieval is formulated in the fuzzy set theory; (2) This database can treat multimedia data such as document data, sensitive impression, location information, and imagedata. (3) It is possible to retrieve the stored data based on sensitive impression and the location data such as "joyful pictures which have a mountain in the center and there is a tree in the right"; (4) Users can input impression words as a retrieval condition, and estimate their grades such as "low," "medium," and "high"; (5) For the result of information retrieval, the satisfaction grade is calculated based on fuzzy retrieval model; and (6) The stored data are about 400 fine arts paintings which are inserted by the textbook of fine arts currently used at the junior high school and high school in Japan. These features of this system give an effects of the fine arts education, and should be useful for information retrieval of fine arts. The results of this study will become increasingly important in connection with development of multimedia technology.

A complex fuzzy adaptive decision feedback equalizer based on the RLS algorithm is proposed. The proposed equalizer not only improves the performance but also reduces the computational complexity compared with the conventional complex fuzzy adaptive equalizers under the assumption of perfect knowledge of the linear and nonlinear channels.

In the direct product space of a complete metric linear space X and its related space Y, a fuzzy mapping G is introduced as an operator by which we can define a projective fuzzy set G(x,y) for any xX and yY. An original system is represented by a completely continuous operator f(x)Y, e.g., in the form x=λ(f(x)), (λ is a linear operator), and a nondeterministic or fuzzy fluctuation induced into the original system is represented by a generalized form of system equation xβG(x,f(x)). By establishing a new fixed point theorem for the fuzzy mapping G, the existence and evaluation problems of solution are discussed for this generalized equation. The analysis developed here for the fluctuation problem goes beyond the scope of the perturbation theory.