应用模糊集保护隐私信息

数据转换是保护数据隐私的一种有效方法。针对如何保持转换后数据的可用性问题,提出了一种基于模糊集的隐私保护方法。该方法把隐私属性值转换成模糊值,然后把转换后的数据及其模糊偏移度一起公开,既保护了数据隐私,也标示了数据的相对大小,很好地保持了数据的可用性。实验采用k-平均聚类方法对转换前后的数据进行聚类分析对比,结果表明,转换前后数据的聚类结果有很高的相似性,满足保护隐私和保持可用性的要求。     

Database discovery using fuzzy sets

In this work we consider a fuzzy set based approach to the issue of discovery in databases (database mining). The concept of linguistic summaries is described and shown to be a user friendly way to present information contained in a database. We discuss methods for measuring the amount of information provided by a linguistic summary. The issue of conjecturing, how to decide on which summaries may be informative, is discussed. We suggest two approaches to help us focus on relevant summaries. The first method, called the template method, makes use of linguistic concepts related to the domain of the attributes involved in the summaries. The second approach uses the mountain clustering method to help focus our summaries. © 1996 John Wiley & Sons, Inc.     

Tolerance analysis using fuzzy sets

A method for the analysis of the effects of subjective and objective tolerances in networks and systems is presented in this paper. The imprecision of the components is represented using fuzzy sets and then the value of the desired attribute is computed. The resulting attribute is also fuzzy and is obtained in the form of a fuzzy set. This fuzzy set contains the extremal and other values of the desired attribute along with their grades of membership. Thus, apart from getting the extremel values, we get the overall picture of the attribute. Since this method is directly applicable for the analysis of subjective tolerances, networks representing humanistic systems may be analysed using this method.     

Image fusion using intuitionistic fuzzy sets

Image fusion is the process of combining one or more images which are obtained from different environment into a single image which is more useful for further image processing tasks. Image registration and image fusion are of great importance in defence and civilian sectors, particularly for recognizing a ground/air force vehicle and medical imaging. In this paper a new way is drawn to fuse two or more images by using maximum, minimum operations in intuitionistic fuzzy sets (IFSs). IFSs are more suitable for image processing since every digital image have lot of uncertainties. In processing phase, images are reformed into intuitionistic fuzzy images (IFIs). Entropy is employed to obtain the optimum value of the parameter in membership and non-membership function. Then the resulting IFIs are disintegrated into image blocks and the corresponding blocks of the images are reunioned by finding the count of blackness and whiteness of the blocks. This paper evaluates the performance of simple averaging (AVG), principal component analysis (PCA), discrete wavelet transform (DWT), stationary wavelet transform (SWT), dual tree complex wavelet transform (DTCWT), multi-resolution singular value decomposition (MSVD), nonsubsampled contourlet transform (NSCT) and IFS (proposed method) in terms of various performance measure. The experimental and comparison results show that luminance and contrast is of great importance for image processing and prove that the proposed method is better than all other methods.     

Pattern recognition using type-II fuzzy sets

Type II fuzzy sets are a generalization of the ordinary fuzzy sets in which the membership value for each member of the set is itself a fuzzy set in [0,1]. We introduce a similarity measure for measuring the similarity, or compatibility, between two type-II fuzzy sets. With this new similarity measure we show that type-II fuzzy sets provide us with a natural language for formulating classification problems in pattern recognition.     

A new extension of fuzzy sets using rough sets: R-fuzzy sets

This paper presents a new extension of fuzzy sets: R-fuzzy sets. The membership of an element of a R-fuzzy set is represented as a rough set. This new extension facilitates the representation of an uncertain fuzzy membership with a rough approximation. Based on our definition of R-fuzzy sets and their operations, the relationships between R-fuzzy sets and other fuzzy sets are discussed and some examples are provided.     

Image thresholding using type II fuzzy sets

Image thresholding is a necessary task in some image processing applications. However, due to disturbing factors, e.g. non-uniform illumination, or inherent image vagueness, the result of image thresholding is not always satisfactory. In recent years, various researchers have introduced new thresholding techniques based on fuzzy set theory to overcome this problem. Regarding images as fuzzy sets (or subsets), different fuzzy thresholding techniques have been developed to remove the grayness ambiguity/vagueness during the task of threshold selection. In this paper, a new thresholding technique is introduced which processes thresholds as type II fuzzy sets. A new measure of ultrafuzziness is also introduced and experimental results using laser cladding images are provided.     

Case generation using rough sets with fuzzy representation

We propose a rough-fuzzy hybridization scheme for case generation. Fuzzy set theory is used for linguistic representation of patterns, thereby producing a fuzzy granulation of the feature space. Rough set theory is used to obtain dependency rules which model informative regions in the granulated feature space. The fuzzy membership functions corresponding to the informative regions are stored as cases along with the strength values. Case retrieval is made using a similarity measure based on these membership functions. Unlike the existing case selection methods, the cases here are cluster granules and not sample points. Also, each case involves a reduced number of relevant features. These makes the algorithm suitable for mining data sets, large both in dimension and size, due to its low-time requirement in case generation as well as retrieval. Superiority of the algorithm in terms of classification accuracy and case generation and retrieval times is demonstrated on some real-life data sets.     

Characterizing non-monotonic fuzzy relations

 This paper is on &-T-monotonic Fuzzy Relations and on the particular case of &-Monotonic Fuzzy Relations (in the crisp case &-Weakly-monotonic and &-Strongly-monotonic Relations, respectively). It goes a little further of the previous work the authors did on this kind of Fuzzy and Crisp Relations by proving a Characterization Theorem of &-T-monotonicity for Reflexive Fuzzy Relations that contains all the former results. This theorem is not only particularized to the crisp case but it is shown that then only crisp Logical States are needed. Of course, also Non-&-T-monotonic Fuzzy Relations and Non-Weak-&-monotonic crisp Relations became characterized. Received: 20 May 1997/Accepted: 18 June 1997     

Soft rough fuzzy sets and soft fuzzy rough sets

Fuzzy set theory, soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the further discussion of the combinations of fuzzy set, rough set and soft set. A new soft rough set model is proposed and its properties are derived. Furthermore, fuzzy soft set is employed to granulate the universe of discourse and a more general model called soft fuzzy rough set is established. The lower and upper approximation operators are presented and their related properties are surveyed.     

Sine-square embedded fuzzy sets versus type-2 fuzzy sets

The uncertainty is an inherent part of real-world applications. Type-2 fuzzy sets minimize the effects of uncertainties that cannot be modeled using type-1 fuzzy sets. However, the computational complexity of the type-2 fuzzy sets is very high and it is more difficult than type-1 fuzzy sets to use and understand. This paper proposes sine-square embedded fuzzy sets and gives a comparison with type-2 and nonstationary fuzzy sets. The sine-square embedded fuzzy sets consist of type-1 fuzzy sets and the sine function. The footprint of uncertainty in the type-2 fuzzy sets is provided with amplitude and frequency of sine-square function in the proposed algorithm. The proposed sine-square embedded fuzzy sets are much simpler than the type-2 fuzzy sets and the nonstationary fuzzy sets. Two control applications that are chosen as position control of a dc motor and simulation of human lifting motion using five-segment human model are carried out to demonstrate the effectiveness of the proposed approach.     

Superharmonic fuzzy sets on recurrent sets in dynamic fuzzy systems

We analyse P-superharmonic fuzzy sets on recurrent sets in dynamic fuzzy systems and we derive a simple estimation for the fuzzy sets. This paper presents a method to calculate an optimal value for Snell's optimal stopping problem.     

A trial for data retrieval using conceptual fuzzy sets

We describe trial applications of fuzzy sets to data retrieval. The objectives are to test their ability to achieve conceptual matching between retrieved objects and the user's intention and to connect real data with symbolic notations. The algorithm proposed retrieves data that conceptually fit the meanings of the entered keyword. An algorithm is described that uses fuzzy sets to handle word ambiguity (the main cause of vagueness in the meaning of a word). It is based on conceptual fuzzy sets (CFSs), which represent the meaning of words by chaining other related words. Two trial applications of this algorithm to data retrieval are described. First, an application to image retrieval shows variation of data retrieval with conceptual matching and transformation of numeric values into symbols. Next, an application to the agent recommending a TV program shows the method that lets CFSs fit to the sense of a user by Hebbian learning     

Hesitant fuzzy sets

Several extensions and generalizations of fuzzy sets have been introduced in the literature, for example, Atanassov's intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets. In this paper, we propose hesitant fuzzy sets. Although from a formal point of view, they can be seen as fuzzy multisets, we will show that their interpretation differs from the two existing approaches for fuzzy multisets. Because of this, together with their definition, we also introduce some basic operations. In addition, we also study their relationship with intuitionistic fuzzy sets. We prove that the envelope of the hesitant fuzzy sets is an intuitionistic fuzzy set. We prove also that the operations we propose are consistent with the ones of intuitionistic fuzzy sets when applied to the envelope of the hesitant fuzzy sets. © 2010 Wiley Periodicals, Inc.     

On edge detection of x-ray images using fuzzy sets

The effectiveness of the theory of fuzzy sets in detecting different regional boundaries of X-ray images is demonstrated. The algorithm includes a prior enhancement of the contrast among the regions (having small change in gray levels) using the contrast intensification (INT) operation along with smoothing in the fuzzy property plane before detecting its edges. The property plane is extracted from the spatial domain using S, ? and (1 ?) functions and the fuzzifiers. Final edge detection is achieved using max or min operator. The system performance for different parameter conditions is illustrated by application to an image of a radiograph of the wrist.     

Image enhancement and a quantitative index using fuzzy sets

The membership function for implementing the enhancement algorithm as described by Pal and King (1981, 1983) is modified here. The modified version enables one to avoid using contrast intensification (INT) operators for enhancement and has been found significantly to reduce the time of computing the algorithm in addition to providing a better approximation to the standard S and Π membership functions. To give a quantitative evaluation of their relative performances, an edge ambiguity index has also been defined through fuzzy measures in a set. The value of the index is maximum for image input and decreases as the ambiguity in detecting edges diminishes. The δ(X) value, as expected, is also found to increase with increasing standard deviation of the noise injected on X.     

Ordinal fuzzy sets

Fuzzy set theory has been used as a framework for interpreting imprecise linguistic expressions. In general, a linguistic term is described by the compatibility ordering induced in some universe of discourse (UoD). A membership function in fuzzy set theory serves to reflect this ordering by assignment of values in [0, 1] for objects in UoD. When we compute the meaning of a linguistic expression such as "young and tall" using fuzzy membership functions, two implicit assumptions are made. First, we assume the membership values have quantitative meaning so that they can be quantitatively manipulated, for example, by adding or subtracting (the extensive scale assumption). Second, we assume that the scales of the membership values used in describing the different linguistic terms are comparable and the same (the common scale assumption). In many cases, these assumptions cannot be justified. Some proposals have been made to address the first issue by using ordinal scale in defining fuzzy membership functions. However, the second issue has not been properly investigated. In this paper, we propose a framework that does not depend on both of these assumptions. Such framework will facilitate our understanding and investigation of qualitative reasoning without the extensive scale and common scale assumptions.     

Complex fuzzy sets

The objective of this paper is to investigate the innovative concept of complex fuzzy sets. The novelty of the complex fuzzy set lies in the range of values its membership function may attain. In contrast to a traditional fuzzy membership function, this range is not limited to [0, 1], but extended to the unit circle in the complex plane. Thus, the complex fuzzy set provides a mathematical framework for describing membership in a set in terms of a complex number. The inherent difficulty in acquiring intuition for the concept of complex-valued membership presents a significant obstacle to the realization of its full potential. Consequently, a major part of this work is dedicated to a discussion of the intuitive interpretation of complex-valued grades of membership. Examples of possible applications, which demonstrate the new concept, include a complex fuzzy representation of solar activity (via measurements of the sunspot number), and a signal processing application. A comprehensive study of the mathematical properties of the complex fuzzy set is presented. Basic set theoretic operations on complex fuzzy sets, such as complex fuzzy complement, union, and intersection, are discussed at length. Two novel operations, namely set rotation and set reflection, are introduced. Complex fuzzy relations are also considered. Index Terms-Complex fuzzy intersection, complex fuzzy relations, complex fuzzy sets, complex fuzzy union, complex-valued grades of membership, fuzzy complex numbers     

An algorithm for rating multiple-aspect alternatives using fuzzy sets

An improved algorithm for determining the (fuzzy) final rating of a multiple-aspect alternative according to a method proposed in an earlier paper (Baas ad Kwakernaak, 1977) is stated and proved.     

Rating and ranking of multiple-aspect alternatives using fuzzy sets

A method is proposed to deal with multiple-alternative decision problems under uncertainty. It is assumed that all the alternatives in the choice set can be characterized by a number of aspects, and that information is available to assign weights to these aspects and to construct a rating scheme for the various aspects of each alternative. The method basically consists of computing weighted final ratings for each alternative and comparing the weighted final ratings. The uncertainty that is assumed to be inherent in the assessments of the ratings and weights is accounted for by considering each of these variables as fuzzy quantities, characterized by appropriate membership functions. Accordingly, the final evaluation of the alternatives consists of a degree of membership in the fuzzy set of alternatives ranking first. A practical method is given to compute membership functions of fuzzy sets induced by mappings, and applied to the problem at hand. A number of examples are worked out. The method is compared to another one proposed by Kahne who approaches the problem probabilistically.