Α-cuts Of Fuzzy Sets Research Articles

Some properties of fuzzy dual cones

The notion of dual cone is generalized to fuzzy case. The definition of fuzzy dual cones is given. It is shown that they obey properties similar to those of crisp dual cones. Relationship between α-cuts of fuzzy sets and their fuzzy dual cones is also studied.

Fuzzy Testing for Regression Coefficient of Fuzzy Numbers

Abstract Statistical regression analysis is one of the important statistical methods and has been widely applied to different scientific areas. Classical regression analysis models are limited to crisp data. In practice, however, data are usually imprecise because data are difficult to measure precisely or data are determined subjectively. When dealing with fuzzy data, using classical regression analysis method to test the regression coefficient would be improper and lead to an incorrect decision. Regarding the topic of fuzzy regression analysis, most of the related literature focused on presenting methods of estimating regression coefficient in order to improve the ability of data interpreting. Unfortunately, those studies ignored the significance of the regression coefficient. That is, after constructing a fuzzy linear regression model, the regression coefficient must be tested as to whether they have the statistical meaning or not. The purpose of this paper is to develop a fuzzy testing method to test the regression coefficient with fuzzy data. Under the environment of crisp hypothesis, crisp critical value, and fuzzy data, the upper bound and lower bound of α-cuts of fuzzy testing statistics can be obtained based on α-cuts of fuzzy sets and extension principle. The membership function of fuzzy testing statistics can then be constructed. Finally, based on the membership function, a fuzzy testing method is developed to analyze those fuzzy data and further to make a statistical decision. Because the proposed testing method is based on membership function, when the data are crisp, the proposed approach can degenerate to the classical testing method.

Fuzzy Distance-Based Range Queries over Uncertain Moving Objects

Data obtained from real world are imprecise or uncertain due to the accuracy of positioning devices, updating protocols or characteristics of applications. On the other hand, users sometimes prefer to qualitatively express their requests with vague conditions and different parts of search region are in-equally important in some applications. We address the problem of efficiently processing the fuzzy range queries for uncertain moving objects whose whereabouts in time are not known exactly, for which the basic syntax is find objects always/sometimes near to the query issuer with the qualifying guarantees no less than a given threshold during a given temporal interval. We model the location uncertainty of moving objects on the utilization of probability density functions and describe the indeterminate boundary of query range with fuzzy set. We present the qualifying guarantee evaluation of objects, and propose pruning techniques based on the α-cut of fuzzy set to shrink the search space efficiently. We also design rules to reject non-qualifying objects and validate qualifying objects in order to avoid unnecessary costly numeric integrations in the refinement step. An extensive empirical study has been conducted to demonstrate the efficiency and effectiveness of algorithms under various experimental settings.

Estimation of cell loss probability for self-similar traffic in ATM networks—a fuzzy approach

Abstract Estimating cell loss probability (CLP) in real time for achieving satisfactory call admission control (CAC) remains an important research problem. In estimating CLP which are often specified to be less than 10−9, fuzzy-based techniques have been found to be more promising over crisp statistical techniques. In this paper, we propose a novel fuzzy logic algorithm based on the α-cuts of equivalence relation to estimate CLP in real time for self-similar traffic in ATM networks. The α-cuts of fuzzy sets are used to construct the membership functions of the input and output variables, and to induce necessary fuzzy rules. The proposed fuzzy approach is validated by comparing the estimated values of CLP with the theoretical values. The new approach not only estimates accurate real time CLP, but also achieves it by using fewer appropriate theoretical data.

An approach to stopping problems of a dynamic fuzzy system

We formulate a stopping problem for dynamic fuzzy systems concerning with fuzzy decision environment. It could be regarded as a natural fuzzification of non-fuzzy stopping problem with a deterministic dynamic system. The validity of the approach by α-cuts of fuzzy sets will be discussed in constructing One-step Look Ahead policy of an optimal fuzzy stopping time. A numerical example is given to illustrate the theoretical results and to show a merit to use fuzzy stopping times in dynamic fuzzy systems.