Papers by Keyword: Fuzzy Number

Abstract: To get precise in this paper, study anew fuzzy transform based on the Gupta transform is proposed , where exact solutions for fuzzy first-order differential equations are derived and explained in detail by proving the relevant theorems and properties and by presenting the solution of examples.

Abstract: For the objective fact that elements with different membership degrees should have different contribution to the metric measure between fuzzy numbers, this paper presents Lp-type of fuzzy number metrics weighted by structured element. Firstly, we define a metric weighted by structured element on the family (B[-1,1]) of all the same monotone and standard bounded functions on closed interval [-1,1] , and discuss the completeness and separability of those metric spaces; Next, using the fuzzy functional induced by normal fuzzy structured element, we give out a method that the metric of the closed bounded fuzzy number space is induced by the metric on function space B[-1,1]. Furthermore, a fuzzy number metric weighted by structured element which is induced by is presented ,and analyze completeness and separability of the induced fuzzy number metric spaces; Lastly, the difference and relationship between and the metric defined by traditional method are shown.

Abstract: In this paper, we give the definitions of approximately derivates, and then define the ap-Denjoy integral of fuzzy valued functions using fuzzy approximate Lusin function and investigate some properties of ap-Denjoy integral.

Abstract: The paper presents chosen traditional (based on probability theory) and non-traditional (based on possibility theory) computational tools for analysis of the material, geometric or loading uncertainties in mechanical structures. Uncertainties are introduced as bounded possible values intervals or as fuzzy sets, assuming possibility theory and as random parameters in the case of the probability theory. The main goal was to propose numerical algorithms for fuzzy analysis of stochastic oscillated FE model (truss structure) and to predict fuzzy fatigue damage considering fuzzy S/N curve.

Abstract: To overcome the limitations of the traditional threat assessment algorithms, a new threat sorting approach based on the fuzzy belief is proposed in this paper. In the new approach, the threat degrees described by quantitative number, interval number or linguistic label are all converted into the triangular fuzzy beliefs. The proportional conflict redistribution rule is used to combine the threat degrees of the same kind of assessment factors, the decision discounting rule is used to combine the threat degrees of different kinds of assessment factors, and the centroid method is utilized to make threat sorting. The new approach can not only deal with uncertain threat degrees, but also fuse the quantitative and qualitative threat degrees. The performance of the approach is analyzed in theory in this paper and the experimental results have certified its validity too.

Abstract: The rotary working table of C5250 vertical lathe requires high reliability. Based on the Fault Mode and Effect Analysis, the fault-tree of “guide surface lapping damage about rotary table” was established. To solve the problem of failure probability of bottom events obtaining insufficiently, fuzzy set theory was introduced into the fault tree analysis method. The failure probability distribution of bottom events was described as triangular fuzzy number. The occurrence probability distribution of the top event and the fuzzy importance of basic events were calculated according to fuzzy calculation rule. Through the analysis, the weak reliability links of the fault tree such as hydraulic pump, oil film thickness measuring installation and hydraulic valve were found out.

Abstract: In this paper, a novel approach to ranking fuzzy numbers based on the mean and the fuzzy degree of fuzzy number is proposed. In the approach, a new ranking index that is comprehensive consideration of the mean and the fuzzy degree of fuzzy number is constructed, and then the properties of the ranking index are given. Moreover, to compare the proposed approach with the existing approaches, numerical examples are given. The comparative results illustrate that the approach proposed in this paper is better and has simpler calculations.

Abstract: This paper proposes a new method for analyzing the fuzzy system reliability of a parallel-series and series-parallel systems using fuzzy confidence interval, where the reliability of each component of each system is unknown. To compute system reliability, we are estimated reliability of each component of the systems using fuzzy statistical data with both tools appropriate for modeling fuzzy data and suitable statistical methodology to handle these data. Numerical examples are given to compute fuzzy reliability and its cut set and the calculating was performed by using programming in software R.

Abstract: In this paper, we propose new distance definitions of fuzzy numbers and analysis their properties. Then the paper draws on several important theorems using these new distance definitions of fuzzy numbers.

Abstract: Development of a complicated technical problem encompasses different successive decisions that are based on techical analysis and engineering judgment. In each of these steps, somedegree of non-determinism is inevitable. The paper discusses different types of non-deterministic parameters that may be relevant in different stages of engineering analysis. The entire cycle of development of a product is considered, and it is shown that the relevance of methods isdifferent in different stages of the development cycle. A classification of different types of non-deterministic properties is presented. Based on the nature of these different classes of model properties, it is discussed to what degree each of these fits in the framework of either a probabilistic or a non-probabilistic concept.The availability of realistic data in an appropriate format is another issue that should be taken into account. A validated probabilistic representation is usually only possible after an extensive campaign of data acquisition has been conducted, or at least after suffcient data have been collected to allow for a reliable estimation of a statistical model. A study of scientific literature shows that validated information is not always available. A general conclusion is that probabilistic methods are applicable in later stages of development, when a suffciently large database of product data has been gathered. Probabilistic approaches are perfectly suited for conditions when the product is already in service. Possibilistic analysis on the other hand is best suited for application in cases when the data set about the product at hand is still incomplete.