Ranking fuzzy numbers with integral value

Ranking fuzzy numbers is important in decision making. Since very often the alternatives are evaluated by fuzzy numbers in a vague environment, a comparison between these fuzzy numbers is indeed a comparison between alternatives. This paper proposes a method of ranking fuzzy numbers with integral value. The method, which is independent of the type of membership functions used and the normality of the functions, can rank more than two fuzzy numbers simultaneously. It is relatively simple in computation, especially in ranking triangular and trapezoidal fuzzy numbers. Further, an index of optimism is used to reflect the decision maker's optimistic attitude. Discussion on comparative advantages is included.     

Application of fuzzy differential transform method for solving fuzzy Volterra integral equations

This paper deals with the solutions of fuzzy Volterra integral equations with separable kernel by using fuzzy differential transform method (FDTM). If the equation considered has a solution in terms of the series expansion of known functions, this powerful method catches the exact solution. To this end, we have obtained several new results to solve mentioned problem when FDTM has been applied. In order to show this capability and robustness, some fuzzy Volterra integral equations are solved in detail as numerical examples.     

Solutions to fuzzy integral equations with arbitrary kernels

Using a parametric Riemann integral representation, a numerical algorithm for solving fuzzy Fredholm and Voltera integral equations of the second kind with arbitrary kernel is proposed and illustrated with examples.     

Nonlinear fusion for face recognition using fuzzy integral

Face recognition based only on the visual spectrum is not accurate or robust enough to be used in uncontrolled environments. Recently, infrared (IR) imagery of human face is considered as a promising alternative to visible imagery due to its relative insensitive to illumination changes. However, IR has its own limitations. In order to fuse information from the two modalities to achieve better result, we propose a new fusion recognition scheme based on nonlinear decision fusion, using fuzzy integral to fuse the objective evidence supplied by each modality. The scheme also employs independent component analysis (ICA) for feature extraction and support vector machines (SVMs) for classification evidence. Recognition rate is used to evaluate the proposed scheme. Experimental results show the scheme improves recognition performance substantially.     

A computational method for fuzzy Volterra-Fredholm integral equations

In this paper, we will study the application of homotopy perturbation method for solving fuzzy nonlinear Volterra-Fredholm integral equations of the second kind. Some examples are proposed to exhibit the efficiency of the method.     

Sugeno模糊积分在分形编码中的应用

分形技术已被许多研究者应用于图像编码．在分形编码方案中，L^2距离技普遍采用去评价range块与domain块之间的匹配程度．本文将采用一种新的距离——基于Sugeno模糊积分的模糊距离去替代L^2距离．实验表明，在四叉树算法中，和L^2距离相比，在不损害压缩比和解码质量的前提下，混合或单纯使用模糊距离可提高编码速度35%～50％。     

Bounded solutions for fuzzy differential and integral equations

We find sufficient conditions for the boundness of every solution of first-order fuzzy differential equations as well as certain fuzzy integral equations. Our results are based on several theorems concerning crisp differential and integral inequalities.     

On the monotone convergence theorem for conormed-seminormed fuzzy integral

[In this paper, under the condition that the t-conorm and t-seminorm are continuous, we prove the monotone convergence theorem of conormed-seminormed fuzzy integral for non-decreasing monotone measurable function sequence; also we show that the result cannot be extended to the case of the non-increasing function sequence.     

On the Chebyshev type inequality for seminormed fuzzy integral

The Chebyshev type inequality for seminormed fuzzy integral is discussed. The main results of this paper generalize some previous results obtained by the authors. We also investigate the properties of semiconormed fuzzy integral, and a related inequality for this type of integral is obtained.     

Global solutions for nonlinear fuzzy fractional integral and integrodifferential equations

This paper is devoted to considering the existence and uniqueness results for fuzzy fractional integral equations employing the method of upper and lower solutions. Moreover, the approach is followed to prove the existence of solutions for the fuzzy initial value problem of fractional integrodifferential equations involving Riemann–Liouville differential operators. The method is illustrated by two examples.     

The definite integral

<正>1.What does the definite integral mean?The definite integral of f(x)fromato b is defined the limit of the sum as n→∞.That is limn→∞∑n i=1f(ξi)·Δxi.We divide the interval[a,b]into n subintervals of equal widthΔx=(b-a)n.Let x0=a,x1,x2,…,xn=b be the endpoints of these subintervals and we chooseξiis any point in the ith subinterval,that is,xi-1≤ξi≤xi,then,the sum∑n f(ξi)·Δxiis called a Rie-     

The definite integral

1. What does the definite integral mean？
The definite integral off（x） from a to b is defined the limit of the sum as n→∞.     

The product integral

The basic concepts and properties of the product integral are discussed and various applications of it are examined.Translated fromItogi Nauki i Tekhniki, Ser. Problemy Geometrii, Vol. 22, 1990, pp. 167–215.     

Numerical method for solving linear Fredholm fuzzy integral equations of the second kind

In this paper we use parametric form of fuzzy number and convert a linear fuzzy Fredholm integral equation to two linear system of integral equation of the second kind in crisp case. We can use one of the numerical method such as Nystrom and find the approximation solution of the system and hence obtain an approximation for fuzzy solution of the linear fuzzy Fredholm integral equations of the second kind. The proposed method is illustrated by solving some numerical examples.