Possibilistic linear regression analysis for fuzzy data

Fuzzy data given by expert knowledge can be regarded as a possibility distribution by which possibilistic linear systems are defined. Recently, it has become important to deal with fuzzy data in connection with expert knowledge. Three formulations of possibilistic linear regression analysis are proposed here to deal with fuzzy data. Since our formulations can be reduced to linear programming problems, the merit of our formulations is to be able to obtain easily fuzzy parameters in possibilistic linear models and to add other constraint conditions which might be obtained from expert knowledge of fuzzy parameters. This approach can be regarded as a fuzzy interval analysis in a fuzzy environment.     

Fuzzy data approximation using smoothing cubic splines: Similarity and error analysis

In this paper, a new methodology is developed for defining error and similarity measure indexes, in order to establish a criterion adequate for comparison function approximation using fuzzy data. The proposed similarity measures and error indexes are applied for smoothing with cubic splines, showing a good performance for defining the accuracy of approximation obtained with fuzzy numbers. Examples are given to compare the behavior of the new indexes proposed for different configurations of the smooth cubic splines. A statistical analysis was carried out to verify the homogeneity of the indexes proposed as criteria to determine the correctness or accuracy of such approximation of fuzzy numbers.     

基于模糊收益率的组合投资模型

本文考虑了收益率为模糊数的投资组合选择问题,利用模型约束简化方差约束,建立了投资组合选择的模糊线性规划模型,然后引进模糊期望把模糊线性规划问题化为普通参数线性规划问题,最后给出了一个数值算例.     

On Weighted Possibilistic Mean,Variance and Correlation of Interval-valued Fuzzy Numbers

In this paper, the concept of weighted possibilistic mean of interval- valued fuzzy number is first introduced. Further, the notions of weighted possibilistic variance, covariance and correlation of interval-valued fuzzy numbers are presented. Meantime, some important properties of them and relationships between them are studied.     

Feller’s Scheme in Approximation by Nonlinear Possibilistic Integral Operators

By analogy with Feller’s general probabilistic scheme used in the construction of many classical convergent sequences of linear operators, in this paper, we consider a Feller-kind scheme based on the possibilistic integral, for the construction of convergent sequences of nonlinear operators. In particular, in the discrete case, all the so-called max-product Bernstein-type operators and their qualitative convergence properties are recovered. Also, discrete nonperiodic nonlinear possibilistic convergent operators of Picard type, Gauss–Weierstrass type and Poisson–Cauchy type are studied and the possibility of introduction of discrete periodic(trigonometric) nonlinear possibilistic operators of de la Vallée–Poussin type, of Fejér type and of Jackson type is mentioned as future directions of research.     

Reliable design of a logistics network under uncertainty: A fuzzy possibilistic-queuing model

This paper proposes a bi-objective model for designing a reliable network of bi-directional facilities in logistics network under uncertainties. For this purpose, the model utilizes an effective reliability approach to find a robust logistics network design. The objectives of the model are to minimize the total costs and the expected transportation costs after failures of bi-directional facilities of the logistics network. To solve the model, a new solution approach is proposed by combining queuing theory, fuzzy possibilistic programming and fuzzy multi-objective programming. Finally, the computational experiments are provided to illustrate the effectiveness of the proposed model and solution approach.     

A Cauchy-Schwarz type inequality for fuzzy integrals

In this paper we prove a Cauchy-Schwarz type inequality for fuzzy integrals.     

Efficient domain partitioning algorithms for global optimization of rational and Lipschitz continuous functions

A domain partitioning algorithm for minimizing or maximizing a Lipschitz continuous function is enhanced to yield two new, more efficient algorithms. The use of interval arithmetic in the case of rational functions and the estimates of Lipschitz constants valid in subsets of the domain in the case of others and the addition of local optimization have resulted in an algorithm which, in tests on standard functions, performs well.     

A Chebyshev type inequality for fuzzy integrals

In this paper, we prove a Chebyshev type inequality for fuzzy integrals. More precisely, we show that:

where μ is the Lebesgue measure on and f,g:[0,1]→[0,∞) are two continuous and strictly monotone functions, both increasing or both decreasing. Also, some examples and applications are presented.     

Comparison of fuzzy sets on the same decision space

Some methods of making fuzzy decisions include a comparison of fuzzy sets on the same space. Methods have been published which suffer from lack of discrimination between alternatives and occasional conflict with intuitive choice. These methods are reviewed in this paper and then a new approach is described which overcomes their drawbacks. Methods of evaluating the parameter used in decision-making are given which can be varied to incorporate different utility functions.     

A class of strong forms of fuzzy complete continuity

The aim of this paper is devoted to make use of operations on I^X of a fuzzy topological space X to unify and generalize classes of strong forms of fuzzy complete continuity. Furthermore, we add more types of strong forms of fuzzy completely continuous functions by choosing special operations. A comparison between these types of functions is of interest. Preservations of some fuzzy aspects under these functions are studied.     

Tangentially continuous directional derivatives in nonsmooth analysis

In this paper, we introduce a new class of nonsmooth functions in terms of a continuity property of the usual directional derivative. Under this approach, we study the subregular and the semismooth functions. Finally, we give conditions for a marginal function to be subregular and semismooth.This research was supported in part by the Fondo Nacional de Ciencias, Santiago, Chile.The authors thank A. Auslender and L. Thibault for discussions on the subject.     

Convex fuzzy random variables

A theory of fuzzy random variables is developed that applies to situations involving both randomness and fuzziness. The use of membership functions that are quasi-concave play an important role in the theory. The expectation of a fuzzy random variable is a fuzzy variable (fuzzy set). The usual linearity properties of probabilistic expectation carry over to fuzzy random variables. A special case of a fuzzy Law of Large Number is proven.     

Computation of the optimal tolls on the traffic network

The present paper is devoted to the computation of optimal tolls on a traffic network that is described as fuzzy bilevel optimization problem. As a fuzzy bilevel optimization problem we consider bilinear optimization problem with crisp upper level and fuzzy lower level. An effective algorithm for computation optimal tolls for the upper level decision-maker is developed under assumption that the lower level decision-maker chooses the optimal solution as well. The algorithm is based on the membership function approach. This algorithm provides us with a global optimal solution of the fuzzy bilevel optimization problem.     

A Multivariate Global Optimization Using Linear Bounding Functions

Recently linear bounding functions (LBFs) were proposed and used to find -global minima. This paper presents an LBF-based algorithm for multivariate global optimization problems. The algorithm consists of three phases. In the global phase, big subregions not containing a solution are quickly eliminated and those which possibly contain the solution are detected. An efficient scheme for the local phase is developed using our previous local minimization algorithm, which is globally convergent with superlinear/quadratic rate and does not require evaluation of gradients and Hessian matrices. To ensure that the found minimizers are indeed the global solutions or save computation effort, a third phase called the verification phase is often needed. Under adequate conditions the algorithm finds the -global solution(s) within finite steps. Numerical testing results illustrate how the algorithm works, and demonstrate its potential and feasibility.     

带有梯形模糊数的均值-方差投资组合模型比较分析

采用梯形模糊数来描述证券的收益率,并建立基于梯形模糊数的收益最大化单目标均值-方差模型、风险最小化单目标均值-方差模型、和收益最大化风险最小化的双目标均值-方差模型.对上述三种模型进行实例分析,讨论投资比例系数上界为1和0.7两种不同情况下三种模型的对比,进而证明模型的可行性以及分析不同模型之间的差异性.     

New Classes of Globally Convexized Filled Functions for Global Optimization

We propose new classes of globally convexized filled functions. Unlike the globally convexized filled functions previously proposed in literature, the ones proposed in this paper are continuously differentiable and, under suitable assumptions, their unconstrained minimization allows to escape from any local minima of the original objective function. Moreover we show that the properties of the proposed functions can be extended to the case of box constrained minimization problems. We also report the results of a preliminary numerical experience.     

Monomial geometric programming with fuzzy relation equation constraints

Monomials are widely used. They are basic structural units of geometric programming. In the process of optimization, many objective functions can be denoted by monomials. We can often see them in resource allocation and structure optimization and technology management, etc. Fuzzy relation equations are important elements of fuzzy mathematics, and they have recently been widely applied in fuzzy comprehensive evaluation and cybernetics. In view of the importance of monomial functions and fuzzy relation equations, we present a fuzzy relation geometric programming model with a monomial objective function subject to the fuzzy relation equation constraints, and develop an algorithm to find an optimal solution based on the structure of the solution set of fuzzy relation equations. Two numerical examples are given to verify the developed algorithm. Our numerical results show that the algorithm is feasible and effective.     

The minimum spanning tree problem with fuzzy costs

In this paper the minimum spanning tree problem in a given connected graph is considered. It is assumed that the edge costs are not precisely known and they are specified as fuzzy intervals. Possibility theory is applied to characterize the optimality of edges of the graph and to choose a spanning tree under fuzzy costs.