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本文提出了一类目标函数为正项式,约束是取大乘积型模糊关系方程的优化 问题,我们在本文中阐述了取大乘积型模糊关系方程解的结构以及求解的方法,基于目标 函数中每个单项式的指数取值情况讨论了最优解,并且给出了解决此类优化问题的一个程 序,为了说明该方法的有效性给出了两个具体例子. 相似文献
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An minimization problem with a linear objective function subject to fuzzy relation equations using max-product composition has been considered by Loetamonphong and Fang. They first reduced the problem by exploring the special structure of the problem and then proposed a branch-and-bound method to solve this 0-1 integer programming problem. In this paper, we provide a necessary condition for an optimal solution of the minimization problems in terms of one maximum solution derived from the fuzzy relation equations. This necessary condition enables us to derive efficient procedures for solving such optimization problems. Numerical examples are provided to illustrate our procedures. 相似文献
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提出了一类目标函数为线性函数,约束是直觉模糊关系方程的最优化问题.这是一类非凸非光滑最优化问题,基于可行域的结构,给出了求全局最优解和最优值的一个算法,最后通过数值例子验证了算法的可行性. 相似文献
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An optimization model with one linear objective function and fuzzy relation equation constraints was presented by Fang and
Li (1999) as well as an efficient solution procedure was designed by them for solving such a problem. A more general case
of the problem, an optimization model with one linear objective function and finitely many constraints of fuzzy relation inequalities,
is investigated in this paper. A new approach for solving this problem is proposed based on a necessary condition of optimality
given in the paper. Compared with the known methods, the proposed algorithm shrinks the searching region and hence obtains
an optimal solution fast. For some special cases, the proposed algorithm reaches an optimal solution very fast since there
is only one minimum solution in the shrunk searching region. At the end of the paper, two numerical examples are given to
illustrate this difference between the proposed algorithm and the known ones. 相似文献
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The fuzzy relation programming problem is a minimization problem with a linear objective function subject to fuzzy relation equations using certain algebraic compositions. Previously, Guu and Wu considered a fuzzy relation programming problem with max-product composition and provided a necessary condition for an optimal solution in terms of the maximum solution derived from the fuzzy relation equations. To be more precise, for an optimal solution, each of its components is either 0 or the corresponding component's value of the maximum solution. In this paper, we extend this useful property for fuzzy relation programming problem with max-strict-t-norm composition and present it as a supplemental note of our previous work. 相似文献
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Bing-Yuan Cao 《Fuzzy Optimization and Decision Making》2006,5(2):123-139
An optimization is made in this paper by means of classical geometric programming and geometric programming under the fuzzy
environment, although the optimization is complicated in an economical radius for power supply from substations. The latter
involves discussing geometric programmings of soft constraints and fuzzy coefficients, which are new models, aiming to enlarge
the radius of power supply as much as possible with the least investment and the reduction of waste. Besides, by numerical
examples, more satisfactory results are obtained in the paper, which testify the mentioned effects and the solution to the
model as well. And finally, the paper demonstrates that the models built here contain more information than a classical static
controlling optimum model. 相似文献
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Michael Smithson 《Fuzzy Sets and Systems》1984,14(1):1-3
Linear programming problems with fuzzy parameters are formulated by fuzzy functions. The ambiguity considered here is not randomness, but fuzziness which is associated with the lack of a sharp transition from membership to nonmembership. Parameters on constraint and objective functions are given by fuzzy numbers. In this paper, our object is the formulation of a fuzzy linear programming problem to obtain a reasonable solution under consideration of the ambiguity of parameters. This fuzzy linear programming problem with fuzzy numbers can be regarded as a model of decision problems where human estimation is influential. 相似文献
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In this paper, we focus on the proposed algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max-prod composition that it has been proposed by Ghodousian and Khorram [A. Ghodousian, E. Khorram, An algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max-prod composition, Appl. Math. Comput. 178 (2006) 502–509]. Firstly, we show that the algorithm may not lead to the optimal solution in some cases. Secondly, we propose a new algorithm for solving the presented model by Ghodousian and Khorram (2006), as mentioned above. In fact, it modifies the presented algorithm in the Ghodousian and Khorram’s paper. Also, this algorithm is extended to the presented model by Khorram and Ghodousian [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886.] with max-av composition. Finally, some numerical examples are given for illustrating the purposes. 相似文献
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Ali Abbasi Molai 《Journal of Computational and Applied Mathematics》2010,233(8):2090-2103
This paper studies the optimization model of a linear objective function subject to a system of fuzzy relation inequalities (FRI) with the max-Einstein composition operator. If its feasible domain is non-empty, then we show that its feasible solution set is completely determined by a maximum solution and a finite number of minimal solutions. Also, an efficient algorithm is proposed to solve the model based on the structure of FRI path, the concept of partial solution, and the branch-and-bound approach. The algorithm finds an optimal solution of the model without explicitly generating all the minimal solutions. Some sufficient conditions are given that under them, some of the optimal components of the model are directly determined. Some procedures are presented to reduce the search domain of an optimal solution of the original problem based on the conditions. Then the reduced domain is decomposed (if possible) into several sub-domains with smaller dimensions that finding the components of the optimal solution in each sub-domain is very easy. In order to obtain an optimal solution of the original problem, we propose another more efficient algorithm which combines the first algorithm, these procedures, and the decomposition method. Furthermore, sufficient conditions are suggested that under them, the problem has a unique optimal solution. Also, a comparison between the recently proposed algorithm and the known ones will be made. 相似文献
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In this paper, we extend Guo and Xia’s necessary condition which has been presented by Guo and Xia (Fuzzy optimizat Decis
Mak 5: 33–47, 2006) in order to study the finitely many constraints of fuzzy relation inequalities and optimize a linear objective
function on this region which is defined by the fuzzy max–min operator. The new condition provides a means for removing the
unnecessary paths resulting from Guo and Xia’s paths. Also, an algorithm and two numerical examples are offered to abbreviate
and illustrate the steps of the resolution process of the problem. 相似文献
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Clustering algorithms divide up a dataset into a set of classes/clusters, where similar data objects are assigned to the same
cluster. When the boundary between clusters is ill defined, which yields situations where the same data object belongs to
more than one class, the notion of fuzzy clustering becomes relevant. In this course, each datum belongs to a given class
with some membership grade, between 0 and 1. The most prominent fuzzy clustering algorithm is the fuzzy c-means introduced
by Bezdek (Pattern recognition with fuzzy objective function algorithms, 1981), a fuzzification of the k-means or ISODATA
algorithm. On the other hand, several research issues have been raised regarding both the objective function to be minimized
and the optimization constraints, which help to identify proper cluster shape (Jain et al., ACM Computing Survey 31(3):264–323,
1999). This paper addresses the issue of clustering by evaluating the distance of fuzzy sets in a feature space. Especially,
the fuzzy clustering optimization problem is reformulated when the distance is rather given in terms of divergence distance,
which builds a bridge to the notion of probabilistic distance. This leads to a modified fuzzy clustering, which implicitly
involves the variance–covariance of input terms. The solution of the underlying optimization problem in terms of optimal solution
is determined while the existence and uniqueness of the solution are demonstrated. The performances of the algorithm are assessed
through two numerical applications. The former involves clustering of Gaussian membership functions and the latter tackles
the well-known Iris dataset. Comparisons with standard fuzzy c-means (FCM) are evaluated and discussed. 相似文献
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AbstractThis paper focuses on how to compare two fuzzy sets and, from the viewpoint of set optimization, proposes eight types of fuzzy-set relations based on a convex cone as new comparison criteria of fuzzy sets. Then, difference evaluation functions for fuzzy sets are introduced. Under suitable assumptions of certain compactness and stability of fuzzy sets, we show that these functions correspond well to the fuzzy-set relations. In addition, through transforming these functions stepwise, we deal with numerical calculation methods of them in particular cases. Consequently, we can judge whether each fuzzy-set relation holds or not for given two fuzzy sets with the aid of computers. 相似文献
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The aim of this paper is to deal with a multiobjective linear programming problem with fuzzy random coefficients. Some crisp equivalent models are presented and a traditional algorithm based on an interactive fuzzy satisfying method is proposed to obtain the decision maker’s satisfying solution. In addition, the technique of fuzzy random simulation is adopted to handle general fuzzy random objective functions and fuzzy random constraints which are usually hard to be converted into their crisp equivalents. Furthermore, combined with the techniques of fuzzy random simulation, a genetic algorithm using the compromise approach is designed for solving a fuzzy random multiobjective programming problem. Finally, illustrative examples are given in order to show the application of the proposed models and algorithms. 相似文献
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In this paper, a multiobjective quadratic programming problem having fuzzy random coefficients matrix in the objective and constraints and the decision vector are fuzzy pseudorandom variables is considered. First, we show that the efficient solutions of fuzzy quadratic multiobjective programming problems are resolved into series-optimal-solutions of relative scalar fuzzy quadratic programming. Some theorems are proved to find an optimal solution of the relative scalar quadratic multiobjective programming with fuzzy coefficients, having decision vectors as fuzzy variables. At the end, numerical examples are illustrated in the support of the obtained results. 相似文献
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In multi-objective geometric programming problem there are more than one objective functions. There is no single optimal solution which simultaneously optimizes all the objective functions. Under these conditions the decision makers always search for the most “preferred” solution, in contrast to the optimal solution. A few mathematical programming methods namely fuzzy programming, goal programming and weighting methods have been applied in the recent past to find the compromise solution. In this paper ?-constraint method has been applied to find the non-inferior solution. A brief solution procedure of ?-constraint method has been presented to find the non-inferior solution of the multi-objective programming problems. Further, the multi-objective programming problems is solved by the fuzzy programming technique to find the optimal compromise solution. Finally, two numerical examples are solved by both the methods and compared with their obtained solutions. 相似文献
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Xiang Li Yang Zhang Hau-San Wong Zhongfeng Qin 《Journal of Computational and Applied Mathematics》2009,233(2):264-278
Portfolio selection theory with fuzzy returns has been well developed and widely applied. Within the framework of credibility theory, several fuzzy portfolio selection models have been proposed such as mean–variance model, entropy optimization model, chance constrained programming model and so on. In order to solve these nonlinear optimization models, a hybrid intelligent algorithm is designed by integrating simulated annealing algorithm, neural network and fuzzy simulation techniques, where the neural network is used to approximate the expected value and variance for fuzzy returns and the fuzzy simulation is used to generate the training data for neural network. Since these models are used to be solved by genetic algorithm, some comparisons between the hybrid intelligent algorithm and genetic algorithm are given in terms of numerical examples, which imply that the hybrid intelligent algorithm is robust and more effective. In particular, it reduces the running time significantly for large size problems. 相似文献
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A generalized model for a two person zero sum matrix game with fuzzy goals and fuzzy payoffs via fuzzy relation approach is
introduced, and it is shown to be equivalent to two semi-infinite optimization problems. Further, in certain special cases,
it is observed that the two semi-infinite optimization problems reduce to (finite) linear programming problems which are dual
to each other either in the fuzzy sense or in the crisp sense. 相似文献
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In this paper some fuzzy relation equations provided with one solution on a finite set are characterized: we consider fuzzy relation equations H ° Q = T with Q?F(XxY) and card X ? cardY. After recalling the definition of equivalent fuzzy relation equations, we introduce the definition of ρ-equivalent ones, which allows us to constrain our research without loss of generality to fuzzy relation equations where T does not have zero-components. 相似文献