1,032 research outputs found

    Solving the four index fully fuzzy transportation problem

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    In this paper, we will solve the four index fully fuzzy transportation problem (textit{FFTP4_{4}}) with some adapted classical methods. All problem\u27s data will be presented as fuzzy numbers. In order to defuzificate these data, we will use the ranking function procedure. Our method to solve the textit{FFTP4_{4}} composed of two phases; in the first one, we will use an adaptation of well-known algorithms to find an initial feasible solution, which are the least cost, Russell\u27s approximation and Vogel\u27s approximation methods. In the second phase, we will test the optimality of the initial solution, if it is not optimal, we will improve it. A numerical analysis of the proposed methods is performed by solving different examples of different sizes; it is determined that they are stable, robust, and efficient. A proper comparative study between the adapted methods identifies the suitable method for solving textit{FFTP4_{4}}

    Fuzzy linear programming problems : models and solutions

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    We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, alpha-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately

    Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs

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    Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.Comment: 13 figures, 35 reference

    Linear kernels for outbranching problems in sparse digraphs

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    In the kk-Leaf Out-Branching and kk-Internal Out-Branching problems we are given a directed graph DD with a designated root rr and a nonnegative integer kk. The question is to determine the existence of an outbranching rooted at rr that has at least kk leaves, or at least kk internal vertices, respectively. Both these problems were intensively studied from the points of view of parameterized complexity and kernelization, and in particular for both of them kernels with O(k2)O(k^2) vertices are known on general graphs. In this work we show that kk-Leaf Out-Branching admits a kernel with O(k)O(k) vertices on H\mathcal{H}-minor-free graphs, for any fixed family of graphs H\mathcal{H}, whereas kk-Internal Out-Branching admits a kernel with O(k)O(k) vertices on any graph class of bounded expansion.Comment: Extended abstract accepted for IPEC'15, 27 page
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