Adding an additional degree of non-membership, K. T. Atanassov introduced the concept of the intuitionistic fuzzy (IF) set (IF-set), which has rarely been applied to the game theory yet. The aim of this paper is to de...
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Adding an additional degree of non-membership, K. T. Atanassov introduced the concept of the intuitionistic fuzzy (IF) set (IF-set), which has rarely been applied to the game theory yet. The aim of this paper is to develop the concept and methodology of matrix games with IF-set goals in which goals of players are expressed with IF-sets and payoffs are expressed with real numbers rather than IF-sets. In this methodology, the concepts of IF-set goals and the solutions of matrix games with IF-set goals are proposed. It is proven that solutions of matrix games with IF-set goals can be obtained through solving the developed auxiliary linear programming models, which are the generalization of matrix games with fuzzy goals. The proposed methodology is illustrated with a numerical example. Furthermore, comparison analysis of the proposed methodology is conducted to show its advantages over matrix games with fuzzy goals.
Matrix game theory is concerned with how two players make decisions when they are faced with known exact payoffs. The aim of this paper is to develop a simple and an effective linear programming method for solving mat...
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Matrix game theory is concerned with how two players make decisions when they are faced with known exact payoffs. The aim of this paper is to develop a simple and an effective linear programming method for solving matrix games in which the payoffs are expressed with intervals. Because the payoffs of the matrix game are intervals, the value of the matrix game is an interval as well. Based on the definition of the value for matrix games, the value of the matrix game may be regarded as a function of values in the payoff intervals, which is proven to be non-decreasing. A pair of auxiliary linear programming models is formulated to obtain the upper bound and the lower bound of the value of the interval-valued matrix game by using the upper bounds and the lower bounds of the payoff intervals, respectively. By the duality theorem of linear programming, it is proven that two players have the identical interval-type value of the interval-valued matrix game. Also it is proven that the linear programming models and method proposed in this paper extend those of the classical matrix games. The linear programming method proposed in this paper is demonstrated with a real investment decision example and compared with other similar methods to show the validity, applicability and superiority. (C) 2011 Elsevier Ltd. All rights reserved.
In this paper we formulate a network design model in which the traffic flows satisfy dynamic user equilibrium conditions for a single destination. The model presented here incorporates the Cell Transmission Model (CTM...
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In this paper we formulate a network design model in which the traffic flows satisfy dynamic user equilibrium conditions for a single destination. The model presented here incorporates the Cell Transmission Model (CTM);a traffic flow model capable of capturing shockwaves and link spillovers. Comparisons are made between the properties of the Dynamic User equilibrium Network Design Problem (DUE NDP) and an existing Dynamic System Optimal (DSO) NDP formulation. Both network design models have different objective functions with similar constraint sets which are linear and convex. Numerical demonstrations are made on multiple networks to demonstrate the efficacy of the model and demonstrate important differences between the DUE and DSO NDP approaches. In addition, the flexibility of the approach is demonstrated by extending the formulation to account for demand uncertainty. This is formulated as a stochastic programming problem and initial test results are demonstrated on test networks. It is observed that not accounting for demand uncertainty explicitly, provides sub-optimal solution to the DUE NDP problem.
Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that ...
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Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are performed exactly and bounds are derived on the number of elementary arithmetic operations necessary, or the cost of all arithmetic operations is considered through a bit-complexity analysis. Yet in practice, implementations typically use limited-precision arithmetic. In this paper we introduce the idea of a limited-precision LP oracle and study how such an oracle could be used within a larger framework to compute exact precision solutions to LPs. Under mild assumptions, it is shown that a polynomial number of calls to such an oracle and a polynomial number of bit operations, is sufficient to compute an exact solution to an LP. This work provides a foundation for understanding and analyzing the behavior of the methods that are currently most effective in practice for solving LPs exactly.
A linear programming (LP) model was developed to optimize the amount of system peak load reduction through scheduling of control periods in commercial/industry and residential load control programs at Florida Power an...
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A linear programming (LP) model was developed to optimize the amount of system peak load reduction through scheduling of control periods in commercial/industry and residential load control programs at Florida Power and Light Company. The LP model can be used to determine both long and short term control scheduling strategies and for planning the number of customers which should be enrolled in each program. Results of applying the model to a forecasted late 1990s summer Beak day load shape are presented. It is concluded that LP Solutions provide a relatively inexpensive and powerful approach to planning and scheduling load control. Also, it is not necessary to model completely general scheduling of control periods in order to obtain near best solutions to peak load reduction.
The parallel time complexity of the linear programming problem with at most two variables per inequality is discussed. Let n and m denote the number of variables and the number of inequalities, respectively, in a line...
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The parallel time complexity of the linear programming problem with at most two variables per inequality is discussed. Let n and m denote the number of variables and the number of inequalities, respectively, in a linear programming problem. It is assumed that all inequalities are weak. Under the concurrent-read-exclusive-write PRAM model, an O((log
68Q25
90G05
parallel computation
linear programming
poly-log time
Software effort estimation studies still suffer from discordant empirical results (i.e., conclusion instability) mainly due to the lack of rigorous benchmarking methods. So far only one baseline model, namely, Automat...
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Software effort estimation studies still suffer from discordant empirical results (i.e., conclusion instability) mainly due to the lack of rigorous benchmarking methods. So far only one baseline model, namely, Automatically Transformed linear Model (ATLM), has been proposed yet it has not been extensively assessed. In this article, we propose a novel method based on linear programming (dubbed as linear programming for Effort Estimation, LP4EE) and carry out a thorough empirical study to evaluate the effectiveness of both LP4EE and ATLM for benchmarking widely used effort estimation techniques. The results of our study confirm the need to benchmark every other proposal against accurate and robust baselines. They also reveal that LP4EE is more accurate than ATLM for 17% of the experiments and more robust than ATLM against different data splits and cross-validation methods for 44% of the cases. These results suggest that using LP4EE as a baseline can help reduce conclusion instability. We make publicly available an open-source implementation of LP4EE in order to facilitate its adoption in future studies.
Integrated renewable energy systems (IRES) which utilize different manifestations of solar energy to satisfy various energy needs are well suited for the remote rural areas of developing countries. By employing a line...
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Integrated renewable energy systems (IRES) which utilize different manifestations of solar energy to satisfy various energy needs are well suited for the remote rural areas of developing countries. By employing a linear programming approach, this paper develops a methodology for the design of IRES. The method is quite general and it minimizes an objective function of total annual cost, subject to a set of energy and power constraints. A numerical example is included to illustrate the design procedure.
A novel optimum extreme learning machines (ELM) construction method was proposed. We define an extended covering matrix with smooth function, relax the objective and constraints to formulate a more general linear prog...
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A novel optimum extreme learning machines (ELM) construction method was proposed. We define an extended covering matrix with smooth function, relax the objective and constraints to formulate a more general linear programming method for the minimum sphere set covering problem. We call this method linear programming minimum sphere set covering (LPMSSC). We also present a corresponding kernelized LPMSSC and extended LPMSSC with non-Euclidean L1 and L-infinity metric. We then propose to apply the LPMSSC method to ELM and propose a data dependent ELM (DDELM) algorithm. We can obtain compact ELM for pattern classification via LPMSSC. We investigate the performances of the proposed method through UCI benchmark data sets. (c) 2007 Elsevier B.V. All rights reserved.
For linear dynamical systems with linear state and control constraints the regulator problem can be formulated as a linear programming problem. A regulator, built around a standard LP program and operating in the Open...
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For linear dynamical systems with linear state and control constraints the regulator problem can be formulated as a linear programming problem. A regulator, built around a standard LP program and operating in the Open Loop Optimal Feedback (OLOF) fashion, is presented. The LP-OLOF regulator was implemented on a VAX 11/780 computer to control, in real time, a double water tank laboratory process, and the water level of a hydroelectric power station reservoir. The reservoir control experiment showed that even with an assumed simple process model, satisfactory performance was achieved. In particular it was beneficial that the LP-OLOF regulator allows dynamic changes of the water flow bounds corresponding to the number of generators available at different operating conditions, and that the regulator can predict the water level.
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