This paper proposes a fractional programming approach to construct the membership function for fuzzy weighted average. Based on the alpha -cut representation of fuzzy sets and the extension principle, a pair of fracti...
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This paper proposes a fractional programming approach to construct the membership function for fuzzy weighted average. Based on the alpha -cut representation of fuzzy sets and the extension principle, a pair of fractional programs is formulated to find the alpha -cut of fuzzy weighted average. Owing to the special structure of the fractional programs, in most cases, the optimal solution can be found analytically. Consequently, the exact form of the membership function can be derived by taking the inverse function of the alpha -cut. For other cases, a discrete but exact solution to fuzzy weighted average is provided via an efficient solution method. Examples are given for illustration. (C) 2001 Elsevier Science BY. All rights reserved.
Owing to more vague concepts frequently represented in decision data, mathematical objects introduced by K. T. Atanassov and studied under the name "intuitionistic fuzzy set'' (IFS) are more flexibly used...
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Owing to more vague concepts frequently represented in decision data, mathematical objects introduced by K. T. Atanassov and studied under the name "intuitionistic fuzzy set'' (IFS) are more flexibly used to model real-life decision situations. The aim of this paper is to develop a new methodology for solving multi-attribute group decision-making problems using IFS, in which multiple attributes are explicitly considered. In this methodology, for each decision maker in the group two auxiliary fractional programming models are derived from the TOPSIS to determine the relative closeness coefficient intervals of alternatives, which are aggregated for the group to generate the ranking order of all alternatives by computing their optimal degrees of membership based on the ranking method of interval numbers. The implementation process of the method proposed in this paper is illustrated with a numerical example. (C) 2008 Elsevier B.V. All rights reserved.
One of the most difficult fractional programs encountered so far is the sum-of-ratios problem. Contrary to earlier expectations it is much more removed from convex programming than other multi-ratio problems analyzed ...
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One of the most difficult fractional programs encountered so far is the sum-of-ratios problem. Contrary to earlier expectations it is much more removed from convex programming than other multi-ratio problems analyzed before. It really should be viewed in the context of global optimization. It proves to be essentially NP-hard in spite of its special structure under the usual assumptions on numerators and denominators. The article provides a recent survey of applications, theoretical results and various algorithmic approaches for this challenging problem.
This letter addresses two distinctly poised objectives, i.e., data rate and energy harvesting (EH) in Simultaneous Wireless Information and Power Transfer (SWIPT) systems with Reconfigurable Intelligent Surface (RIS) ...
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This letter addresses two distinctly poised objectives, i.e., data rate and energy harvesting (EH) in Simultaneous Wireless Information and Power Transfer (SWIPT) systems with Reconfigurable Intelligent Surface (RIS) by tackling a weighted objective to maximize data rate, EH, and transmit power utilization for multi-antenna BS and multiple RIS-User scenarios. This approach optimizes power splitting (PS) ratio at the end-user and transmit power using an optimized practical phase-dependent amplitude model for each RIS element reflectivity. fractional programming-based Dinkelbach and Quadratic transform-related algorithms are proposed and compared with Karush-Kuhn-Tucker (KKT) conditions based solutions. Optimized discrete phase shift (DPS) level has been sought. Numerical results show that deploying more RIS elements and placing them closer together enhances both information rate and EH, whereas it nearly saturates with increasing DPS levels.
The notion of quasi-differentiability is examined and related to fractional programming. Necessary and sufficient conditions are given and various other properties of quasi-differentiable functions are discussed. Diff...
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The notion of quasi-differentiability is examined and related to fractional programming. Necessary and sufficient conditions are given and various other properties of quasi-differentiable functions are discussed. Differentiability is not assumed.
fractional programming is presented as a tool for studying the sustainability of agricultural systems. The essentials of the technique in both the single and the multi-objective cases are outlined. The lack of friendl...
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fractional programming is presented as a tool for studying the sustainability of agricultural systems. The essentials of the technique in both the single and the multi-objective cases are outlined. The lack of friendly algorithms embedded in programming packages to solve the models is a shortcoming for the extensive use of a technique well adapted to represent many problems in economics. Two procedures for avoiding this shortcoming in the multiple objective case are discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.
作者：
SNIEDOVICH, MCSIR
NATL RES INST MATH SCIPOB 395PRETORIA 0001SOUTH AFRICA
A new format is proposed for fractional programming problems. This format gives full expression to the fact that the parametric approach to fractional programming problems is rooted in a first-order necessary and suff...
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A new format is proposed for fractional programming problems. This format gives full expression to the fact that the parametric approach to fractional programming problems is rooted in a first-order necessary and sufficient optimality condition. It is thus shown that although traditionally it has not been construed as such, the parametric approach is in fact classical par excellence. [ABSTRACT FROM AUTHOR]
This paper considers two popular inventory models: the continuous review and periodic review reorder-point, order-quantity, control systems. Specifically we present two procedures which determine optimal values for th...
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This paper considers two popular inventory models: the continuous review and periodic review reorder-point, order-quantity, control systems. Specifically we present two procedures which determine optimal values for the two control parameters (i.e., reorder-point and order-quantity) when the holding-and-shortage costs are non-quasi-convex. This cost structure may arise when non-linear cost rate is considered, for instance when the shortage cost is the shadow cost of a service-level constraint. The algorithms based on a fractional programming method are intuitive and efficient, and as the holding-and-shortage cost functions become quasi-convex, they are compatible to existing algorithms. (C) 2003 Elsevier B.V. All rights reserved.
This paper considers two popular inventory models: the continuous review and periodic review reorder-point, order-quantity, control systems. Specifically we present two procedures which determine optimal values for th...
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This paper considers two popular inventory models: the continuous review and periodic review reorder-point, order-quantity, control systems. Specifically we present two procedures which determine optimal values for the two control parameters (i.e., reorder-point and order-quantity) when the holding-and-shortage costs are non-quasi-convex. This cost structure may arise when non-linear cost rate is considered, for instance when the shortage cost is the shadow cost of a service-level constraint. The algorithms based on a fractional programming method are intuitive and efficient, and as the holding-and-shortage cost functions become quasi-convex, they are compatible to existing algorithms. (C) 2003 Elsevier B.V. All rights reserved.
Waveform diversity(WD) represents a dynamic and transformative technology widely used in radar systems to enhance sensitivity and discrimination capabilities. Recently, WD techniques have been extensively explored for...
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Waveform diversity(WD) represents a dynamic and transformative technology widely used in radar systems to enhance sensitivity and discrimination capabilities. Recently, WD techniques have been extensively explored for their potential ambiguity suppression within synthetic aperture radar(SAR) *** these, the alternate transmitting mode combined with orthogonal waveforms emerges as a particularly promising solution. This study focuses on optimizing the power spectrum density(PSD) of signals to design and generate an orthogonal waveform pair that achieves both a low cross-correlation-to-autocorrelation ratio(CAR) and satisfactory imaging performance. Initially, we construct a fractional programming model with convex constraints to minimize the CAR. To address this challenge, we introduce an iterative optimization procedure for the PSD variable, which sequentially reduces the CAR. Each optimization step can be efficiently solved using a quadratically constrained quadratic program, ensuring that the resulting computational complexity remains low. Building on the optimized PSD, we established a parametric piecewise linear model to generate an orthogonal waveform pair. This model not only maintains a low CAR but achieves satisfactory imaging performance in real-time applications. Consequently, this orthogonal waveform pair effectively suppresses range ambiguity in SAR systems. Finally, we demonstrated the practicability and effectiveness of the proposed orthogonal waveforms through detailed simulation experiments, specifically targeting ambiguity suppression in conventional quad-polarization SAR systems.
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