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Crisp-linear-and Models in Fuzzy Multiple Objective Linear Fractional Programming

机译:模糊多目标线性分数规划的清脆线性和模型

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摘要

The aim of this paper is to introduce two crisp linear models to solve fuzzy multiple objective linear fractional programming problems. In a novel manner we construct two piece-wise linear membership functions to describe the fuzzy goal linked to a linear fractional objective. They are related to the numerator and denominator of the fractional objective function; and we show that using the fuzzy-and operator to aggregate them a convenient description of the original fractional fuzzy goal is obtained. Further on, with the help of the fuzzy-and operator we aggregate all fuzzy goals and constraints, formulate a crisp linear model, and use it to provide a solution to the initial fuzzy multiple objective linear fractional programming problem. The second model embeds in distinct ways the positive and negative information, the desires and restrictions respectively; and aggregates in a bipolar manner the goals and constraints. The main advantage of using the new models lies in the fact that they are linear, and can generate distinct solutions to the multiple objective problem by varying the thresholds and tolerance limits imposed on the fuzzy goals.
机译:本文的目的是引入两种清晰的线性模型来解决模糊多目标线性分数规划问题。以一种新颖的方式,我们构建了两个方向的线性隶属函数,以描述与线性分数目标相关的模糊目标。它们与分数目标函数的分子和分母有关;我们表明,使用模糊和操作员聚合它们的方便描述,获得了原始的分数模糊目标。此外,在模糊和操作员的帮助下,我们聚合所有模糊的目标和约束,配制了清晰的线性模型,并使用它来提供初始模糊多目标线性分数规划问题的解决方案。第二种模型以不同的方式嵌入了正面和负面信息,欲望和限制;并以双极方式聚集目标和约束。使用新模型的主要优点在于它们是线性的,并且可以通过改变对模糊目标施加的阈值和公差限制来产生多个客观问题的不同解决方案。

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