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A Novel Approach to Decision Analysis Using Dominance-Based Soft Rough Sets

机译：基于优势的软粗糙集的决策分析方法

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摘要

A number of useful mathematical tools such as fuzzy sets, rough sets and soft sets have been developed to deal with problems involving various uncertainties. These theories have been found to be particularly useful in decision making under uncertainty. This study develops the theory of dominance-based soft rough sets, which is used to propose a new method for analyzing conflicts in decision-making problems. The approach establishes a preference relation among the given objects subject to the available information, and based on this relation it approximates a given concept. The lower approximation is utilized to design an algorithm to handle problems involving both multi-attribute and multi-decision and preference. The algorithm aims at electing objects or actions based on their conditional attributes. The domain of conditional and decision attributes contains preference-ordered values. To achieve an optimal solution, we first collect alternatives (actions) graded as best by all the decision makers. We then use DBSR lower approximations to develop an algorithm to reach the optimal solution. This approach addresses some limitations of models based on Pawlak conflict analysis theory. There are two main contributions of this paper. One is a hybrid model based on rough and soft set theories that can handle preference-based domains. The other is a new approach that can handle multi-agent conflict analysis decision-making problems.
机译：已经开发了许多有用的数学工具，如模糊集，粗糙集和软组来处理涉及各种不确定性的问题。已发现这些理论在不确定性下的决策中特别有用。本研究发展了基于优势的软粗糙集理论，用于提出一种新方法来分析决策问题的冲突。该方法在经过可用信息的情况下建立给定的对象之间的偏好关系，并且基于该关系，它近似于给定的概念。较低的近似用于设计一种处理涉及多属性和多决定和偏好的问题的算法。该算法旨在根据其条件属性选举对象或动作。条件和决策属性的域包含优先订购值。为了实现最佳解决方案，我们首先收集所有决策者最佳地分级的替代方案（行动）。然后，我们使用DBSR较低的近似来开发算法来达到最佳解决方案。该方法解决了基于Pawlak冲突分析理论的模型的一些局限性。本文有两个主要贡献。一个是基于粗糙和软设置理论的混合模型，可以处理基于偏好的域。另一个是一种能够处理多代理冲突分析决策问题的新方法。

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