勾股模糊粗糙集及其在多属性决策中的应用

Pythagorean Fuzzy Rough Sets and its Applications in Multi-attribute Decision Making

最近,许多粗糙集模型的扩展模型相继被提出.同时,基于双论域的粗糙集模型受到了越来越多的关注,并应用到实际的决策问题之中.通过结合经典粗糙集和勾股模糊关系,本文提出了一种新的模糊粗糙集叫做勾股模糊粗糙集.我们给出了勾股模糊粗糙集的定义,同时也讨论了勾股模糊粗糙集的若干性质.为了研究实际决策问题,我们给出了双论域上的勾股模糊粗糙集模型,为粗糙集在多属性决策问题中的应用提供了新的手段与方法.最后,通过一个职业测评的例子说明了本文提出的方法在多属性决策中的有效性.本文提出的方法充分利用了模糊集与粗糙集在不确定决策中的优势,为决策者提供了有价值的决策模型.

Recently,many extended rough set models were proposed in succession. At the same time,an increasingly amount of attentions have been given to the rough set models based on two universes,and they have been utilized in many real life decision making problems. The objective of this paper is to develop a newfuzzy rough set model called Pythagorean fuzzy rough set（ PFRS） by combining the classical rough set and Pythagorean fuzzy relation. We not only propose the definition of Pythagorean fuzzy rough set,but also study some properties. In order to research the real life decision making problems,we extend the proposed PFRS model over two universes and present a newmethod for solving multi-attribute decision making problems. Finally,we illustrate the newly proposed approach,by presenting an occupation match evaluation problem,which shows the effectiveness in the domain of multi-attribute decision making. The presented Pythagorean fuzzy rough set model takes full advantage of the superiorities of fuzzy set and rough set theory in uncertain decision making,which provides a valuable decision making model for decision makers.