【作者】 李娜；

【导师】 高雷阜；

【作者基本信息】 辽宁工程技术大学 ， 系统工程， 2019， 博士

【摘要】 随着信息技术和大数据的迅速发展,人们所处的实际决策环境越来越复杂。鉴于自身的知识能力和经验方面的不足,管理科学与工程中的复杂决策问题常常以Pythagorean模糊形式来表示决策信息。本文对决策信息由Pythagorean模糊形式表示的多属性决策问题展开了深入的研究,探索了现实管理问题中Pythagorean模糊多属性决策方法和算子理论。主要工作如下:(1)考虑到实际决策问题中决策者心理因素对决策结果具有重要影响,针对决策属性信息为Pythagorean模糊数、属性权重未知的复杂多属性决策问题进行了研究。提出了考虑后悔与失望规避的风险型Pythagorean模糊决策方法,为兼顾决策者风险规避行为的一类决策问题提供了新的求解方法。此外,给出区间Pythagorean模糊相对熵的概念,基于这种相对熵,提出了区间Pythagorean模糊多属性AQM决策方法。通过方案间合成的0-1优先关系矩阵,依据方案的综合度获得方案的排序结果。(2)针对属性信息由Pythagorean模糊数表达且属性相互关联的多属性决策问题,提出了诱导型广义Pythagorean模糊Choquet积分算子。同时,研究属性信息由区间Pythagorean模糊数表达的多属性群决策问题,定义了连续区间Pythagorean模糊集结算子,集结过程中同时考虑了区间端点信息和区间内部数据信息,提升了 Pythagorean模糊集结算子的精度。(3)研究了属性信息为Pythagorean模糊二元语义的多属性决策问题。定义了新的Pythagorean模糊二元语义运算,其特点为满足封闭性。基于该运算提出了新的Pythagorean模糊二元语义代数算子和几何算子,进一步,将Pythagorean模糊二元语义集结算子扩展到区间Pythagorean模糊决策环境,研究了这些算子的优良性质,并应用这些算子解决复杂多属性决策问题。深入研究了 Pythagorean模糊信息环境下的多属性决策方法和集结算子,为解决复杂模糊多属性决策问题提供了新的方法。该论文有图6幅,表51个,参考文献184篇。更多还原

【Abstract】 With the rapid development of information technology and big data,the practical decision making environment is becoming more and more complex.In view of the shortage of knowledge and experience for decision makers,Pythagorean fuzzy information is often used to express decision information in the face of complex decision problems in management science and engineering.In this paper,the multiple attribute decision making problems are deeply studied,in which the decision information is represented by Pythagorean fuzzy numbers.This paper explores the method and the aggregation operator theory of the Pythagorean fuzzy multiple attribute decision making in practical management problems.The main aim is given as follows:(1)Considering that the decision maker’s psychological factors play an important role in the decision making results,the complex multiple attribute decision making problems with Pythagorean fuzzy number and unknown attribute weight are studied.A risk-based Pythagorean fuzzy decision making approach considering regret and disappointment aversion is proposed,it provides a new method for solving a class of decision making problems which take into account the decision makers’ risk aversion feature.In addition,the concept of interval valued Pythagorean fuzzy relative entropy is given.Based on the new relative entropy,an interval valued Pythagorean fuzzy multiple attribute AQM decision making method is developed.By using the comprehensive 0-1 priority relation matrix among alternatives,the ranking results of alternatives are obtained according to the comprehensive degree of alternatives.(2)For the multiple attribute decision making problems in which the attribute information is expressed by Pythagorean fuzzy numbers and attributes are interrelated,an inductive generalized Pythagorean fuzzy Choquet integral aggregation operator is proposed.At the same time,the problem of multiple attribute group decision making with attribute information expressed by interval valued Pythagorean fuzzy numbers is studied,and a continuous interval valued Pythagorean fuzzy aggregation operator is defined.In the process of aggregation,both interval endpoint information and interval interior data information are considered,which improves the precision of Pythagorean fuzzy aggregation operator.(3)The multiple attribute decision making problem with Pythagorean fuzzy 2-tuple linguistic information is studied.A new Pythagorean fuzzy 2-tuple linguistic operation is defined,the characteristic of proposed operation is closed.Based on this operation,some new Pythagorean fuzzy 2-tuple algebraic aggregation operators and geometric aggregation operators are presented.Further,the Pythagorean fuzzy 2-tuple linguistic aggregation operators are extended to interval valued Pythagorean fuzzy decision environment.The good properties of these proposed aggregation operators are studied and applied to deal with complex multiple attribute decision making problems.The multiple attribute decision making approach and aggregation operators under Pythagorean fuzzy information environment are studied deeply,which provides a new method for settling complex fuzzy multiple attribute decision making problems.The paper consists of 6 drawings,51 tables and 184 references.更多还原