基于软集合理论的不确定性多属性决策方法研究

【作者】 缪彬；

【导师】 段万春；

【作者基本信息】 昆明理工大学 ， 管理科学与工程， 2014， 博士

【摘要】 随着社会的不断进步、科学技术的不断发展,人类对于客观世界的认识和理解不断深入,人类社会的活动也越来越多样化、丰富化和复杂化。决策作为人类的一项基础性活动,普遍存在于社会活动和日常生活的方方面面,决策问题的规模变得越来越大,需要考虑的因素也越来越多,决策目标也越来越复杂。依据单一准则进行的决策方法在很多情况下已经很难满足社会发展的需要,多准则决策也成为众多专家学者研究和关注的热点领域。作为多准则决策的重要分支多属性决策MADM具有重要的应用价值和广泛的应用领域,然而MADM本身却面临着很多需要进一步研究和解决的问题,本文针对决策参与者缺乏先验知识、无法准确获取数据、属性取值难以量化、知识背景不同等问题带来的决策信息不确定性,展开对不确定性MADM问题的进一步研究。本文通过深入分析不确定性MADM问题的特征,在大量检索国内外相关成果、前沿理论和最新技术的基础之上,充分发挥学科交叉的优势,将软集合理论、多属性决策理论、群决策理论等相互融合,运用管理学、行为科学、统计学、集合论、规划论、信息科学等相关知识,在系统观点指导下,重点研究了软集合的信息表述与处理、软集合属性约简、基于软集合的决策模型、基于软集合的群决策模型,提出了一套基于软集合理论的多属性决策和群决策方法。在研究的过程中,针对研究出来的各种方法、模型,采用算例计算、数学推导的方法,对计算结果进行分析,验证了这套方法的可行性、有效性、合理性和可应用性。论文的主要研究工作可以总结如下：(一)系统研究了软集合不确定性信息的表述与处理。介绍了Molodtsov提出的经典软集合定义、表示方式、基本运算,在此基础上整理了软集合的扩展研究成果,包括模糊软集合、直觉模糊软集合、区间值模糊软集合、Vague软集合等。重点阐述了软集合的“参数化”特点,从“程度化”、“粒度化”、“参数化”三者结合的角度来描述软集合作为不确定性信息表述、处理工具的合理性和有效性。(二)研究了基于软集合相关理论的属性约简问题。属性约简在多属性决策中占有重要的地位,多属性决策原则上要求属性集最小,对于复杂决策参数约简也可以简化计算。本文在梳理基于软集合的参数约简前期研究成果的基础上,提出基于经典软集合的一种启发式算法,提高了参数约简的计算效率,同时结合粗糙集合的“切割集”思想,提出基于相似关系的软集合参数约简方法。(三)研究了基于软集合理论的统一决策方法体系。随着软集合理论的不断发展和深入,基于“选择值”的决策方法也在不断演进和深入,形成了基于经典软集合、模糊软集合、Vague软集合等不同的决策理论和决策方法,同时有很多应用成果不断涌现出来。本文通过对这些决策方法的实质进行分析和把握,建立了统一的基于软集合的决策规则和决策方法,为基于软集合的决策理论应用探索了更加一致的方法,拓宽软集合应用于决策问题的研究渠道和研究思路。(四)研究了基于软集合理论群决策方法。群决策在社会、经济、管理及工程等诸多领域有着十分广泛的需求,本文利用软集合的信息载体功能、信息处理能力,将软集合作为群决策的偏爱集结的工具,提出基于满意度的软集合群决策方法、知识背景不同的决策参与者的群决策方法,探索出了软集合理论应用于群决策问题研究的基本思路和方法,拓宽了软集合理论的应用领域。更多还原

【Abstract】 With the continuous progress of the society and development of science and technology, human’s understands of the objective world being more and more deep, and the activities of human society are becoming more and more diversified, colorful and complicated. As a basic human activity, decisions generally exist in every aspect of society and daily life; the size of the decision problem is becoming bigger, so more factors need to be taken into consideration and decision goal is becoming more and more complex. Decision-making methods based on a single criterion are hard to meet the needs of social development in many cases; Multi-Criteria Decision-Making has become a focus research field of many experts and scholars. As an important branch of Multi-Criteria Decision-Making, Multiple-Attribute Decision-Making (MADM) has important application value and broad application fields. However MADM itself is faced with a lot of problems which need to be further studied and settled. This paper focus on the uncertainty led by such matters as participants’ lacking of prior knowledge, unable to acquiring data accurately, difficult to quantify attribute values and different knowledge-background and so on, then tries to make a further study of the uncertain MADM problem.This paper makes an in-depth analysis about the characteristic of the uncertain MADM problem. On the basis of retrieving domestic and foreign relevant results, the frontier theory, and the latest technology, this paper gives full play to the advantage of subject crossing, and then integrates the soft set theory, multi-attribute decision making theory, group decision theory with each other. Under the guidance of system concept, together with the management, behavior science, statistics, set theory, information science and other related knowledge, the research mainly focuses on the expression and information processing by the Soft Set theory, Soft Set attribute reduction, the decision model based on Soft Set and the group decision-making model based on Soft Set, and finally puts forward a set of MADM model and group-decision method based on Soft Set. In the process of the research, in order to verify the feasibility, validity, rationality, and applicability of such methods and models, this paper adopts the method of example computation, mathematical derivation to analyze the results. The main research work can be summarized as follows:Firstly, the paper systematically studies the expression and processing of uncertainty information by Soft Set. After introducing the classic soft set definition, representation and basic operation which putted by Molodtsov, the expansion research is summarized, including Fuzzy Soft Set, Intuitionist Fuzzy Soft Set, Interval-Value Fuzzy Soft Set, Vague Soft Set etc. The paper expounds Parameterization characteristics of the Soft Set, and described the rationality and validity when soft sets used as an uncertainty information expression, and the processing tools, by combining the Gradualness, Gramilarity and Parameterization characteristics.Secondly, the paper studies the attribute reduction problem of Soft Set. Attribute reduction is very important in MADM. In principle, MADM requires minimum attribute set, and this also can simplify the calculation for complex decision parameter reduction. By combing parameter reduction of Soft Set research results, the paper puts forward a new heuristic algorithm based on the classical Soft Set, which improves the efficiency of parameter reduction calculation. Furthermore, by combining with rough set, the paper proposes the parameter reduction of Soft Set method based on similarity relations.Thirdly, this paper proposes a unified decision method based on Soft Set theory. With the continuous development of the soft set theory, the decision-making method based on Choice Value is also in constant evolution, based on Classical Soft Set, Fuzzy Soft Set and Vague Soft Set, different decision-making theory and methods appear. At the same time there are a lot of application achievements constantly emerges. By analyzing the essence of these decision-making methods, this paper establishes a unified decision rules and decision making method of Soft Sets, explores a more consistent approach for decision-making method of Soft Sets, widens the research channel and ideals of the soft set applied to the decision-making problem.Lastly, this paper studies a Group Decision-Making method based on soft set theory. In many fields such as society, economy, management and the project, Group Decision-Making has a very wide application range. By taking advantage of information carrier and processing functions of Soft Set, this article uses Soft Set as a group decision tool for preference aggregation, proposes a Soft Set Group Decision method based on Satisfaction Theory, and different knowledge-background decision participants’ Group Decision methods. The results explore the basic thinking and methods of Soft Set Group Decision; widen the application field of Soft Set.更多还原