本文選題：集對分析 + 集對推理��； 參考：《華北理工大學(xué)》2015年碩士論文

【摘要】：科學(xué)決策一直是數(shù)學(xué)和管理學(xué)科的重要課題。將格理論的相關(guān)研究應(yīng)用到?jīng)Q策模型中,是對理性行為決策理論的一種發(fā)展與完善。集對分析是一種新的處理不確定信息的工具,它的同異反聯(lián)系度能夠更加客觀合理的描述不確定性問題。因此,對集對聯(lián)系數(shù)進行格結(jié)構(gòu)的刻畫,并應(yīng)用到?jīng)Q策系統(tǒng)中,對格序決策的發(fā)展與完善有著重要的理論意義。首先在二值邏輯和模糊邏輯的基礎(chǔ)上提出了集對邏輯的概念,并給出了集對邏輯的演算規(guī)則,討論了單論域和雙論域上的模糊集對推理的基本概念和基本形式;其次提出了集對效用函數(shù)的概念,探討了它的三維優(yōu)先關(guān)系,給出了格結(jié)構(gòu)的構(gòu)建原理與方法,建立了基于集對效用函數(shù)的格序決策模型;最后針對模糊條件下的推理關(guān)系,給出了集對聯(lián)系數(shù)形式的真域表達式以及推理運算規(guī)則,并結(jié)合決策原理,建立了真值聯(lián)系函數(shù)集,給出了格結(jié)構(gòu)的構(gòu)建原理與方法,建立基于集對推理的格序決策模型。集對推理是一種更加符合客觀實際的推理形式,這種集對推理模式能夠更加客觀的反應(yīng)人們對不確定性問題的刻畫與描述;在決策系統(tǒng)中,集對聯(lián)系數(shù)的格序化研究,為解決多屬性決策問題提供了一個新方法,同時也是對格序決策理論的發(fā)展與完善。
[Abstract]:Scientific decision-making has always been an important subject in mathematics and management. The application of lattice theory to decision-making model is a development and perfection of rational behavior decision theory. Set pair analysis (SPA) is a new tool for dealing with uncertain information, and its similarity, difference and inverse relation can describe uncertainty more objectively and reasonably. Therefore, it is of great theoretical significance for the development and perfection of lattice order decision making to characterize the lattice structure of the set couplet coefficient and apply it to the decision-making system. Firstly, on the basis of binary logic and fuzzy logic, the concept of set pair logic is put forward, the calculus rules of set pair logic are given, and the basic concepts and forms of fuzzy set pair reasoning on single and double fields are discussed. Secondly, the concept of set pair utility function is put forward, its three dimensional priority relation is discussed, the construction principle and method of lattice structure are given, and the lattice order decision model based on set pair utility function is established. In this paper, the true domain expression of the set couplet coefficient and the rules of reasoning operation are given. Combining with the decision principle, the set of truth relation functions is established, the construction principle and method of lattice structure are given, and the lattice order decision model based on set pair reasoning is established. Set pair reasoning is a kind of reasoning form which is more in line with objective reality. This kind of set pair reasoning model can more objectively reflect the characterization and description of uncertain problems, and in the decision system, the lattice order of set couplet coefficients is studied. It provides a new method for solving the problem of multi-attribute decision making, and it is also the development and perfection of the theory of lattice order decision making.
【學(xué)位授予單位】：華北理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O153.1;O225

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