【摘要】：多屬性決策是決策領(lǐng)域的一個(gè)熱門話題。但現(xiàn)存的多屬性決策方法大多建立在假設(shè)人是絕對(duì)理性的期望效用理論上。在現(xiàn)實(shí)生活中,由于決策問題本身的復(fù)雜性和決策者認(rèn)知的有限性,決策者往往是有限理性的。TODIM是一個(gè)基于前景理論的基礎(chǔ)上的行為決策方法,可以較好地刻畫決策者的有限理性行為。然而經(jīng)典的TODIM方法只適用于精確數(shù)環(huán)境下的單個(gè)決策者的多屬性決策問題,對(duì)于模糊環(huán)境下的群決策問題卻無(wú)能為力。因此,本文為了使行為決策方法更適用于現(xiàn)實(shí),本文充分考慮決策信息的不確定性,將TODIM方法拓展到模糊的環(huán)境中。同時(shí),由于社會(huì)復(fù)雜性增加,單個(gè)決策者很難將所有的相關(guān)因素考慮進(jìn)去,所以將行為決策拓展到群決策具有很強(qiáng)的現(xiàn)實(shí)意義。基于這兩個(gè)思想,論文主要完成了以下工作:首先,將TODIM方法拓展到多粒度語(yǔ)言,二維模糊語(yǔ)言及三角直覺模糊環(huán)境中,從而更好地反映了環(huán)境的不確定性及決策者的偏好信息。同時(shí),在三角直覺模糊環(huán)境下,將TODIM方法擴(kuò)展到群決策領(lǐng)域,從而使得決策問題考慮得更加的全面。其次,針對(duì)語(yǔ)言信息的處理,本文提出了一個(gè)將多粒度語(yǔ)言轉(zhuǎn)化成區(qū)間直覺模糊數(shù)的方法,相比與將其轉(zhuǎn)換為模糊數(shù)和直覺模糊數(shù),能更好地處理語(yǔ)言信息的模糊性及不確定性。新定義了一個(gè)二維直覺模糊語(yǔ)言變量,使決策者不僅能對(duì)評(píng)估對(duì)象做出評(píng)價(jià),還能對(duì)自身所做評(píng)價(jià)的可靠性再評(píng)價(jià)。然后,從概率的角度為三角直覺模糊數(shù)提出了交叉影響的運(yùn)算法則,包括加法運(yùn)算、乘法運(yùn)算和冪運(yùn)算。在這些新的運(yùn)算基礎(chǔ)上,提出了兩個(gè)基于交叉影響的三角直覺模糊環(huán)境下的平均算子,分別為三角直覺模糊加權(quán)平均算子和三角直覺模糊算術(shù)平均算子。通過(guò)數(shù)學(xué)歸納法在理論上給出了嚴(yán)密的證明。最后,在考慮屬性權(quán)重未知的情況時(shí),本文提出了采用信息熵的方法來(lái)處理語(yǔ)言環(huán)境下的屬性權(quán)重,采用相似度的方法處理三角模糊環(huán)境下的屬性權(quán)重。對(duì)于群決策問題,本文基于一致性的思想來(lái)確定專家的權(quán)重,分別提出了基于灰色關(guān)聯(lián)度的共識(shí)模型與基于相似度的線性規(guī)劃模型,以協(xié)調(diào)各種不同的意見和看法,最終形成群體總的評(píng)價(jià)。
[Abstract]:Multi-attribute decision making is a hot topic in the field of decision making. However, most of the existing multi-attribute decision-making methods are based on the expected utility theory which assumes that human beings are absolutely rational. In real life, because of the complexity of decision-making problem itself and the limitation of decision-maker's cognition, decision-maker is often bounded rational. TODIM is a behavioral decision-making method based on prospect theory, which can depict the bounded rational behavior of decision-maker well. However, the classical TODIM method is only suitable for the multi-attribute decision making problem of a single decision maker in the exact number environment, but it is powerless for the group decision problem in fuzzy environment. Therefore, in order to make the behavioral decision-making method more suitable for reality, this paper fully considers the uncertainty of decision-making information, and extends the TODIM method to the fuzzy environment. At the same time, because of the increase of social complexity, it is difficult for a single decision maker to take all the relevant factors into account, so it is of great practical significance to extend behavioral decision to group decision making. Based on these two ideas, the main work of this paper is as follows: firstly, the TODIM method is extended to multi-granularity language, two-dimensional fuzzy language and triangular intuitionistic fuzzy environment, so as to better reflect the uncertainty of the environment and the preference information of decision makers. At the same time, in the triangular intuitionistic fuzzy environment, the TODIM method is extended to the field of group decision making, which makes the decision problem more comprehensive. Secondly, aiming at the processing of language information, this paper proposes a method to transform multi-granularity language into interval intuitionistic fuzzy number, which can deal with the fuzziness and uncertainty of language information better than converting it into fuzzy number and intuitionistic fuzzy number. A new two-dimensional intuitionistic fuzzy language variable is defined, which enables decision makers not only to evaluate the evaluation object, but also to re-evaluate the reliability of their own evaluation. Then, from the point of view of probability, the algorithm of cross influence is proposed for triangular intuitionistic fuzzy numbers, including addition operation, multiplication operation and power operation. On the basis of these new operations, two average operators in triangular intuitionistic fuzzy environment based on cross influence are proposed, which are triangular intuitionistic fuzzy weighted average operator and triangular intuitionistic fuzzy arithmetic average operator, respectively. Through the mathematical induction method, the strict proof is given in theory. Finally, when considering the unknown attribute weight, this paper proposes an information entropy method to deal with the attribute weight in the language environment, and the similarity method to deal with the attribute weight in the triangular fuzzy environment. For the group decision problem, this paper determines the weight of experts based on the idea of consistency, and puts forward the consensus model based on grey correlation degree and the linear programming model based on similarity respectively, in order to coordinate all kinds of different opinions and opinions, and finally form the overall evaluation of the group.
【學(xué)位授予單位】：深圳大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F224

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