本文選題：模糊選擇函數(shù) + 雙元素可選集　； 參考：《太原理工大學(xué)》2017年碩士論文

【摘要】：本文在Georgescu模糊選擇函數(shù)意義下,參照Banerjee模糊選擇函數(shù)的相關(guān)結(jié)論,系統(tǒng)地研究了雙元素可選集的模糊收縮擴張條件Fα2、Fβ2與模糊一致性公理等其他合理性條件之間的關(guān)系.首先,我們回顧了 Banerjee模糊選擇函數(shù)的相關(guān)定義,給出了模糊一致性公理等合理性條件的定義以及相關(guān)結(jié)論.同時,我們研究了雙元素可選集的模糊收縮擴張條件Fα2、Fβ2與FC1、FC3之間的關(guān)系,得到一些新的結(jié)論.其次,我們在Georgescu模糊選擇函數(shù)中重新定義了合理性條件Fα2、Fβ、Fβ(+)且新定義了條件Fβ'、Fβ2、Fδ2,并對這些條件之間的聯(lián)系進行了系統(tǒng)地研究,得出了一些新結(jié)論.這些研究圍繞雙元素可選集的模糊收縮擴張條件,其主要結(jié)論為:當(dāng)*為取小t-模時,若H1,WH2成立,則條件Fα2和Fβ2、條件Fα2和Fβ'、條件Fα和Fβ、條件Fα和Fβ(+)及條件WFCA是等價的.接著,從占優(yōu)度概念出發(fā),我們重新定義了 Georgescu模糊一致性公理FC*1、FC*2、FC*3 且新定義了FC*4、FC*5、FC*6及WAFRP 及同時,我們討論了基于雙元素可選集的Georgescu模糊選擇函數(shù)收縮擴張條件Fα2、Fβ2與FC*1、WAFRP*等合理性條件之間的關(guān)系.其主要結(jié)果為:當(dāng)*為取小t-模時,若H1,WH2成立,則FC*1、FC*2、FC*3、FC*4、FC*5和條件Fα2、FC*6和條件Fα2、WAFRP*及條件Fα2和Fβ2是等價的.
[Abstract]:In this paper, in the sense of Georgescu fuzzy selection function and referring to the relevant conclusions of Banerjee fuzzy selection function, we systematically study the relationship between the fuzzy contraction extension condition F 偽 2N F 尾 2 and other rational conditions such as fuzzy consistency axiom. Firstly, we review the definition of Banerjee fuzzy selection function, and give the definition of fuzzy consistency axiom and the relevant conclusions. At the same time, we study the relation between the fuzzy contraction extension condition F 偽 2N F 尾 2 and FC 1 F C 3 of the selectable set of two elements, and obtain some new conclusions. Secondly, in the Georgescu fuzzy selection function, we redefine the rational condition F 偽 2N F 尾 F 尾 () and define the condition F 尾 2 F 尾 2 F 未 2. The relationship between these conditions is studied systematically and some new conclusions are obtained. These studies focus on the fuzzy contractive extension conditions of the selectable set of two elements. The main conclusions are as follows: when * is a small tnorm, if H _ 1H _ H _ 2 holds, then conditions F 偽 _ 2 and F 尾 _ 2, conditions F _ 偽 and F 尾, conditions F _ 偽 and F 尾 () and conditional WFCA are equivalent. Then, starting from the concept of dominance degree, we redefine Georgescu fuzzy consistency axiom FC1 / FC2 / FC3, and define FC4 / FC5 / FC5 / FC6 and WAFRP and at the same time, In this paper, we discuss the relations between the contraction and extension conditions of Georgescu fuzzy selection function based on the two-element selectable set F 偽 2N F 尾 2 and the rational conditions such as FCU 1WAF RP *. The main results are as follows: when * is a small t- module, if H _ 1H _ 2 holds, then FCU _ (1) F _ (C) ~ (2) ~ (2) F _ (C) ~ (3) C ~ (3) C ~ (3) + F ~ (2) + F ~ (2) + F ~ (2) C ~ (6) and condition F 偽 _ (2) WAFRP* and condition F 偽 _ (2) and F 尾 _ 2 are equivalent.
【學(xué)位授予單位】：太原理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O159

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