基于双元素可选集的模糊收缩扩张条件的研究

发布时间：2018-05-14 18:48

本文选题：模糊选择函数 + 双元素可选集　；参考：《太原理工大学》2017年硕士论文

【摘要】：本文在Georgescu模糊选择函数意义下,参照Banerjee模糊选择函数的相关结论,系统地研究了双元素可选集的模糊收缩扩张条件Fα2、Fβ2与模糊一致性公理等其他合理性条件之间的关系.首先,我们回顾了 Banerjee模糊选择函数的相关定义,给出了模糊一致性公理等合理性条件的定义以及相关结论.同时,我们研究了双元素可选集的模糊收缩扩张条件Fα2、Fβ2与FC1、FC3之间的关系,得到一些新的结论.其次,我们在Georgescu模糊选择函数中重新定义了合理性条件Fα2、Fβ、Fβ(+)且新定义了条件Fβ'、Fβ2、Fδ2,并对这些条件之间的联系进行了系统地研究,得出了一些新结论.这些研究围绕双元素可选集的模糊收缩扩张条件,其主要结论为:当*为取小t-模时,若H1,WH2成立,则条件Fα2和Fβ2、条件Fα2和Fβ'、条件Fα和Fβ、条件Fα和Fβ(+)及条件WFCA是等价的.接着,从占优度概念出发,我们重新定义了 Georgescu模糊一致性公理FC*1、FC*2、FC*3 且新定义了FC*4、FC*5、FC*6及WAFRP 及同时,我们讨论了基于双元素可选集的Georgescu模糊选择函数收缩扩张条件Fα2、Fβ2与FC*1、WAFRP*等合理性条件之间的关系.其主要结果为:当*为取小t-模时,若H1,WH2成立,则FC*1、FC*2、FC*3、FC*4、FC*5和条件Fα2、FC*6和条件Fα2、WAFRP*及条件Fα2和Fβ2是等价的.
[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 伪 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 伪 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 伪 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 伪 _ 2 and F 尾 _ 2, conditions F _ 伪 and F 尾, conditions F _ 伪 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 伪 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 伪 _ (2) WAFRP* and condition F 伪 _ (2) and F 尾 _ 2 are equivalent.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159

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