本文選題：模糊關(guān)系　切入點(diǎn)：t-模　出處：《太原理工大學(xué)》2017年碩士論文

【摘要】：本文系統(tǒng)地討論了模糊關(guān)系的T-傳遞一致性及其指標(biāo),其主要研究?jī)?nèi)容如下:首先,我們簡(jiǎn)單回顧了普通二元關(guān)系、模糊邏輯聯(lián)結(jié)運(yùn)算以及模糊二元關(guān)系的定義及性質(zhì).其次,我們系統(tǒng)地總結(jié)了普通二元關(guān)系傳遞一致性的研究成果,并對(duì)傳遞一致性的性質(zhì)進(jìn)行了一些研究,從而完善了普通二元關(guān)系傳遞一致性的研究.接著,我們利用t-模,將普通二元關(guān)系的傳遞一致性推廣到了模糊情況下.同時(shí),討論了模糊關(guān)系的T-傳遞一致性、T-傳遞性、T-擬傳遞性以及T-非循環(huán)性之間的關(guān)系,并對(duì)模糊關(guān)系的T-傳遞一致性的性質(zhì)做了詳細(xì)研究.最后,我們定義了模糊關(guān)系的T-傳遞一致性指標(biāo).同時(shí),討論了模糊關(guān)系的T-傳遞一致性指標(biāo)、T-傳遞性指標(biāo)、T-擬傳遞性指標(biāo)以及T-非循環(huán)性指標(biāo)之間的關(guān)系,并且研究了模糊關(guān)系的T-傳遞一致性指標(biāo)的一些性質(zhì).我們注意到,在我們的假設(shè)下,普通二元關(guān)系傳遞一致性的大部分結(jié)論都得到了相應(yīng)的模糊以及指標(biāo)推廣,但仍然有一些結(jié)論不再成立,為此,我們給出例子進(jìn)行了說(shuō)明.總之,通過(guò)我們的研究,對(duì)模糊關(guān)系的T-傳遞一致性以及T-傳遞一致性指標(biāo)有了更為深入的了解.這些研究對(duì)模糊決策理論的發(fā)展有一定的意義.
[Abstract]:In this paper, the T-transitive consistency and its index of fuzzy relations are discussed systematically. The main research contents are as follows: firstly, we briefly review the definitions and properties of ordinary binary relations, fuzzy logic join operations and fuzzy binary relations. In this paper, we systematically summarize the research results of transitive consistency of ordinary binary relations, and do some research on the properties of transitive consistency, so as to perfect the research of transitive consistency of ordinary binary relations. In this paper, the transitive consistency of ordinary binary relations is extended to fuzzy case. At the same time, the relations between T- transitive consistency and T- transitive quasi-transitivity and T- non-circularity of fuzzy relations are discussed. Finally, we define the T- transitive consistency index of fuzzy relations. In this paper, we discuss the relations between T- transitive consistency index and T- transitive index of fuzzy relation, and study some properties of T- transitive consistency index of fuzzy relation. Under our assumption, most of the conclusions of transitive consistency of ordinary binary relations have been generalized by corresponding fuzzy and index, but there are still some conclusions that no longer hold true. For this reason, we give an example to illustrate. Through our research, we have a deeper understanding of the T- transitive consistency and the T- transitive consistency of fuzzy relations, which are of significance to the development of fuzzy decision theory.
【學(xué)位授予單位】：太原理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O159

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 郭帥帥;王緒柱;;模糊關(guān)系的非循環(huán)度量[J];模糊系統(tǒng)與數(shù)學(xué);2017年01期

2 薛曄,王緒柱;模糊關(guān)系運(yùn)算的傳遞性[J];太原理工大學(xué)學(xué)報(bào);2003年01期

相關(guān)碩士學(xué)位論文 前1條

1 蘇俊萍;擬傳遞性指標(biāo)及其在模糊選擇函數(shù)中應(yīng)用研究[D];太原理工大學(xué);2012年

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本文編號(hào)：1663888