【摘要】：本文定義了模糊關(guān)系的非循環(huán)性與負(fù)非循環(huán)性,并對其性質(zhì)進(jìn)行了詳細(xì)地研究。對模糊關(guān)系的T-非循環(huán)性研究包括模糊關(guān)系的T-非循環(huán)性及其嚴(yán)格部分的T-非循環(huán)性.對模糊關(guān)系非循環(huán)性的研究包括:首先,在T左連續(xù)下,討論了T-非循環(huán)性與T-傳遞閉包及其非自反性的關(guān)系;其次,在取小t-模下,討論了minT-非循環(huán)性與其截集的非循環(huán)性之間的關(guān)系.對模糊關(guān)系嚴(yán)格部分的T-非循環(huán)性的研究包括:首先,討論了T-非循環(huán)性與其嚴(yán)格部分T-非循環(huán)性以及T-非對稱性之間的關(guān)系;其次,在所涉及的t-模是左連續(xù)和n_T是強(qiáng)非的條件下,給出了嚴(yán)格部分T-非循環(huán)性的一個(gè)等價(jià)陳述;然后,在左連續(xù)t-模下,研究了嚴(yán)格部分T-非循環(huán)性與T-傳遞的關(guān)系;最后,在左連續(xù)t-模和De Morgan三元組的條件下,研究了嚴(yán)格部分的T-非循環(huán)性與SS-負(fù)傳遞的關(guān)系。然后,我們對模糊關(guān)系的S-負(fù)非循環(huán)性進(jìn)行了討論,包括模糊關(guān)系的S-負(fù)非循環(huán)性及與T-非循環(huán)性之間的關(guān)系.在所涉及的t-余模是右連續(xù)的情況下,討論了S-負(fù)非循環(huán)性與S-負(fù)傳遞內(nèi)部及其自反性的關(guān)系.對模糊關(guān)系負(fù)非循環(huán)性與非循環(huán)關(guān)系的研究包括:首先,在取小t-模、取大t-余模下,研究了S-負(fù)非循環(huán)性與嚴(yán)格部分的T-非循環(huán)性的關(guān)系;然后,在De Morgan三元組下,討論了S-負(fù)非循環(huán)性與嚴(yán)格部分的T-非循環(huán)性及其余關(guān)系的T-非循環(huán)性之間的關(guān)系。
[Abstract]:In this paper, the non-circularity and negative non-circularity of fuzzy relations are defined, and their properties are studied in detail. The study of Tacyclic property of fuzzy relation includes the Tacyclic property of fuzzy relation and the Tacyclic property of strict part of fuzzy relation. The research on the non-circularity of fuzzy relations includes: firstly, the relationship between T-acyclic property and T-transitive closure and its non-reflexivity is discussed under T-left continuous condition; Secondly, under the small t-module, we discuss the relationship between the non-circularity of minT- and the non-circularity of its truncated set. The research on Tacyclic property of strict part of fuzzy relation includes: firstly, the relationship between Tacyclic property and its strict part Tacyclic property as well as Tasymmetry is discussed. Secondly, an equivalent statement of the strictly partial T-acyclic property is given under the condition that the t-modules involved are left-continuous and the n-T is strongly non-cyclic. Then, under the left continuous t-module, the relation between strictly partial T-acyclic property and T-transfer is studied. Finally, under the condition of left continuous t-module and De Morgan triple, the relation between the T-acyclic property of strict part and the negative transfer of SS- is studied. Then, we discuss the S-negative non-circularity of fuzzy relations, including the S-negative non-circularity of fuzzy relations and the relationship between S-negative non-circularity and T-non-circularity of fuzzy relations. In this paper, the relation between S-negative acyclic property and S-negative transitive interior and its reflexivity is discussed when the t-comodule involved is right-continuous. The research on negative non-circularity and acyclic relation of fuzzy relation includes: firstly, the relation between S-negative acyclic property and strict part of T-acyclic property is studied under the condition of taking small t-module and large t-comodule, and the relation between S-negative acyclic property and strict part of T-acyclic property is studied. Then, under the De Morgan triple, the relations between the S-negative acyclic property, the strict part Tacyclic property and the other relations of the Tacyclic property are discussed.
【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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本文編號：2442158