本文選題：剩余格 + t-濾子�。� 參考：《江南大學(xué)》2016年碩士論文

【摘要】：模糊邏輯研究的一個(gè)重要方向是研究其邏輯代數(shù)系統(tǒng).邏輯代數(shù)系統(tǒng)中一般以偏序集和一些運(yùn)算為模型來建立邏輯與代數(shù)的橋梁,用代數(shù)方法解決邏輯問題.剩余格是一類比較重要的代數(shù)系統(tǒng).本文探討了剩余格上的t-濾子、I-濾子、EIMTL-濾子等濾子的性質(zhì),給出剩余格上n-維模糊濾子、n-維模糊EIMTL-濾子、n-維模糊t-濾子、n-維模糊同余關(guān)系的定義,還研究了它們的性質(zhì).取得的主要結(jié)果概括如下：在第二章中,討論了t-濾子和I-濾子的關(guān)系.將EIMTL-濾子和associative濾子的定義推廣到剩余格并研究了它們的性質(zhì),討論了在什么條件下,EIMTL-濾子一定是t-濾子.證明了每個(gè)剩余格都有真EIMTL-濾子.另外,還討論了剩余格滿足什么條件有真associative濾子.最后將EIMTL-濾子定義推廣到非可換剩余格,并研究了它的性質(zhì).在第三章中,將剩余格上一維模糊模糊濾子概念進(jìn)行推廣給出了n-維模糊濾子的概念,并討論了它的等價(jià)刻畫,討論了n-維模糊濾子與其上截集的關(guān)系.給出了n-維模糊EIMTL-濾子的概念,并討論了它的等價(jià)刻畫,也討論了n-維模糊EIMTL-濾子與其上截集的關(guān)系.給出了n-維模糊t-濾子的概念,并研究了它的性質(zhì),運(yùn)用n-維模糊t-濾子,得到n-維模糊divisible濾子和n-維模糊strong濾子的定義及其刻畫.在第四章中,給出剩余格上n-維模糊同余關(guān)系定義,并研究它的一些性質(zhì).引入n-維模糊關(guān)系的上截集定義,并且討論它與n-維模糊同余關(guān)系的關(guān)系.給出剩余格上n-維模糊濾子和n-維模糊同余關(guān)系的一一對應(yīng).還討論了n-維模糊等價(jià)關(guān)系與其α-水平關(guān)系的關(guān)系.
[Abstract]:An important research direction of fuzzy logic is to study its logic algebraic system.In the logic algebra system, the partial ordered set and some operations are generally used as the models to build the bridge between logic and algebra, and the algebraic method is used to solve the logic problem.Residual lattices are a class of more important algebraic systems.In this paper, we discuss the properties of n-dimensional fuzzy filters on residual lattices, and give the definitions of n-dimensional fuzzy t- filters and n-dimensional fuzzy t- filters on residual lattices, and study their properties.The main results are summarized as follows: in chapter 2, the relationship between t- filter and I- filter is discussed.The definitions of EIMTL-filter and associative filter are generalized to residual lattices and their properties are studied. The conditions under which EIMTL-filters must be tfilters are discussed.It is proved that every residual lattice has true EIMTL- filter.In addition, we also discuss what conditions the residual lattices satisfy to have true associative filters.Finally, the definition of EIMTL- filter is extended to non-commutative residuals and its properties are studied.In chapter 3, we generalize the concept of one-dimensional fuzzy filter on residual lattices, give the concept of n-dimensional fuzzy filter, discuss its equivalent characterization, and discuss the relation between n-dimensional fuzzy filter and its upper cut set.In this paper, the concept of n-dimensional fuzzy EIMTL-filter is given, its equivalent characterization is discussed, and the relation between n-dimensional fuzzy EIMTL-filter and its upper cut set is also discussed.In this paper, the concept of n-dimensional fuzzy tfilters is given, and its properties are studied. By using n-dimensional fuzzy tfilters, the definitions and characterizations of n- dimensional fuzzy divisible filters and n- dimensional fuzzy strong filters are obtained.In chapter 4, we give the definition of n-dimensional fuzzy congruence relation on residual lattices and study its properties.This paper introduces the definition of upper cut set of n-dimensional fuzzy relation and discusses its relation with n-dimensional fuzzy congruence relation.The one-to-one correspondence between n-dimensional fuzzy filters and n-dimensional fuzzy congruences on residual lattices is given.The relationship between the n- dimensional fuzzy equivalence relation and its 偽-level relation is also discussed.
【學(xué)位授予單位】：江南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：O159

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