partial ordered set 中文意思是什麼

The mp - filters and fuzzy filters of a implication algebra on a partial ordered set are studied with the condition given in chapter 2 which implicative operator should satisfy

利用上述得到的關于蘊涵代數中蘊涵運算元的條件，研究偏序集上具有條件（ c ）的蘊涵代數的mp濾子及fuzzy濾子。

The primary studies in this paper are the following : ( 1 ) we define a generalized alexandroff topology on an l - fuzzy quasi ordered set which is a generalization of the alexandroff topology on an ordinary quasi ordered set, prove that the generalized alexandroff topology on an l - quasi ordered set ( x, e ) can be obtained by the join of a family of the alexandroff topologies on it, a topology on any topological space can be represented as a generalized alexandroff topology on some l - quasi ordered set, and the generalized alexandroff topologies on l - fuzzy quasi ordered sets are generalizations of the generalized alexandroff topologies on generalized ultrametric spaces which are defined by j. j. m. m. rutten etc. ( 2 ) by introducing the concepts of the join of l - fuzzy set on an l - fuzzy partial ordered set with respect to the l - fuzzy partial order and l - fuzzy directed set on an l - fuzzy quasi ordered set ( with respect to the l - fuzzy quasi order ), we define l - fuzzy directed - complete l - fuzzy partial ordered set ( or briefly, l - fuzzy dcpo or l - fuzzy domain ) and l - fuzzy scott continuous mapping, prove that they are respectively generalizations of ordinary dcpo and scott continuous mapping, when l is a completely distributive lattice with order - reversing involution, the category l - fdom of l - fuzzy domains and l - fuzzy scott continuous mappings is isomorphic to a special kind of the category of v - domains and scott continuous mappings, that is, the category l - dcqum of directed - complete l - quasi ultrametric spaces and scott continuous mappings, and when l is a completely distributive lattice in which 1 is a molecule, l - fuzzy domains and l - fuzzy scott continuous mappings are consistent to directed lim inf complete categories and lim inf co ntinuous mappings in [ 59 ]

本文主要工作是： （ 1 ）在l - fuzzy擬序集上定義廣義alexandroff拓撲，證明了它是通常擬序集上alexandroff拓撲的推廣，一個l - fuzzy擬序集（ x ， e ）上的廣義alexandroff拓撲可以由其上一族alexandroff拓撲取並得到，任意一個拓撲空間的拓撲都可以表示為某個l - fuzzy擬序集上的廣義alexandroff拓撲，以及l - fuzzy擬序集上的廣義alexandroff拓撲是j . j . m . m . rutten等定義的廣義超度量空間上廣義alexandroff拓撲的推廣。 （ 2 ）通過引入l - fuzzy偏序集上的l - fuzzy集關于l - fuzzy偏序的並以及l - fuzzy擬序集上（關于l - fuzzy擬序）的l - fuzzy定向集等概念，定義了l - fuzzy定向完備的l - fuzzy偏序集（簡稱l - fuzzydcpo ，又叫l - fuzzydomain ）和l - fuzzyscott連續映射，證明了它們分別是通常的dcpo和scott連續映射的推廣，當l是帶有逆序對合對應的完全分配格時，以l - fuzzydomain為對象， l - fuzzyscott連續映射為態射的范疇l - fdom同構於一類特殊的v - domain范疇，即以定向完備的l -值擬超度量空間為對象， scott連續映射為態射的范疇l - dcqum ，以及當l是1為分子的完全分配格時， l - fuzzydomain和l - fuzzyscott連續映射一致於k . wagner在[ 59 ]中定義的定向liminf完備的-范疇和liminf連續映射。

The representation theories of mp - filter which is created by an non - empty set of a implication algebra on a partial ordered set with condition ( c ) are obtained at first. and it ' s proved that the set which contains all mp - filters of a implication algebra x, denoted by mf ( x ) = { f x f is a filter of x }, is a distributive lattice and a complete lattice also in the view of the concept of mp - filter. then the fuzzy filter of a implication algebra is discussed, and the relations between mp - filter and fuzzy filter are obtained

藉助于mp -濾子的概念，得到了偏序集上具有條件（ c ）的蘊涵代數中由非空集合所生成mp濾子的表示定理，證明了由其上所有mp -濾子組成的集合mf （ x ）是一個完備的分配格；得到了蘊涵代數中fuzzy濾子與mp濾子的關系，給出了fuzzy濾子成為fuzzy素濾子的若干刻畫；並利用mp -濾子和fuzzy濾子，刻畫了一類偏序集上蘊涵代數的結構。

The relations between heyting algebra and implication algebra with some conditions on a partial ordered set are discussed. then some conditions when a implication algebra is a boolean algebra are given. 3

系統地研究了偏序集上蘊涵代數與heyting代數之間的關系，得到了蘊涵代數中蘊涵運算元的一個較好的條件，並給出了偏序集上蘊涵代數成為布爾代數的一些條件。

Fuzzy logic is studied with algebraic tools in this paper. a kind of algebraic abstract of fuzzy logic, implication algebra on a partial ordered set, is given. the relations between implication algebra and other algebraic structures, such as mv - algebra and heyting algebra etc., and the filter and the structure of implication algebra on a partial ordered set are studied

本文的目的是使用代數工具對模糊邏輯進行研究，給出模糊邏輯的一類代數抽象，即偏序集上的蘊涵代數，研究偏序集上蘊涵代數與其它代數結構，如mv -代數， heyting代數之間的關系，以及偏序集上蘊涵代數的濾子與其結構等。

A kind of operator of trigonometric interpolation polynomials with bivariate product was constructed based on an equidistant node set, so that the operator could be converged uniformly to bivariate continuous functions with periodicity of 27 on whole plane, and the convergence order of the approximation would be optimal for a body of functions with arbitrary - ordered continuous partial deritives

摘要構造了一類基於等距結點組上的二元三角插值多項式運算元，使得該運算元在全平面上一致收斂到每個以2為周期的二元連續函數，並且對具有任意階連續偏導數的函數全體的逼近具有最佳收斂階。

The concept of basic implication algebra and implication algebra on a partial ordered set are obtained by studying the conditions which the implicative operator in a logic system should be satisfied. then the basic properties with different conditions and the characterizes of implication algebra are given. the iff conditions of a ( basic ) implication algebra to be regular are discussed

基於對邏輯系統中蘊涵運算元應滿足條件的分析，引進了偏序集上基礎蘊涵代數和偏序集上蘊涵代數的概念，得到了其在不同條件下的基本性質，給出了（基礎）蘊涵代數的特徵刻畫，以及偏序集上（基礎）蘊涵代數成為正則的充分必要條件。