partial ordering set meaning in English
偏序集合
Examples
- 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
利用上述得到的关于蕴涵代数中蕴涵算子的条件，研究偏序集上具有条件( c )的蕴涵代数的mp滤子及fuzzy滤子。 - 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
系统地研究了偏序集上蕴涵代数与heyting代数之间的关系，得到了蕴涵代数中蕴涵算子的一个较好的条件，并给出了偏序集上蕴涵代数成为布尔代数的一些条件。 - 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数工具对模糊逻辑进行研究，给出模糊逻辑的一类代数抽象，即偏序集上的蕴涵代数，研究偏序集上蕴涵代数与其它代数结构，如mv -代数， heyting代数之间的关系，以及偏序集上蕴涵代数的滤子与其结构等。 - 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
借助于mp -滤子的概念，得到了偏序集上具有条件( c )的蕴涵代数中由非空集合所生成mp滤子的表示定理，证明了由其上所有mp -滤子组成的集合mf ( x )是一个完备的分配格；得到了蕴涵代数中fuzzy滤子与mp滤子的关系，给出了fuzzy滤子成为fuzzy素滤子的若干刻画；并利用mp -滤子和fuzzy滤子，刻画了一类偏序集上蕴涵代数的结构。 - 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拟序集上定义广义alexandroff拓扑，证明了它是通常拟序集上alexandroff拓扑的推广，一个l - fuzzy拟序集( x ， e )上的广义alexandroff拓扑可以由其上一族alexandroff拓扑取并得到，任意一个拓扑空间的拓扑都可以表示为某个l - fuzzy拟序集上的广义alexandroff拓扑，以及l - fuzzy拟序集上的广义alexandroff拓扑是j . j . m . m . rutten等定义的广义超度量空间上广义alexandroff拓扑的推广。 ( 2 )通过引入l - fuzzy偏序集上的l - fuzzy集关于l - fuzzy偏序的并以及l - fuzzy拟序集上(关于l - fuzzy拟序)的l - fuzzy定向集等概念，定义了l - fuzzy定向完备的l - fuzzy偏序集(简称l - fuzzydcpo ，又叫l - fuzzydomain )和l - fuzzyscott连续映射，证明了它们分别是通常的dcpo和scott连续映射的推广，当l是带有逆序对合对应的完全分配格时，以l - fuzzydomain为对象， l - fuzzyscott连续映射为态射的范畴l - fdom同构于一类特殊的v - domain范畴，即以定向完备的l -值拟超度量空间为对象， scott连续映射为态射的范畴l - dcqum ，以及当l是1为分子的完全分配格时， l - fuzzydomain和l - fuzzyscott连续映射一致于k . wagner在[ 59 ]中定义的定向liminf完备的-范畴和liminf连续映射。