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双语推荐：直觉模糊滤子

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在BL-代数和直觉模糊集理论的基础上,应用直觉模糊集的方法,定义了BL-代数上直觉模糊滤子和直觉模糊素滤子.然后,讨论了直觉模糊滤子和直觉模糊素滤子的相关性质以及如何由直觉模糊集生成直觉模糊滤子的方法;最后,研究了BL-代数上的直觉模糊滤子的全体的代数结构.
Based on the theory of BL-algebras and intuitionistic fuzzy sets ,intuitionistic fuzzy filters and intuitionistic fuzzy prime filters are defined through the method of intuitionistic sets .Moreover ,some properties of intuitionistic fuzzy filters and intuitionistic fuzzy prime filters of BL-algebras are discussed and the relations between them are studied .Then ,the intuitionistic fuzzy filters generated by intuition-istic fuzzy set in BL-algebras is studied .Finally ,the algebraic structure of all intuitionistic fuzzy filters is discussed .

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在直觉模糊信息系统上,直觉模糊信息熵和直觉模糊信息粒度是两种有效地进行不确定性研究的重要工具。在直觉模糊信息系统上,引入直觉模糊粒结构的交、并、差、补等四种运算。提出了基于直觉模糊粒结构的直觉模糊信息熵;并研究了直觉模糊信息熵与直觉模糊信息粒度之间的关系。
Intuitionistic fuzzy information entropy and intuitionistic fuzzy information granularity are an important tool to effectively measure the uncertainty of intuitionistic fuzzy information systems. Intersection, union, subtraction and com-plement operators of granular structures in intuitionistic fuzzy information systems are proposed in this paper. Intuitionistic fuzzy information entropy based on intuitionistic fuzzy granular structures is presented, and the relationships between intui-tionistic fuzzy information entropy and intuitionistic fuzzy information granularity are established.

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将直觉模糊粗糙集理论引入到逻辑推理中,通过对粗糙集、直觉模糊集、数理逻辑等基本理论的融合,给出了直觉模糊粗糙逻辑的语义及其推理方法。首先给出直觉模糊命题逻辑的5个逻辑值,即直觉模糊真、直觉模糊假、直觉模糊粗糙真、直觉模糊粗糙假和直觉模糊粗糙不相容,在此基础上定义了直觉模糊粗糙逻辑的运算,然后讨论了近似空间中直觉模糊粗糙命题公式的语义,最后针对含有不同逻辑连接词的直觉模糊粗糙命题公式给出了其语义推理方法。
The theory of the intuitionistic fuzzy rough set is introduced into the logic reasoning .By the combination of such basic theories as rough sets , intuitionistic fuzzy sets and mathematical logic , the semantic and reasoning methods of intuitionistic fuzzy rough logic are given .Initially, five logic values for the intuitionistic fuzzy proposition logic are given, i.e.intuitionistic fuzzy true , intuitionistic fuzzy false , intuitionistic fuzzy rough true , intuitionistic fuzzy rough false and intuitionistic fuzzy rough incompatible , and on the basis of this , the intuitionistic fuzzy rough logic operations are given;then the semantic of intuitionistic fuzzy rough proposition formulas in approximate space is discussed;finally, the semantic reasoning methods are proposed as for the intuitionistic fuzzy rough propositional formula containing different logical conjunctions .

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把商空间理论推广到直觉模糊集理论中，建立直觉模糊商空间。定义直觉模糊等价关系和直觉模糊距离。建立基于直觉模糊等价关系的商空间基本定理。证明由有序的直觉模糊等价关系簇诱导的直觉模糊商空间构成一个完备半序格。
The quotient space theory is extended into intuitionistic fuzzy set theory, and intuitionistic fuzzy quotient space is established. An intuitionistic fuzzy equivalent relation and distance are defined. An elementary theory of intuitionistic fuzzy quotient space based on intuitionistic fuzzy equivalent relation is established. A cluster of intuitionistic fuzzy quotient spaces induced by a cluster of ordered intuitionistic fuzzy equivalent relations constitutes a complete semi-order lattice.

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基于语言真值直觉模糊格,提出一种语言值直觉模糊二元组表示模型.讨论模型中语言值直觉模糊对的运算及其性质.给出语言值直觉模糊聚合算子,即语言值直觉模糊算术平均算子和语言值直觉模糊加权平均算子,实现语言值直觉模糊对的聚合,减少语言值直觉模糊对聚合过程中的信息损失.将此方法用于模糊模式识别中,并以疾病诊断识别过程说明该方法在具有正反两面证据的模糊环境下的有效性.
A kind of linguistic-valued intuitionistic fuzzy 2-tuple representation model is proposed based on the linguistic truth-valued intuitionistic fuzzy lattice. The operations and the properties of linguistic-valued intuitionistic fuzzy pair are discussed. Based on the proposed model, a kind of linguistic-valued intuitionistic fuzzy aggregation approach is defined. Arithmetic mean aggregation operator and weighted average aggregation operator are given respectively. Using the aggregation operations of the linguistic-valued intuitionistic fuzzy pairs, the information loss is reduced in the process of the aggregation for linguistic-valued intuitionisttic fuzzy pair. A recognition process of disease diagnosis is given to illustrate that the proposed approach is more effective for pattern recognition under a fuzzy environment with both positive evidence and negative evidence.

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依据决策者的风险偏好,将区间直觉模糊数转化为含参数直觉模糊数,然后基于直觉模糊数投票模型和人们从众心理分析直觉模糊数的犹豫度对其得分的影响,进而定义直觉模糊数新的得分函数,并以此作为区间直觉模糊数的排序指标,提出一种新的区间直觉模糊数模糊决策方法,最后通过例子验证该方法的可行性和有效性.
We present a new method for multi-criteria fuzzy decision making based on interval-valued intuitionistic fuzzy sets.First the decision maker''s risk attitude is induced for converting an interval-valued intuitionistic fuzzy number to be a parametric intuitionistic fuzzy number. Then by considering decision makers''herd behavior when he/she hesitates in an election,the hesitancy degree impacts on the scores of intuitionistic fuzzy numbers.According to above anal-ysis,a new score function is defined and used for ranking interval-valued intuitionistic fuzzy numbers.Furthermore,a method is proposed to deal with multi-criteria fuzzy decision making problems based on the new score function.Finally,a numerical example is given to illustrate the feasibility and effectiveness of the new method.

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对区间直觉模糊信息系统中近似集的不确定性进行了研究,给出了区间直觉模糊粗糙集的不确定性度量公式。首先在区间直觉模糊近似空间中,定义了一对具有对称性的新的区间直觉模糊上、下近似算子;其次给出了区间直觉模糊集粗糙隶属函数的定义并讨论了相关性质;最后利用区间直觉模糊粗糙隶属函数的区间直觉模糊熵,定义了区间直觉模糊粗糙集的模糊熵,并讨论了区间直觉模糊粗糙集的模糊熵为零的充要条件,证明了在区间直觉模糊近似空间中经典集合和它的余集的粗糙度量是相等的,以此说明定义的合理性。
The uncertainty of an approximate set in interval-value intuitionistic fuzzy information system is re-searched in this paper and the uncertainty measurement formula of interval-value intuitionistic fuzzy rough sets are given.Firstly, a pair of new interval-value intuitionistic fuzzy upper and lower approximation operators with symme-try is defined in the interval-value intuitionistic fuzzy approximation space.Secondly, the corresponding definition of rough membership functions on interval-value intuitionistic fuzzy is given and properties are discussed.Finally, the fuzzy entropy of interval-value intuitionistic fuzzy rough set is defined by interval-value intuitionistic fuzzy entropy of the interval-value intuitionistic fuzzy rough membership functions.The necessary and sufficient conditions when the fuzzy entropy on interval intuitice fuzzy rough set is zero are discussed.In addition, the rough measurement values of classic set and residual set are equal in the interval-valu

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在K.Atanassov提出的直觉模糊集的概念基础上,利用T-范数和S-范数,定义了（T,S）-凸直觉模糊集,（T,S）-直觉模糊子空间和（T,S）-直觉模糊仿射集,并讨论了（T,S）-凸直觉模糊集的一些性质,（T,S）-直觉模糊子空间和（T,S）-直觉模糊仿射集之间的关系。
On the basis of the concept of the intuitionistic fuzzy set was introduced by K.Atanassov, the definitions of (T , S )-intuitionistic fuzzy set, (T , S )-intuitionistic fuzzy subspace and (T , S )-intuitionistic fuzzy affine set were introduced by T-norm and S-norm, some properties of (T , S )-convex intuitionistic fuzzy set and the relations between the (T , S )-intuitionistic fuzzy subspace and (T , S )-intuitionistic fuzzy affine set were discussed.

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利用模糊熵工具将近似集的不确定性度量方法应用在区间直觉模糊信息系统中,给出了区间直觉模糊近似算子的不确定性度量公式.通过在区间直觉模糊近似空间中定义一对新的区间直觉模糊上、下近似算子,将模糊粗糙隶属函数的定义推广到了区间直觉模糊集的粗糙隶属函数;然后利用区间直觉模糊粗糙隶属函数的模糊熵,定义了区间直觉模糊粗糙集的熵;进而解决了区间直觉模糊粗糙集的不确定性度量问题,并讨论了度量的一些相关性质,以此说明定义的合理性.
The uncertainty measurement method of approximate set was used in the interval-valued intuitionis-tic fuzzy information system by using fuzzy entropy, the uncertainty measuring formula of the interval-valued intuitionistic fuzzy approximate operators was given. The definition of fuzzy rough membership function was generalized to rough membership function of interval-valued intuitionistic fuzzy sets through defining a new in-terval-valued intuitionistic fuzzy upper and lower approximate operators in the interval-valued intuitionistic fuzzy approximate space. Then, the entropy of interval-valued intuitionistic fuzzy rough set was defined by using fuzzy entropy of the interval-valued intuitionistic fuzzy rough membership functions, and the problem of uncertainty measurement on interval-valued intuitionistic fuzzy rough set was solved, some related properties of measure was discussed, so as to prove the rationality of the definition.

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针对直觉模糊集中模糊性和直觉性对不确定信息的综合影响以及直觉模糊熵连续变化等问题,提出2种直觉模糊熵的几何构造方法,完善传统直觉模糊熵的构造准则。利用几何方法,分别通过建立等熵平面和等熵圆弧,结合距离构造2种新的直觉模糊熵,并证明其相关性质。论述直觉模糊熵的一般构造方法,对算例与现存的一些熵公式进行比较分析。将直觉模糊熵应用到多属性决策中,验证该方法的正确性和合理性。
Focusing on combining effects of uncertain information with the fuzziness and intuitionism and the continuous change of intuitionistic fuzzy entropy, this paper presents two geometry construction methods for intuitionistic fuzzy entropy. The classical construction criterion of intuitionistic fuzzy entropy is refined. By use of geometry methods, two new intuitionistic fuzzy entropies are presented through establishing isentropic plane and isentropic circle and distance, respectively, and relative properties are also proved. At the same time, the general construction method of intuitionistic fuzzy entropy is discussed, and compared with other existed entropy formulas by example. The reasonability and correction of the proposed methods are verified by applying the intuitionistic fuzzy entropy in multi-attributes decision-making problem.

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