数区间

For the question of material transportation in emergency situation ,the paper gives an arithmetic operators,which changes the interval number order into real number order,and gives the arithmetic of interval number shortest path.

针对紧急状态下物资调配时间为区间数问题，在经典的Dijkstra算法基础上，通过定义一个算子，把区间数序关系转换成实数序关系，对区间数进行排序，给出了区间数的最短路算法。

Based on these operational laws, some aggregation operators, including pure interval-valued intuitionistic fuzzy weighted arithmetric averaging operator and pure interval-valued intuitionistic fuzzy ordered weighted averaging operator, are proposed.

论文摘要：对纯区间直觉模糊信息的集结算子进行了进一步研究，引入了区间直觉模糊数的一些运算法则、区间直觉模糊数的得分函数和精确函数，并基于这些运算法则，提出了一些新算子：纯区间直觉模糊数加权算术平均算子和纯区间直觉模糊数有序加权平均算子。

Interval-valued intuitionistic fuzzy numbers; operation laws; pure interval-valued intuitionistic fuzzy weighted arithmetric averagingoperator; pure interval-valued intuitionistic fuzzy ordered weighted averaging operator

区间直觉模糊数；运算法则；纯区间直觉模糊数加权算术平均算子；纯区间直觉模糊数有序加权平均算子

Some operational laws of interval-valued intuitionistic fuzzy numbers, score function and accuracy function of interval-valued intuitionistic fuzzy numbers are intriduced. Based on these operational laws, some aggregation operators, including interval-valued intuitionistic fuzzy ordered weighted arithmetic averaging operator and interval-valued intuitionistic fuzzy hybrid aggregation operator, are proposed.

论文摘要：对区间直觉模糊信息的集结算子进行了进一步研究，引入了区间直觉模糊数的一些运算法则、区间直觉模糊数的得分函数和精确函数，并基于这些运算法则，提出了一些新算子：区间直觉模糊数有序加权算术平均算子和区间直觉模糊数混合集结算子。

The main contributions of this dissertation can be summarized as follows: First of all, operation and compositor between interval numbers are summarized. Homology and dissimilarity between interval number and grey number are compared.

本文讨论了含有区间数的一类不确定性优化问题，主要研究内容如下：第一，对区间数之间的运算和排序进行了综述，对区间数和灰数从7个方面作了比较。

The concepts of interval grey number and the rules of four fundamental operations of interval grey number are simply stated, and then the distributive law for multiplication of interval grey number at some conditions is put forward and the distance between two interval grey number is defined.

第三章，简述了区间型灰数的概念及运算规则，给出了关于同性单性区间型灰数分配律定理，定义了区间型灰数的距离，然后利用最优化原理建立了灰关联模式识别公式，从而形成了一种新的灰关联模式识别方法。

The conceptions of the superiority, inferiority and equipollence position degrees of the interval grey number were defined, and it was proved that the sum of three position degrees for a certain interval grey number related to another grey number is 1, and that the relation set of the position degrees is a whole order set of the interval grey numbers.

运用灰色系统思想和系统工程的理论，揭示了人们在灰信息条件下的博弈心理与博弈决策规则；提出了区间灰数的优势、均势和劣势的概念；证明了与某一区间灰数相对的另一区间的各种灰数势之和为1，且灰数势大小关系的集合是一个全序集。

According to the definition of an interval number complementary judgment matrix, the definition of complete consistency and satisfactory were introduced.

根据区间数判断矩阵的概念给出了区间数判断矩阵的完全一致性定义，通过对完全一致性性质的讨论演绎出区间数判断矩阵的一致性和满意一致性定义及其判别方法，并且研究了一致性和满意一致性定义的合理性，提出了求解区间数判断矩阵排序向量的递推排序方法，最后用算例验证了方法的有效性。

First, based on the mathematics model of comprehensive decision at present, the concept of evaluation function is introduced. Based on the thinking stability of decision-maker, the essential meaning of comprehensive decision model is discussed, therefore, and a new improved approach on the comprehensive decision model is put forward. Second, the mathematics model of interval number comprehensive decision is systematically discussed, and the ranking method of interval number based on the decision-maker's attitude is provided. Finally, the concept of valuation order relation is introduced, the valuation order relation of interval number and fuzzy number are systematically discussed in detail, it provides a new method to research the order relations of interval number and fuzzy number, therefore, these achievements can be applied in the intelligent system.

首先，针对常用的综合决策模型，给出了评判函数的概念，讨论了综合决策模型的本质意义，指出决策者的思维应具有稳定性，从而给出了综合决策模型的一种改进方法；第二，在此基础上，给出了区间数的综合决策模型，并详细讨论了基于决策者的决策心态的区间数的排序方法；第三，引入了赋值序关系的概念，详细讨论了区间数和模糊数的赋值序关系，为区间数和模糊数的序关系研究提供了新的思路与方法，这些均有望在智能系统中得到广泛的应用。

Based on the transformation between interval number reciprocal judgment matrix and interval number complementary judgment matrix, this paper proposes the definitions of additive consistency and multiplicative consistency for interval number complementary judgment and correlative definitions as well, and studies the particular proprieties of the consistency interval number judgment matrix. At the same time, it also puts forward a simple algorithm that can judge whether an interval number complementary has the propriety of satisfied transitivity.

利用区间数互反判断矩阵与区间数互补判断矩阵之间的转换关系，给出了乘性一致性与加性一致性区间数互补判断矩阵的定义，并研究了一致性区间数判断矩阵的一些特殊性质；同时给出了区间数互补判断矩阵满意一致性的一个简单的判断方法与算法。

He is the most remarkable man that I have ever known.

他是我知道的人中最值得注意的人。

Increased appearance of lymphocele was noticed in patients with diabetic nephropathy, congenital malformations of the urinary tract, and inflammatory diseases, including glomerulopathy and extraglomerular ones, after high-voltage radiotherapy and after removal of the renal graft.

经过高压放射疗法和切除移植肾后，在糖尿病肾病患者、泌尿系统先天性畸形患者和炎症患者身上发现淋巴囊肿有所增加，包括肾小球病和球外疾病等。