基于区间数度量的区间值模糊集合的相似度、模糊度和包含度的关系研究

区间值模糊集合的相似度、模糊度和包含度及其关系研究是区间值模糊集合的一个研究热点。考虑到区间值模糊集合所表示信息的丰富性,本文使用区间数而非实数来刻画区间值模糊集合的包含度,首先给出基于区间数度量的区间值模糊集合的包含度的公理化定义,然后通过五个定理详细研究了基于公理化定义的区间值模糊集合的相似度、包含度和模糊度之间的相互转换,最后,给出了若干计算公式来计算基于区间数度量的区间值模糊集合的相似度、模糊度和包含度。这些结论,一方面丰富了区间值模糊集合的信息测度(相似度、模糊度和包含度)的内容,另一方面也为区间值模糊集合的近似推理、决策分析、模式识别等领域的应用提供了新方法和新理论。     

连续函数图象的业细计盒维数及其刻划

将分形理论中的一个重要概念计盒维数推广为精细计盒维数，讨论此定义的等价表示。并且给出了Ｒ＾ｎ上连续函数图象的精细计盒维数用函数空间刻划的充要条件。     

连续函数图象的精细计盒维数及其刻划

将分形理论中的一个重要概念计盒维数推广为精细计盒维数，讨论此定义的等价表示。并且给出了Rn上连续函数图象的精细计盒维数用函数空间刻划的充要条件。     

基于梯形直觉模糊数的改进DEMATEL方法

针对传统DEMATEL方法在评价复杂系统因素间影响关系时,表征评估信息时存在模糊性、反映专家判断时存在不确定性等问题,提出基于梯形直觉模糊数的改进DEMATEL方法。该方法运用可转化为梯形直觉模糊数的语言变量表征专家对复杂系统因素之间影响程度的评分,清晰化综合关系模糊影响矩阵得到系统中各影响因素的原因度和中心度,并且通过实例结果证明了该方法的有效性。     

基于直觉模糊多属性群决策的风险排序方法

为了解决信息收集时的模糊性和不确定性问题,避免单人决策的失误,并全面描述风险的不同特征,本文将直觉三角模糊数和多属性群决策理论结合起来,提出了一种基于直觉模糊多属性群决策的风险排序方法,提高了风险排序的准确度.首先,运用直觉三角模糊数收集专家的判断信息;其次,通过分别计算三角模糊数和直觉模糊数的熵权得到组合权重,从而确定不同方案的风险综合值;再次,利用逼近理想解法对不同方案的风险综合值进行排序;最后,给出实例验证了该方法的有效性和可行性.     

四元数射影空间QP^n（c）中全实有小子流形

给出了四元数射影空间中奇维全实级小子流形Ｒｉｃｃｉ曲率的Ｐｉｎｃｈｉｎｇ定理，改进了沈一兵相应的Ｐｉｎｃｈｉｎｇ常数。     

四元数射影空间QP~n(c)中全实极小子流形

给出了四元数射影空间中奇维全实极小子流形Ｒｉｃｃｉ曲率的Ｐｉｎｃｈｉｎｇ定理，改进了沈一兵［１］相应的Ｐｉｎｃｈｉｎｇ常数     

基于区间值描述的自适应直觉模糊神经网络

针对模糊集合在语义描述上存在的不足,为提高自适应模糊神经网络的紧凑性,提出了自适应直觉模糊神经网络。首先,推导了适合神经网络计算的直觉模糊规则。接着,给出了自适应直觉模糊神经网络的结构和各层的含义,并给出了网络学习算法和收敛性分析。最后,通过典型实例仿真试验,表明提出的自适应模糊神经网络结构更为紧凑,学习算法的泛化性能更佳。     

模糊信息的信息量及其计算

定义了有关信息的基本概念，给出了一种关于位置的模糊信息即闭区间[a，b]上模糊数的信息量计算公式，讨论了模糊数信息量的性质，最后介绍了在模糊层次分析的比较判断矩阵构造中的算例。     

模糊数学方法在机械设计中的应用

本文应用模糊数学理论,针对模糊设计计算问题,提出了基于模糊数的设计计算方法,并给出了具体的设计计算实例。     

Trapezoidal Intuitionistic Fuzzy Aggregation Operator Based on Choquet Integral and Its Application to Multi-Criteria Decision-Making Problems

The Choquet integral can serve as a useful tool to aggregate interacting criteria in an uncertain environment. In this paper, a trapezoidal intuitionistic fuzzy aggregation operator based on the Choquet integral is proposed for multi-criteria decision-making problems. The decision information takes the form of trapezoidal intuitionistic fuzzy numbers and both the importance and the interaction information among decision-making criteria are considered. On the basis of the introduction of trapezoidal intuitionistic fuzzy numbers, its operational laws and expected value are defined. A trapezoidal intuitionistic fuzzy aggregation operator based on the Choquet integral is then defined and some of its properties are investigated. A new multi-criteria decision-making method based on a trapezoidal intuitionistic fuzzy Choquet integral operator is proposed. Finally, an illustrative example is used to show the feasibility and availability of the proposed method.     

Improved fuzzy ranking procedure for decision making in product design

In this paper, we present a method for ranking any number of normal fuzzy numbers using trapezoidal fuzzy numbers as a general form, where rectangular and triangular fuzzy numbers are particular cases of such a form. This general form is supported by 29 cases, which is enough to consider all the possible situations between two normal fuzzy numbers, such as trapezoidal, triangular, or rectangular. The ranking procedure is performed using four ordering criteria into a pseudo-order preference model considering the type of the fuzzy preference relation. Two examples are given to illustrate and validate the applicability and practicality of this fuzzy ranking method. A comparison and an analysis of the proposed method is presented to demonstrate its usefulness and its contribution to the improvement of the decision making processes as a result of its management of vague or imprecise information, and whether or not that information should be allowed to be entered into such processes.     

Intuitionistic fuzzy approach for enhancement of low contrast mammogram images

Mammogram image enhancement is very much necessary in diagnosing breast cancer or tumor at an early stage. Nonuniform illumination and low contrast images are commonly encountered in mammogram images. Conventional enhancement algorithms produce either some artifacts or cannot highlight minute details present in the images, particularly when dealing with mammogram images. In this article, we propose a new mammogram image enhancement scheme using Atanassov's intuitionistic fuzzy set (IFS) theory. IFS considers two uncertainties—membership and nonmembership degree apart from membership degree as in fuzzy set theory. As mammogram images are low contrast images and many of the image definitions are vague/unclear, so IFS theory may be suitable for better image enhancement. Initially, the image is transformed to an intuitionistic fuzzy image using a novel intuitionistic fuzzy generator. Hesitation degree is computed and using the hesitation degree, two membership levels are computed to form an interval type 2 fuzzy set. These two membership functions are then combined using Zadeh's fuzzy t-conorm to form a new membership function. Threshold of interval type 2 fuzzy image is obtained using restricted equivalence function. Using the threshold, modified fuzzy hyperbolization is carried out. Real data experiments demonstrate that the proposed algorithm has better performance on contrast and visual quality of the images both quantitatively and qualitatively when compared with different existing methods.     

Intuitionistic Fuzzy Petri Nets Model Based on Back Propagation Algorithm for Information Services

Intuitionistic fuzzy Petri net is an important class of Petri nets, which can be used to model the knowledge base system based on intuitionistic fuzzy production rules. In order to solve the problem of poor self-learning ability of intuitionistic fuzzy systems, a new Petri net modeling method is proposed by introducing BP (Error Back Propagation) algorithm in neural networks. By judging whether the transition is ignited by continuous function, the intuitionistic fuzziness of classical BP algorithm is extended to the parameter learning and training, which makes Petri network have stronger generalization ability and adaptive function, and the reasoning result is more accurate and credible, which is useful for information services. Finally, a typical example is given to verify the effectiveness and superiority of the parameter optimization method.     

模糊群决策方法在物流服务商选择中的应用

针对物流服务商选择中评价指标的不确定性和模糊性,提出用三角形模糊数来描述评价指标;构造了基于三角形模糊数和群决策理论的基本算法;并利用模糊数排序公式对决策方案进行排序和择优.最后进行了实例分析.数值结果表明该方法可行且有效.     

The incorporation of the Taguchi and the VIKOR methods to optimize multi-response problems in intuitionistic fuzzy environments

The Taguchi method is a powerful method of solving quality problems in various fields of engineering. However, this method was developed to optimize single-response processes. In many multi-response optimization problems, the important response is determined subjectively, based on knowledge or experience. However, using only exact numbers to represent this importance is problematic, because there is uncertainty and vagueness. The concept of intuitionistic fuzzy sets (IFSs) is a powerful method for characterization, using a membership function and a non-membership function. This paper proposes an efficient VIKOR method that optimizes multi-response problems in intuitionistic fuzzy environments. The importance weights of various responses are evaluated in terms of IFSs. In the proposed method, the similarity measure between IFSs is used to determine the crisp weights of the responses. This scheme eliminates the need for complicated intuitionistic fuzzy arithmetic operations and increases efficiency in solving multi-response optimization problems in intuitionistic fuzzy environments. Two case studies: plasma-enhanced chemical vapor deposition and a double-sided surface mount technology electronic assembly operation are used to demonstrate the effectiveness of the proposed method.     

Integrals of random fuzzy sets

This paper tries to give a systematic investigation of integration of random fuzzy sets. Besides the widely used Aumann-integral adaptions of Pettis- and Bochner-integration for random elements in Banach spaces are introduced. The mutual relationships of these competing concepts will be explored comprehensively, completing and improving former results from literature. As a by product dominated convergence theorems, strong laws of large numbers and central limit theorems for random fuzzy sets can be derived. They are based on weaker assumptions than previous versions from literature.     

Multi-objective mixed integer programming and an application in a pharmaceutical supply chain

Multi-objective integer linear and/or mixed integer linear programming (MOILP/MOMILP) are very useful for many areas of application as any model that incorporates discrete phenomena requires the consideration of integer variables. However, the research on the methods for the general multi-objective integer/mixed integer model has been scant when compared to multi-objective linear programming with continuous variables. In this paper, an MOMILP is proposed, which integrates various conflicting objectives. We give importance to the imprecise nature of some of the critical factors used in the modelling that can influence the effectiveness of the model. The uncertainty and the hesitation arising from estimating such imprecise parameters are represented by intuitionistic fuzzy numbers. The MOMILP model with intuitionistic fuzzy parameters is first converted into a crisp MOMILP model, using appropriate defuzzification strategies. Thereafter, the MOMILP is transformed into a single objective problem to yield a compromise solution with an acceptable degree of satisfaction, using suitable scalarisation techniques such as the gamma-connective technique and the minimum bounded sum operator technique. The proposed solution method is applied to several test problems and a multi-objective pharmaceutical supply chain management model with self generated random data.     

基于直觉模糊优化的双边匹配决策

为了实现不确定信息环境下的双边满意匹配，提出基于直觉模糊优化的匹配决策方法。利用直觉模糊集理论中隶属度和非隶属度的概念，将经典匹配决策模型中双目标函数转换为反映匹配双方总体满意度的单目标函数，模型中同时纳入公平性因素。通过设计交互式算法，在满足一定的公平性条件下实现总体满意度最大化。该算法为匹配决策过程注入了灵活性和协调性，具有一定的实用性和参考价值。     

决策实施的直觉模糊集方法

阐述<卓越绩效评价准则>决策实施的重要意义以及应用直觉模糊集的必要性.提出方案优选中多准则直觉模糊集评价,各准则权重实质重要度,方案优选的正负理想解以及直觉模糊集距离的概念及计算方法.在此基础上提出各方案评价指数的概念,由其大小决定方案的优劣.举出上海某通信有限责任公司销售代理商优选决策的示例,得出A3优于A1优于A2优于A4的结论.