基于可能性测度的计算树逻辑

首先,提出了可能的Kripke结构的定义,建立了可能的Kripke结构的可能性测度空间,并分析了可能的Kripke结构的一系列性质,即任一路径转移的可能性可由其初始状态的可能性分布与各转移的可能性取下确界而得到;依据可能的Kripke结构所定义的可能性测度具有其合理性等等。其次,给出了可能性计算树逻辑(PoCTL)的概念,讨论了两个PoCTL状态公式以及PoCTL与经典计算树逻辑(CTL)公式的等价性。最后,证明了PoCTL公式有与CTL*公式中"一致性"相对应的公式。     

子空间可能性聚类机制研究

可能性C-均值(PCM)聚类作为经典的基于原型的聚类方法,在处理高维数据集时性能骤降,无法检测出高维空间中嵌入的有效子空间。针对此不足,在PCM基础上引入子空间聚类机制,提出子空间可能性聚类算法SPC。该方法保留了PCM方法的优点,且对高维数据具有较好的适应性,能够有效检测各类所处的子空间。仿真实验验证了SPC算法的有效性。     

Fuzzy uncertainty modelling for project planning: application to helicopter maintenance

Maintenance is an activity of growing interest, especially for critical systems. In particular, aircraft maintenance costs are becoming an important issue in the aeronautical industry. Managing an aircraft maintenance centre is a complex activity. One of the difficulties comes from the numerous uncertainties that affect the activity and disturb the plans in the short and medium term. Based on a helicopter maintenance planning and scheduling problem, we study in this paper the integration of uncertainties into tactical and operational multi-resource, multi-project planning (respectively Rough Cut Capacity Planning and the Resource Constraint Project Scheduling Problem). Our main contributions are in modelling the periodic workload on a tactical level considering uncertainties in macro-task work content, and modelling the continuous workload on the operational level considering uncertainties in task duration. We model uncertainties using a fuzzy/possibilistic approach instead of a stochastic approach since very limited data are available. We refer to the problems as the Fuzzy Rough Cut Capacity Problem (FRCCP) and the Fuzzy Resource Constraint Project Scheduling Problem (RCPSP). We apply our models to helicopter maintenance activity within the frame of the Helimaintenance project, an industrial project approved by the French Aerospace Valley cluster that aims at building a centre for civil helicopter maintenance.     

Blood supply chain network design considering blood group compatibility under uncertainty

This paper addresses the design of a blood supply chain (SC) network considering blood group compatibility. To this aim, a bi-objective mathematical programming model is developed which minimises the total cost as well as the maximum unsatisfied demand. Due to uncertain nature of some input parameters, two novel robust possibilistic programming models are proposed based on credibility measure. The data of a real case study are then used to illustrate the applicability and performance of the proposed models as well as validating the proposed robust possibilistic programming approach. The obtained results show the superiority of the developed models and significant cost savings compared to current existed blood SC network.     

Vector quantization in DCT domain using fuzzy possibilistic c-means based on penalized and compensated constraints

In this paper, fuzzy possibilistic c-means (FPCM) approach based on penalized and compensated constraints are proposed to vector quantization (VQ) in discrete cosine transform (DCT) for image compression. These approaches are named penalized fuzzy possibilistic c-means (PFPCM) and compensated fuzzy possibilistic c-means (CFPCM). The main purpose is to modify the FPCM strategy with penalized or compensated constraints so that the cluster centroids can be updated with penalized or compensated terms iteratively in order to find near-global solution in optimal problem. The information transformed by DCT was separated into DC and AC coefficients. Then, the AC coefficients are trained by using the proposed methods to generate better codebook based on VQ. The compression performances using the proposed approaches are compared with FPCM and conventional VQ method. From the experimental results, the promising performances can be obtained using the proposed approaches.     

QUO VADIS FUZZY SYSTEMS: A CRITICAL EVALUATION OF RECENT METHODOLOGICAL TRENDS

The paper critically examines some foundational aspects of Fuzzy Sets and Systems. The systemic character of Zadeh's approach is stressed, as is the neccessity of understanding the interplay of holism and atomism for the proper evaluation of the formalized epistemology of fuzzy sets. This link between holism and atomism is provided by the systemic epistemology of T. G. Masaryk, adumbrated in Sec. 2. The linguistic theories of the Prague School, which are based on the epistemology utilizing the notions purpose, function, communication, meaning, normative structure etc. are also discussed, and their relevance to the methodology of Fuzzy Sets and Systems is stressed. Section 5 is devoted to formal analysis of possibilistic constructions and structures. It is demonstrated that the so called “Theory of possibility” is just one special instance of the general possibilistic construction.

The paper of Zelený, appearing elsewhere in this issue, is critically evaluated, as is the Graham-Johnstone controversy. The latter contained heated discussions about pros and cons of research concerning fuzzy sets. The phenomenon of the epistemological and methodological split within the field of fuzzy systems (which I refer to as “The schism of the third decade”) is observed and its causes briefly analyzed.     

Continuity and completeness of lattice-valued possibilistic measures

Properties such as continuity from above and from below and various kinds of completeness are analysed when investigating set functions, in particular probabilistic and possibilistic measures and the relations of these properties to properties such as (σ)-additivity of probability measures or (complete) maxitivity of possibilistic measures are proved. In this work, the notions of continuity from above and from below are introduced for non-numerical possibilistic measures, taking their values in a complete lattice and at least for some relations valid for real-valued possibilistic measures of their analogies for lattice-valued possibilistic measures are stated and proved.     

面向可能性数据库的异构双极信息查询策略研究

在日常交流中,人们常常会对同一事物同时使用正面的描述和负面的描述来表达其愿望和不满,由于不要求正、负面的描述必须相互对称,此类信息因而被称为异构双极(Heterogeneous bipolarity)信息.传统信息系统中的模糊查询方法,不能很好地处理用户查询需求中所含有的异构双极信息.本文基于可能性数据库,在限定的条件下,以在模糊查询选择操作的基本查询条件中,能够处理异构双极信息为目标,将Vague集用于异构双极信息的建模,并给出了在基本查询条件中含有异构双极信息的情况下,查询结果相关可能性测度和必要性测度的计算公式,同时还通过实例讨论了该方法的语义、特点及其与基于可能性理论方法的一致性.     

A two-phase possibilistic linear programming methodology for multi-objective supplier evaluation and order allocation problems

In this study, an integration of the analytic hierarchy process (AHP) and a multi-objective possibilistic linear programming (MOPLP) technique is developed to account for all tangible, intangible, quantitative, and qualitative factors which are used to evaluate and select suppliers and to define the optimum order quantities assigned to each. A multi-objective linear programming technique is first employed to solve the problem. To model the uncertainties encountered in the integrated supplier evaluation and order allocation methodology, fuzzy theory is adopted. Hence, possibilistic linear programming (PLP) is proposed for solving the problem, as it is believed to be the best approach for absorbing the imprecise nature of the real world. In the supplier evaluation phase, environmental criteria are also considered.     

一个基于专家知识的不确定性分析推理系统

本文介绍EXDASS系统中进行不确定性分析的推理系统.该系统的工作方式是依据专 家对不确定性作出判断的有关知识信息,通过人机交互的动态过程以实现对决策的支持.专 家知识的量化表示及其推理机制的实现以可能性证据理论为基础.文中描述了系统的设计思 想和工作原理,重点介绍了在知识表示方面的自学习特性,并且给出了应用实例.