An approach to fuzzy default reasoning for function approximation

This paper discusses fuzzy reasoning for approximately realizing nonlinear functions by a small number of fuzzy if-then rules with different specificity levels. Our fuzzy rule base is a mixture of general and specific rules, which overlap with each other in the input space. General rules work as default rules in our fuzzy rule base. First, we briefly describe existing approaches to the handling of default rules in the framework of possibility theory. Next, we show that standard interpolation-based fuzzy reasoning leads to counterintuitive results when general rules include specific rules with different consequents. Then, we demonstrate that intuitively acceptable results are obtained from a non-standard inclusion-based fuzzy reasoning method. Our approach is based on the preference for more specific rules, which is a commonly used idea in the field of default reasoning. When a general rule includes a specific rule and they are both compatible with an input vector, the weight of the general rule is discounted in fuzzy reasoning. We also discuss the case where general rules do not perfectly but partially include specific rules. Then we propose a genetics-based machine learning (GBML) algorithm for extracting a small number of fuzzy if-then rules with different specificity levels from numerical data using our inclusion-based fuzzy reasoning method. Finally, we describe how our approach can be applied to the approximate realization of fuzzy number-valued nonlinear functions     

A fuzzy sets theoretic approach to approximate spatial reasoning

Relational composition-based reasoning has become the most prevalent method for qualitative reasoning since Allen's 1983 work on temporal intervals. Underlying this reasoning technique is the concept of a jointly exhaustive and pairwise disjoint set of relations. Systems of relations such as RCC5 and RCC8 were originally developed for ideal regions, not subject to imperfections such as vagueness or fuzziness which are found in many applications in geographic analysis and image understanding. This paper, however, presents a general method for classifying binary topological relations involving fuzzy regions using the RCC5 or the RCC8 theory. Our approach is based on fuzzy set theory and the theory of consonant random set. Some complete classifications of topological relations between fuzzy regions are also given. Furthermore, two composition operators on spatial relations between fuzzy regions are introduced in this paper. These composition operators provide reasonable relational composition-based reasoning engine for spatial reasoning involving fuzzy regions.     

A new approach to fuzzy reasoning

 Over the last years fuzzy control has become a very popular and successful control paradigm. The basic idea of fuzzy control is to incorporate human expert knowledge. This expert knowledge is specified in a rule based manner on a high and granular level of abstraction. By using vague predicates a fuzzy rule base neglects useless details and concentrates on important relations. Following L.A. Zadeh’s famous principle of incompatibility, this technique is most promising when applied to large and complex problems. Nevertheless, nowadays most fuzzy rule bases are small and represent simple knowledge. From our point of view this surprising and somewhat disappointing observation is due to a major lack of understanding how to handle a fuzzy rule base. In this paper we present a new theory for fuzzy reasoning. This theory is twofold. In general, a fuzzy rule base is both partially inconsistent and partially incomplete. This is the price to pay for abstraction and granularization. We show that if a fuzzy rule base maximizes consistency at the cost of completeness, the well-known possibilistic approach to fuzzy inference is the right choice. For a fuzzy rule base that maximizes completeness at the cost of consistency, we derive a new type of inference called σ-reasoning. Together, both mechanisms form an embracing theory for fuzzy reasoning in general. We propose a combined approach to be applied in order to manage complex rule bases.     

规则摄动时模糊蕴涵算子对模糊推理的鲁棒性的影响

列举了模糊规则发生摄动的常见情形,建立了一般性的模糊推理算法对规则摄动的鲁棒性的概念;就多重、链式和多维模糊推理情形,重点研究了一般性的模糊蕴涵算子对几个重要的模糊推理算法的这种鲁棒性的影响,并分别给出了相应的充分必要条件;初步尝试了通过一定的摄动制约来改善这种鲁棒性;同时指出了很多现有的模糊蕴涵算子使得所讨论的这些推理算法拥有好的鲁棒性,此时,即使规则中的隶属度有适度的粗糙或摄动,推理仍是可行的、安全的．文中工作对模糊系统的分析、模糊蕴涵算子的选择以及规则获取过程有一定的指导意义．     

模糊层次分析法在方案优选方面的应用

给出了一种实用的层次分析方法(AHP)，即模糊层次分析法(FAHP)，讨论了它的原理和步骤。特别是模糊层次分析法，它是基于模糊集合理论的。它采用模糊一致关系去实现模糊推导，使用模糊一致矩阵去实现动态自适应。分析了该方法的适用范围，并提供了具有一般特点的方案优选的实例。提出了模糊层次分析方法的不足之处。     

A fuzzy case based reasoning approach to value engineering

This paper is intended to assist the experts during the creativity phase of value engineering through utilizing the past experiences and avoid them in a specific domain from repeating the same experience. To this purpose, a general fuzzy case based reasoning (CBR) system is developed. Our system benefits from a fuzzy clustering model for fuzzy data to facilitate case retrieval and reduce the time complexity. The inherent analogical nature of a case-based reasoning (CBR) model and its integration with fuzzy theory would facilitate access to more precise and systematically classified information during a VE workshop. In order to test the performance of the proposed system, it is applied to suburban highway design data extracted from National Cooperative Highway Research Program (NCHRP) Report 282.     

证据推理的进展及存在的问题

综合论述了证据推理的进展和存在的问题,把证据推理与贝叶斯推理、模糊逻辑推理、基于规则的推理、随机集理流体进行了横向比较,讨论了其间的必然的联系和为语气推理的发展的基础,随后总结了证据推理的改进及其在概率范围在模糊集等方面推广的进展,最后提出了证据推理的广泛应用及其研究方向。     

机电设备故障诊断模糊推理机研究

通过分析机电设备的故障机理,运用模糊理论及其推理方法设计了一种机电设备故障诊断模糊推理机。重点对基于模糊数学理论和模糊推理方法的推理机制进行了研究,该推理机能够有效处理由于知识的模糊性所引起的不确定性问题。     

一种基于区间值模糊推理的控制器设计

本文在区间值模糊匹配推理基础上，设计了一种区间值模糊控制器。为了应用区间值模糊匹配推理方法，文中给出了一种清晰量的区间值模糊化方法，最后用实例说明区间值模糊控制器设计过程以及给出Matlab仿真控制效果。     

基于蕴涵算子L-λ-0-λ-G的模糊推理的三I算法

研究了基于蕴涵算子L-λ-0-λ-G模糊推理的FMP三I支持算法,给出了FMP模型和FMT模型的三I算法的计算公式。