Membership function

About: Membership function is a research topic. Over the lifetime, 15795 publications have been published within this topic receiving 418366 citations.

Analysis of fuzzy queues

Abstract: A general approach for queuing systems in a fuzzy environment is proposed based on Zadeh's extension principle, the possibility concept and fuzzy Markov chains. To illustrate the approach, analytical results for M/F/1 and FM/FM/1 systems are presented. Fuzzy queues are much more realistic than the commonly used crisp queues in many practical situations. A simple numerical example is also presented.

On Robust Fuzzy Rough Set Models

Abstract: Rough sets, especially fuzzy rough sets, are supposedly a powerful mathematical tool to deal with uncertainty in data analysis. This theory has been applied to feature selection, dimensionality reduction, and rule learning. However, it is pointed out that the classical model of fuzzy rough sets is sensitive to noisy information, which is considered as a main source of uncertainty in applications. This disadvantage limits the applicability of fuzzy rough sets. In this paper, we reveal why the classical fuzzy rough set model is sensitive to noise and how noisy samples impose influence on fuzzy rough computation. Based on this discussion, we study the properties of some current fuzzy rough models in dealing with noisy data and introduce several new robust models. The properties of the proposed models are also discussed. Finally, a robust classification algorithm is designed based on fuzzy lower approximations. Some numerical experiments are given to illustrate the effectiveness of the models. The classifiers that are developed with the proposed models achieve good generalization performance.

Fuzzy Expert Systems

Abstract: In this chapter, the steps necessary to develop a fuzzy expert system (FES) from the initial model design through to final system evaluation will be presented The current state-of-the-art of fuzzy modelling can be summed up informally as “anything goes” What this actually means is that the developer of the fuzzy model is faced with many steps in the process each with many options from which selections must be made In general, there is no specific or prescriptive method that can be used to make these choices, there are simply heuristics (“rules-of-thumb”) which may be employed to help guide the process Each of the steps will be described in detail, a summary of the main options available will be provided and the available heuristics to guide selection will be reviewed The steps will be illustrated by describing two cases studies: one will be a mock example of a fuzzy expert system for financial forecasting and the other will be a real example of a fuzzy expert system for a medical application The expert system framework considered here is restricted to rule-based systems While there are other frameworks that have been proposed for processing information utilising fuzzy methodologies, these are generally less popular in the context of fuzzy expert systems As a note on terminology, the term model is used to refer to the abstract conception of the process being studied and hence fuzzy model is the notional representation of the process in terms of fuzzy variables, rules and methods that together define the input-output mapping relationship In contrast, the term system (as in fuzzy expert system) is used to refer to the embodiment, realisation or implementation of the theoretical model in some software language or package A single model may be realised in different forms, for example, via differing software languages or differing hardware platforms Thus it should be realised that there is a subtle, but important, distinction between the evaluation of a fuzzy model of expertise and the evaluation of (one or more of) its corresponding fuzzy expert systems A model may be evaluated as accurately capturing or representing the domain problem under consideration, whereas