Showing papers on "Membership function published in 2005"

A heuristic fuzzy logic approach to EMG pattern recognition for multifunctional prosthesis control

Abstract: This paper presents a heuristic fuzzy logic approach to multiple electromyogram (EMG) pattern recognition for multifunctional prosthesis control. Basic signal statistics (mean and standard deviation) are used for membership function construction, and fuzzy c-means (FCMs) data clustering is used to automate the construction of a simple amplitude-driven inference rule base. The result is a system that is transparent to, and easily "tweaked" by, the prosthetist/clinician. Other algorithms in current literature assume a longer period of unperceivable delay, while the system we present has an update rate of 45.7 ms with little postprocessing time, making it suitable for real-time application. Five subjects were investigated (three with intact limbs, one with a unilateral transradial amputation, and one with a unilateral transradial limb-deficiency from birth). Four subjects were used for system offline analysis, and the remaining intact-limbed subject was used for system real-time analysis. We discriminated between four EMG patterns for subjects with intact limbs, and between three patterns for limb-deficient subjects. Overall classification rates ranged from 94% to 99%. The fuzzy algorithm also demonstrated success in real-time classification, both during steady state motions and motion state transitioning. This functionality allows for seamless control of multiple degrees-of-freedom in a multifunctional prosthesis.

On the generalization of fuzzy rough sets

Abstract: Rough sets and fuzzy sets have been proved to be powerful mathematical tools to deal with uncertainty, it soon raises a natural question of whether it is possible to connect rough sets and fuzzy sets. The existing generalizations of fuzzy rough sets are all based on special fuzzy relations (fuzzy similarity relations, T-similarity relations), it is advantageous to generalize the fuzzy rough sets by means of arbitrary fuzzy relations and present a general framework for the study of fuzzy rough sets by using both constructive and axiomatic approaches. In this paper, from the viewpoint of constructive approach, we first propose some definitions of upper and lower approximation operators of fuzzy sets by means of arbitrary fuzzy relations and study the relations among them, the connections between special fuzzy relations and upper and lower approximation operators of fuzzy sets are also examined. In axiomatic approach, we characterize different classes of generalized upper and lower approximation operators of fuzzy sets by different sets of axioms. The lattice and topological structures of fuzzy rough sets are also proposed. In order to demonstrate that our proposed generalization of fuzzy rough sets have wider range of applications than the existing fuzzy rough sets, a special lower approximation operator is applied to a fuzzy reasoning system, which coincides with the Mamdani algorithm.

From soft sets to information systems

Abstract: This paper discusses the relationship between soft sets and information systems. It is shown that soft sets are a class of special information systems. After soft sets are extended to several classes of general cases, the more general results also show that partition-type soft sets and information systems have the same formal structures, and that fuzzy soft sets and fuzzy information systems are equivalent.

Fuzzy Cluster Analysis

Abstract: Usually in cluster analysis, an object is a member of one and only one cluster, a property described as ‘crisp’ membership. Fuzzy cluster analysis allows an object to have partial membership in more than one cluster. Selecting a good membership function is important to the success of the methods. The Grade of Membership model – which has a long history of usage in other contexts – is proposed as a straightforward way of performing fuzzy cluster analysis. The Grade of Membership model is illustrated by an example involving gene expression data. Keywords: Fuzzy cluster; grade of membership; membership function

Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making

Abstract: Intuitionistic fuzzy sets are extensions of fuzzy sets. Their elements have two degrees – a degree of membership and a degree of non-membership so that their sum is smaller or equal to 1. Intuitionistic fuzzy interpretations of the processes of multi-person and of multi-measurement tool multi-criteria decision makings are discussed in this paper.

Study on the Universality of the Normal Cloud Model

Abstract: The distribution function is an important tool in the study of the stochastic variances. The normal distribution is very popular in the nature and our society. The idea of membership functions is the foundation of the fuzzy sets theory. While the fuzzy theory is widely used, the completely certain membership function that has no any fuzziness at all has been the bottleneck of the applications of this theory.Cloud models are the effective tools in transforming between qualitative concepts and their quantitative expressions. It can represent the fuzziness and randomness and their relations of uncertain concepts. Also cloud models can show the concept granularity in multi-scale spaces by the digital characteristic Entropy (En). The normal cloud model not only broadens the form conditions of the normal distribution but also makes the normal membership function be the expectation of the random membership degree. In this paper, the universality of the normal cloud model is proved, which is more superior and easier, and can fit the fuzziness and gentleness of human cognitive processing.It would be more applicable and universal in the representation of uncertain notions.

Application of fuzzy goal programming technique to land use planning in agricultural system

Abstract: This paper presents how fuzzy goal programming can be efficiently used for modelling and solving land-use planning problems in agricultural systems for optimal production of several seasonal crops in a planning year. In the model formulation of the problem, utilization of total cultivable land, supply of productive resources, aspiration levels of various production of crops as well as the total expected profit from the farm are fuzzily described. In the decision-making situation, minimization of the under-deviational variables of the membership goals with highest membership value (unity) as their achievement levels defined for the membership functions of the fuzzy goals of the problem on the basis of the priorities of importance of achieving the aspired levels of the fuzzy goals to the extent possible is considered. As a study region, the District Nadia, West Bengal, India is taken into account. To expound the potential use of the approach, the model solution is compared with the existing cropping plan of the District as well as a solution of the problem obtained by using the additive fuzzy goal programming model studied by Tiwari et al. (Fuzzy sets and systems 24(1987)27.) previously.

A probabilistic fuzzy logic system for modeling and control

Abstract: In this paper, a probabilistic fuzzy logic system (PFLS) is proposed for the modeling and control problems. Similar to the ordinary fuzzy logic system (FLS), the PFLS consists of the fuzzification, inference engine and defuzzification operation to process the fuzzy information. Different to the FLS, it uses the probabilistic modeling method to improve the stochastic modeling capability. By using a three-dimensional membership function (MF), the PFLS is able to handle the effect of random noise and stochastic uncertainties existing in the process. A unique defuzzification method is proposed to simplify the complex operation. Finally, the proposed PFLS is applied to a function approximation problem and a robotic system. It shows a better performance than an ordinary FLS in stochastic circumstance.

Fuzzy statistics: hypothesis testing

Abstract: Our method of estimation of parameters in statistics uses a set of confidence intervals producing a triangular shaped fuzzy number for the estimator. Using this fuzzy estimator in hypothesis testing produces a fuzzy test statistic and fuzzy critical values in fuzzy hypothesis testing. We show how these fuzzy sets may be used to derive the usual conclusion of: (1) reject the null hypothesis, or (2) do not reject the null hypothesis.

A decision support system applying an integrated fuzzy model for long- term forest fire risk estimation

Abstract: Fire is the main cause of forest destruction in Mediterranean basin countries. Long-term prediction is intended for long-term planning which may serve to characterize and cluster regions as subject to high or low fire risk. This will enable the development of a rational and sensible forest fire prevention and protection policy. The problem with the existing approaches of long-term forest fire risk clustering is that they use crisp sets applying specific cluster boundaries. On the other hand, fuzzy algebra can provide reliable and flexible means of modeling that can be applied by a suitable decision support system. Given a specific area of interest, the evaluation of the long-term forest fire risk can be performed by the use of a triangular and a trapezoidal membership function. The decision support system that has been developed applies an inference mechanism that is based on various aspects of fuzzy sets and fuzzy machine learning techniques. The system has been applied in Greece, but it can be used on a global basis. Results show that the system successfully estimates the forest fire risky areas.

Assigning Membership in a Fuzzy Set Analysis

Abstract: This article provides a largely nontechnical discussion of the acquisition of membership values in fuzzy set analyses. First the basic properties of a membership are discussed. Then the three common strategies of membership assignment—direct subjective assignment, indirect subjective assignment, and transformation—are critically examined in turn. Examples are used to illustrate the techniques. The connection with existing psychometric and statistical methods is particularly emphasized, focusing on the notion of a membership value as a random variable as a means to assess uncertainty in assignment.

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

Multi-criteria Group Decision Making Using A Modified Fuzzy TOPSIS Procedure

Abstract: In this paper we propose a modified fuzzy technique for order performance by similarity to ideal solution (modified fuzzy TOPSIS) for the multi-criteria decision making (MCDM) problem when there is a group of decision makers. Regarding the value of the truth that a fuzzy number is greater than or equal to another fuzzy number, a new distance measure is proposed in this paper. This distance measure calculates the distance of each fuzzy number from both fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS). Then, the alternative which is simultaneously closer to FPIS and farther from FNIS would be selected as the best choice. To clarify our proposed procedure, a numerical example is discussed

Interval-valued Fuzzy Sets, Possibility Theory and Imprecise Probability

Abstract: Interval-valued fuzzy sets were proposed thirty years ago as a natural extension of fuzzy sets. Many variants of these mathematical objects exist, under various names. One popular variant proposed by Atanassov starts by the specification of membership and non-membership functions. This paper focuses on interpretations of such extensions of fuzzy sets, whereby the two membership functions that define them can be justified in the scope of some information representation paradigm. It particularly focuses on a recent proposal by Neumaier, who proposes to use intervalvalued fuzzy sets under the name “clouds”, as an e! cient method to represent a family of probabilities. We show the connection between clouds, interval-valued fuzzy sets and possibility theory.