Fuzzy number

About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.

Analysis of direct action fuzzy PID controller structures

Abstract: The majority of the research work on fuzzy PID controllers focuses on the conventional two-input PI or PD type controller proposed by Mamdani (1974). However, fuzzy PID controller design is still a complex task due to the involvement of a large number of parameters in defining the fuzzy rule base. This paper investigates different fuzzy PID controller structures, including the Mamdani-type controller. By expressing the fuzzy rules in different forms, each PLD structure is distinctly identified. For purpose of analysis, a linear-like fuzzy controller is defined. A simple analytical procedure is developed to deduce the closed form solution for a three-input fuzzy inference. This solution is used to identify the fuzzy PID action of each structure type in the dissociated form. The solution for single-input-single-output nonlinear fuzzy inferences illustrates the effect of nonlinearity tuning. The design of a fuzzy PID controller is then treated as a two-level tuning problem. The first level tunes the nonlinear PID gains and the second level tunes the linear gains, including scale factors of fuzzy variables. By assigning a minimum number of rules to each type, the linear and nonlinear gains are deduced and explicitly presented. The tuning characteristics of different fuzzy PID structures are evaluated with respect to their functional behaviors. The rule decoupled and one-input rule structures proposed in this paper provide greater flexibility and better functional properties than the conventional fuzzy PHD structures.

A novel intuitionistic fuzzy C means clustering algorithm and its application to medical images

Abstract: This paper presents a novel intuitionistic fuzzy C means clustering method using intuitionistic fuzzy set theory. The intuitionistic fuzzy set theory considers another uncertainty parameter which is the hesitation degree that arises while defining the membership function and thus the cluster centers may converge to a desirable location than the cluster centers obtained using fuzzy C means algorithm. Also a new objective function which is the intuitionistic fuzzy entropy is incorporated in the conventional fuzzy C means clustering algorithm. This is done to maximize the good points in the class. This clustering method is used in clustering different regions of the CT scan brain images and these may be used to identify the abnormalities in the brain. Experimental results show the effectiveness of the proposed method in contrast to conventional fuzzy C means algorithms and also type II fuzzy algorithm.

A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems

Abstract: The concept of an intuitionistic fuzzy number (IFN) is of importance for quantifying an ill-known quantity, and the ranking of IFNs is a very difficult problem. The aim of this paper is to introduce the concept of a triangular IFN (TIFN) as a special case of the IFN and develop a new methodology for ranking TIFNs. Firstly the concepts of TIFNs and cut sets as well as arithmetical operations are introduced. Then the values and ambiguities of the membership function and the non-membership function for a TIFN are defined. A new ranking method is developed on the basis of the concept of a ratio of the value index to the ambiguity index and applied to multiattribute decision making problems in which the ratings of alternatives on attributes are expressed with TIFNs. The validity and applicability of the proposed method, as well as analysis of the comparison with other methods, are illustrated with a real example.