Membership function

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

Fuzzy sets and their application to pattern classification and clustering analysis

Abstract: Publisher Summary This chapter provides an overview of a conceptual framework for pattern classification and cluster analysis based on the theory of fuzzy sets. There is a connection between the theory of fuzzy sets and pattern classification. The development of the theory of Fuzzy drew much of its initial inspiration from problems relating to pattern classification, especially the analysis of proximity relations and the separation of subsets of Rn by hyperplanes. However, in a more fundamental way, the intimate connection between the theory of fuzzy sets and pattern classification rests on the fact that most real-world classes are fuzzy in nature, in the sense that the transition from membership to nonmembership in such classes is gradual rather than abrupt. Most of the practical problems in pattern classification do not lend themselves to a precise mathematical formulation, with the consequence that the less precise methods based on the linguistic approach prove to be better matched to the imprecision that is intrinsic in such problems.

Vaguely Quantified Rough Sets

Abstract: The hybridization of rough sets and fuzzy sets has focused on creating an end product that extends both contributing computing paradigms in a conservative way As a result, the hybrid theory inherits their respective strengths, but also exhibits some weaknesses In particular, although they allow for gradual membership, fuzzy rough sets are still abrupt in a sense that adding or omitting a single element may drastically alter the outcome of the approximations In this paper, we revisit the hybridization process by introducing vague quantifiers like "some" or "most" into the definition of upper and lower approximation The resulting vaguely quantified rough set (VQRS) model is closely related to Ziarko's variable precision rough set (VPRS) model

Distance and similarity measures for higher order hesitant fuzzy sets

Abstract: In this study, we extend the hesitant fuzzy set (HFS) to its higher order type and refer to it as the higher order hesitant fuzzy set (HOHFS). HOHFS is the actual extension of HFS that enables us to define the membership of a given element in terms of several possible generalized type of fuzzy sets (G-Type FSs). The rationale behind HOHFS can be seen in the case that the decision makers are not satisfied by providing exact values for the membership degrees and therefore the HFS is not applicable. However, in order to indicate HOHFSs have a good performance in decision making, we first introduce some information measures for HOHFSs and then apply them to multiple attribute decision making with higher order hesitant fuzzy information.

A new hybrid algorithm based on optimal fuzzy controller in multimachine power system

Abstract: In this article, a new methodology based on fuzzy proportional-integral-derivative PID controller is proposed to damp low frequency oscillation in multimachine power system where the parameters of proposed controller are optimized offline automatically by hybrid genetic algorithm GA and particle swarm optimization PSO techniques. This newly proposed method is more efficient because it cope with oscillations and different operating points. In this strategy, the controller is tuned online from the knowledge base and fuzzy interference. In the proposed method, for achieving the desired level of robust performance exact tuning of rule base and membership functions MF are very important. The motivation for using the GA and PSO as a hybrid method are to reduce fuzzy effort and take large parametric uncertainties in to account. This newly developed control strategy mixed the advantage of GA and PSO techniques to optimally tune the rule base and MF parameters of fuzzy controller that leads to a flexible controller with simple structure while is easy to implement. The proposed method is tested on three machine nine buses and 16 machine power systems with different operating conditions in present of disturbance and nonlinearity. The effectiveness of proposed controller is compared with robust PSS that tune using PSO and the fuzzy controller which is optimized rule base by GA through figure of demerit and integral of the time multiplied absolute value of the error performance indices. The results evaluation shows that the proposed method achieves good robust performance for a wide range of load change in the presents of disturbance and system nonlinearities and is superior to the other controllers. © 2014 Wiley Periodicals, Inc. Complexity 21: 78-93, 2015