Membership function

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

A generalization of the Wilcoxon signed-rank test and its applications

Abstract: This paper extends the Wilcoxon signed-rank test to the case where the available observations are imprecise quantities, rather than crisp. To do this, the associated test statistic is extended, using the α-cuts approach. In addition, the concept of critical value is generalized to the case when the significance level is given by a fuzzy number. Finally, to accept or reject the null hypothesis of interest, a preference degree between two fuzzy sets is employed for comparing the observed fuzzy test statistic and fuzzy critical value.

Discovering Fuzzy Classification Rules with Genetic Programming and Co-evolution

Abstract: In essence, data mining consists of extracting knowledge from data. This paper proposes a co-evolutionary system for discovering fuzzy classification rules. The system uses two evolutionary algorithms: a genetic programming (GP) algorithm evolving a population of fuzzy rule sets and a simple evolutionary algorithm evolving a population of membership function definitions. The two populations co-evolve, so that the final result of the co-evolutionary process is a fuzzy rule set and a set of membership function definitions which are well adapted to each other. In addition, our system also has some innovative ideas with respect to the encoding of GP individuals representing rule sets. The basic idea is that our individual encoding scheme incorporates several syntactical restrictions that facilitate the handling of rule sets in disjunctive normal form. We have also adapted GP operators to better work with the proposed individual encoding scheme.

Discrete Interval Type 2 Fuzzy System Models Using Uncertainty in Learning Parameters

Abstract: Fuzzy system modeling (FSM) is one of the most prominent tools that can be used to identify the behavior of highly nonlinear systems with uncertainty Conventional FSM techniques utilize type 1 fuzzy sets in order to capture the uncertainty in the system However, since type 1 fuzzy sets express the belongingness of a crisp value x' of a base variable x in a fuzzy set A by a crisp membership value muA(x'), they cannot fully capture the uncertainties due to imprecision in identifying membership functions Higher types of fuzzy sets can be a remedy to address this issue Since, the computational complexity of operations on fuzzy sets are increasing with the increasing type of the fuzzy set, the use of type 2 fuzzy sets and linguistic logical connectives drew a considerable amount of attention in the realm of fuzzy system modeling in the last two decades In this paper, we propose a black-box methodology that can identify robust type 2 Takagi-Sugeno, Mizumoto and Linguistic fuzzy system models with high predictive power One of the essential problems of type 2 fuzzy system models is computational complexity In order to remedy this problem, discrete interval valued type 2 fuzzy system models are proposed with type reduction In the proposed fuzzy system modeling methods, fuzzy C-means (FCM) clustering algorithm is used in order to identify the system structure The proposed discrete interval valued type 2 fuzzy system models are generated by a learning parameter of FCM, known as the level of membership, and its variation over a specific set of values which generate the uncertainty associated with the system structure