Membership function

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

Process capability analyses based on fuzzy measurements and fuzzy control charts

Abstract: Process performance can be analyzed by using process capability indices (PCIs), which are summary statistics to depict the process location and dispersion successfully. Although they are very usable statistics, they have some limitations which prevent a deep and flexible analysis because of the crisp measurements and specification limits (SLs). If the specification limits or measurements are expressed by linguistic variables, traditional PCIs cause some misleading results. In this paper, the fuzzy set theory is used to add more information and flexibility to process capability analyses (PCA). For this aim, linguistic definition of the quality characteristic measurements are converted to fuzzy numbers and fuzzy PCIs are produced based on these measurements and fuzzy specification limits (SLs). Also fuzzy control charts are derived for fuzzy measurements of the related quality characteristic. They are used to increase the accuracy of PCA by determining whether or not the process is in statistical control. The fuzzy formulation of the indices C"p and C"p"k, which are the most used two traditional PCIs, are produced when SLs and measurements are both triangular (TFN) and trapezoidal fuzzy numbers (TrFN). The proposed methodologies are applied in a piston manufacturer in Konya's Industrial Area, Turkey.

Document retrieval using fuzzy-logic inference

Abstract: The results of a full-text, document search by a character string search processor are treated as vector patterns whose elements become a term match grade by use of a membership function of the term match frequency. The closest pattern to the query pattern is found by the similarity between the query pattern and each of the filed sample patterns. The similarity is calculated by use of fuzzy-logic. The similarity is ranked in order of similarity magnitude, thereby reducing the search time. The search time can be shortened by categorizing the filed patterns by term set and similarity to a cluster center pattern. If the cluster center patterns are stored, the closest cluster address can be inferred by fuzzy logic inference from the match between the query document and the term set or the similarity of the query to the cluster center.

Representing membership functions as points in high-dimensional spaces for fuzzy interpolation and extrapolation

Abstract: This paper introduces a new approach for fuzzy interpolation and extrapolation of sparse rule base comprising of membership functions with finite number of characteristic points. The approach calls for representing membership functions as points in high-dimensional Cartesian spaces using the locations of their characteristic points as coordinates. Hence, a fuzzy rule base can be viewed as a set of mappings between the antecedent and consequent spaces and the interpolation and extrapolation problem becomes searching for an image in the consequent space upon given an antecedent observation. The present approach divides observations into two groups: 1) observations within the antecedent spanning set contain the same geometric properties as the given antecedents; and 2) observations lying outside the antecedent spanning set contain new geometric properties beyond those of the given rules. Heuristic reasoning must therefore be applied. In this case, a two-step approach with certain flexibility to accommodate additional criteria and design objectives is formulated.

A genetic fuzzy k-Modes algorithm for clustering categorical data

Abstract: The fuzzy k-Modes algorithm introduced by Huang and Ng [Huang, Z., & Ng, M. (1999). A fuzzy k-modes algorithm for clustering categorical data. IEEE Transactions on Fuzzy Systems, 7(4), 446-452] is very effective for identifying cluster structures from categorical data sets. However, the algorithm may stop at locally optimal solutions. In order to search for appropriate fuzzy membership matrices which can minimize the fuzzy objective function, we present a hybrid genetic fuzzy k-Modes algorithm in this paper. To circumvent the expensive crossover operator in genetic algorithms (GAs), we hybridize GA with the fuzzy k-Modes algorithm and define the crossover operator as a one-step fuzzy k-Modes algorithm. Experiments on two real data sets are carried out to illustrate the performance of the proposed algorithm.

Automatically constructing grade membership functions of fuzzy rules for students' evaluation

Abstract: Some methods have been presented for applying the fuzzy set theory in education grading systems. In this paper, we present a method to automatically construct the grade membership functions of lenient-type grades, strict-type grades and normal-type grades of fuzzy rules, respectively, for students' evaluation. Based on the constructed grade membership functions, the system performs fuzzy reasoning to infer the scores of students. It provides a useful way to evaluate students' answerscripts in a smarter and fairer manner.