Membership Functions From Similarity Relations

2005 ◽  
pp. 267-294
Author(s):  
John N. Mordeson ◽  
Kiran R. Bhutani ◽  
Azriel Rosenfeld
Keyword(s):  
Membership Functions ◽  
Similarity Relations

scholarly journals Rough sets in graphs using similarity relations

2022 ◽  
Vol 7 (4) ◽  
pp. 5790-5807
Author(s):  
Imran Javaid ◽  
◽  
Shahroz Ali ◽  
Shahid Ur Rehman ◽  
Aqsa Shah
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Sufficient Conditions ◽  
Membership Functions ◽  
Similarity Relations ◽  
Complete Bipartite Graphs ◽  
Essential Set ◽  
Essential Sets ◽  
Necessary And Sufficient ◽  
Clustering Criterion

<abstract><p>In this paper, we investigate the theory of rough set to study graphs using the concept of orbits. Rough sets are based on a clustering criterion and we use the idea of similarity of vertices under automorphism as a criterion. We introduce indiscernibility relation in terms of orbits and prove necessary and sufficient conditions under which the indiscernibility partitions remain the same when associated with different attribute sets. We show that automorphisms of the graph $ \mathcal{G} $ preserve the indiscernibility partitions. Further, we prove that for any graph $ \mathcal{G} $ with $ k $ orbits, any reduct $ \mathcal{R} $ consists of one element from $ k-1 $ orbits of the graph. We also study the rough membership functions for paths, cycles, complete and complete bipartite graphs. Moreover, we introduce essential sets and discernibility matrices induced by orbits of graphs and study their relationship. We also prove that every essential set consists of union of any two orbits of the graph.</p></abstract>

PERFORMANCE EVALUATION OF GENETIC DISTRIBUTED FUZZY CONTROLLERS FOR MULTI-PART-TYPE PRODUCTION LINE

2007 ◽  
Vol 06 (02) ◽  
pp. 115-128
Author(s):  
SEYED MAHDI HOMAYOUNI ◽  
TANG SAI HONG ◽  
NAPSIAH ISMAIL
Keyword(s):  
Genetic Algorithm ◽  
Performance Evaluation ◽  
Objective Function ◽  
Production Rate ◽  
Production Line ◽  
Production Systems ◽  
Membership Functions ◽  
Part Type ◽  
High Penalty ◽  
Single Part

Genetic distributed fuzzy (GDF) controllers are proposed for multi-part-type production line. These production systems can produce more than one part type. For these systems, "production rate" and "priority of production" for each part type is determined by production controllers. The GDF controllers have already been applied to single-part-type production systems. The methodology is illustrated and evaluated using a two-part-type production line. For these controllers, genetic algorithm (GA) is used to tune the membership functions (MFs) of GDF. The objective function of the GDF controllers minimizes the surplus level in production line. The results show that GDF controllers can improve the performance of production systems. GDF controllers show their abilities in reducing the backlog level. In production systems in which the backlog has a high penalty or is not allowed, the implementation of GDF controllers is advisable.

scholarly journals Intuitionistic Fuzzy Laplacian Twin Support Vector Machine for Semi-supervised Classification

2021 ◽  
Author(s):  
Jia-Bin Zhou ◽  
Yan-Qin Bai ◽  
Yan-Ru Guo ◽  
Hai-Xiang Lin
Keyword(s):  
Support Vector Machine ◽  
Negative Impact ◽  
Twin Support Vector Machine ◽  
Fuzzy Membership ◽  
Support Vector ◽  
Membership Functions ◽  
Fuzzy Membership Functions ◽  
Intuitionistic Fuzzy ◽  
Benchmark Datasets ◽  
The Impact

AbstractIn general, data contain noises which come from faulty instruments, flawed measurements or faulty communication. Learning with data in the context of classification or regression is inevitably affected by noises in the data. In order to remove or greatly reduce the impact of noises, we introduce the ideas of fuzzy membership functions and the Laplacian twin support vector machine (Lap-TSVM). A formulation of the linear intuitionistic fuzzy Laplacian twin support vector machine (IFLap-TSVM) is presented. Moreover, we extend the linear IFLap-TSVM to the nonlinear case by kernel function. The proposed IFLap-TSVM resolves the negative impact of noises and outliers by using fuzzy membership functions and is a more accurate reasonable classifier by using the geometric distribution information of labeled data and unlabeled data based on manifold regularization. Experiments with constructed artificial datasets, several UCI benchmark datasets and MNIST dataset show that the IFLap-TSVM has better classification accuracy than other state-of-the-art twin support vector machine (TSVM), intuitionistic fuzzy twin support vector machine (IFTSVM) and Lap-TSVM.

Design of back propagation optimized Nagar-Bardini structure-based interval type-2 fuzzy logic systems for fuzzy identification

2021 ◽  
pp. 014233122110066
Author(s):  
Yang Chen ◽  
Jiaxiu Yang
Keyword(s):  
Fuzzy Logic ◽  
Back Propagation ◽  
Membership Functions ◽  
Identification Problems ◽  
Fuzzy Logic Systems ◽  
Fuzzy Identification ◽  
Logic Systems ◽  
Academic Topic ◽  
Interval Type

In recent years, fuzzy identification based on system identification theory has become a hot academic topic. Interval type-2 fuzzy logic systems (IT2 FLSs) have become a rising technology. This paper designs a type of Nagar-Bardini (NB) structure-based singleton IT2 FLSs for fuzzy identification problems. The antecedents of primary membership functions of IT2 FLSs are chosen as Gaussian type-2 primary membership functions with uncertain standard deviations. Then, the back propagation algorithms are used to tune the parameters of IT2 FLSs according to the chain rule of derivation. Compared with the type-1 fuzzy logic systems, simulation studies show that the proposed IT2 FLSs can obtain better abilities of generalization for fuzzy identification problems.

Fuzzy risk assessment for electro-optical target tracker

2016 ◽  
Vol 33 (6) ◽  
pp. 830-851 ◽  
Author(s):  
Soumen Kumar Roy ◽  
A K Sarkar ◽  
Biswajit Mahanty
Keyword(s):  
Failure Mode ◽  
Failure Modes ◽  
Linear Equations ◽  
Mode Analysis ◽  
Failure Behavior ◽  
Membership Functions ◽  
Design And Development ◽  
Effect Analysis ◽  
Content Type ◽  
Criticality Analysis

Purpose – The purpose of this paper is to evolve a guideline for scientists and development engineers to the failure behavior of electro-optical target tracker system (EOTTS) using fuzzy methodology leading to success of short-range homing guided missile (SRHGM) in which this critical subsystems is exploited. Design/methodology/approach – Technology index (TI) and fuzzy failure mode effect analysis (FMEA) are used to build an integrated framework to facilitate the system technology assessment and failure modes. Failure mode analysis is carried out for the system using data gathered from technical experts involved in design and realization of the EOTTS. In order to circumvent the limitations of the traditional failure mode effects and criticality analysis (FMECA), fuzzy FMCEA is adopted for the prioritization of the risks. FMEA parameters – severity, occurrence and detection are fuzzifed with suitable membership functions. These membership functions are used to define failure modes. Open source linear programming solver is used to solve linear equations. Findings – It is found that EOTTS has the highest TI among the major technologies used in the SRHGM. Fuzzy risk priority numbers (FRPN) for all important failure modes of the EOTTS are calculated and the failure modes are ranked to arrive at important monitoring points during design and development of the weapon system. Originality/value – This paper integrates the use of TI, fuzzy logic and experts’ database with FMEA toward assisting the scientists and engineers while conducting failure mode and effect analysis to prioritize failures toward taking corrective measure during the design and development of EOTTS.

scholarly journals A Symmetry-Based Approach to Selecting Membership Functions and Its Relation to Chemical Kinetics

2013 ◽  
Author(s):  
Vladik Kreinovich ◽  
Olga Kosheleva ◽  
Jorge Y. Cabrera ◽  
Mario Gutierrez ◽  
Thavatchai Ngamsantivong
Keyword(s):  
Chemical Kinetics ◽  
Membership Functions
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