Graphical Representation of Intuitionistic Membership Functions for Its Efficient Use in Intuitionistic Fuzzy Systems

2018 ◽  
pp. 239-250
Author(s):  
Amaury Hernandez-Aguila ◽  
Mario Garcia-Valdez ◽  
Oscar Castillo
Keyword(s):  
Fuzzy Systems ◽  
Graphical Representation ◽  
Membership Functions ◽  
Intuitionistic Fuzzy

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.

Computationally Simple and Efficient Method for Solving Real-Life Mixed Intuitionistic Fuzzy 3D Assignment Problems

2022 ◽  
Vol 14 (1) ◽  
pp. 0-0
Keyword(s):  
Assignment Problem ◽  
Graphical Representation ◽  
Real Life ◽  
Optimal Solution ◽  
Future Research ◽  
Assignment Problems ◽  
3 Dimensional ◽  
Intuitionistic Fuzzy ◽  
Comparison Results ◽  
Future Research Directions

This article addresses the 3-dimensional mixed intuitionistic fuzzy assignment problems (3D-MIFAPs). In this article, firstly, the author formulates an assignment problem (AP) and assumes the parameters are in uncertainty with hesitation. Secondly, based on the nature of the parameter the author defines various types of solid assignment problem (SAP) in uncertain environment. Thirdly, to solve 3D-MIFAP the PSK method for finding an optimal solution of fully intuitionistic fuzzy assignment problem (FIFAP) is extended by the author. Fourthly, the author presents the proofs of the proposed theorems and corollary. Fifthly, the proposed approach is illustrated with three numerical examples and the optimal objective value of 3D-MIFAP is obtained in the form of intuitionistic fuzzy number and the solution is checked with MATLAB and their coding are also given by the author. Sixthly, the author presents the comparison results and their graphical representation, merits and demerits of the proposed and existing methods and finally the author presents conclusion and future research directions.

On switched control of discrete-time Takagi-Sugeno fuzzy systems with unknown membership functions

2018 ◽  
Author(s):  
Diogo R. de Oliveira ◽  
Gilberto R. dos Santos ◽  
Marcelo C. M. Teixeira ◽  
Edvaldo Assuncao ◽  
Rodrigo Cardim ◽  
...  
Keyword(s):  
Discrete Time ◽  
Fuzzy Systems ◽  
Membership Functions ◽  
Switched Control ◽  
Takagi Sugeno

scholarly journals THE REAL-WORLD-SEMANTICS INTERPRETABILITY OF LINGUISTIC RULE BASES AND THE APPROXIMATE REASONING METHOD OF FUZZY SYSTEMS

2019 ◽  
Vol 57 (2) ◽  
pp. 233
Author(s):  
Nguyen Thu Anh ◽  
Tran Thai Son
Keyword(s):  
Real World ◽  
Fuzzy Systems ◽  
Graphical Representation ◽  
Approximate Reasoning ◽  
Rule Base ◽  
Computational Semantics ◽  
Mathematical Basis ◽  
The Real ◽  
Computational Structure ◽  
Application Problem

The real-world-semantics interpretability concept of fuzzy systems introduced in [1] is new for the both methodology and application and is necessary to meet the demand of establishing a mathematical basis to construct computational semantics of linguistic words so that a method developed based on handling the computational semantics of linguistic terms to simulate a human method immediately handling words can produce outputs similar to the one produced by the human method. As the real world of each application problem having its own structure which is described by certain linguistic expressions, this requirement can be ensured by imposing constraints on the interpretation assigning computational objects in the appropriate computational structure to the words so that the relationships between the computational semantics in the computational structure is the image of relationships between the real-world objects described by the word-expressions. This study will discuss more clearly the concept of real-world-semantics interpretability and point out that such requirement is a challenge to the study of the interpretability of fuzzy systems, especially for approaches within the fuzzy set framework. A methodological challenge is that it requires both the computational expression representing a given linguistic fuzzy rule base and an approximate reasoning method working on this computation expression must also preserve the real-world semantics of the application problem. Fortunately, the hedge algebra (HA) based approach demonstrates the expectation that the graphical representation of the rule of fuzzy systems and the interpolation reasoning method on them are able to preserve the real-world semantics of the real-world counterpart of the given application problem.

Novel Similarity Measures, Entropy of Intuitionistic Fuzzy Sets and their Application in Software Quality Evaluation

2021 ◽  
Author(s):  
Xuan Thao Nguyen ◽  
Shuo Yan Chou
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Entropy Measure ◽  
Uncertain Information ◽  
Membership Functions ◽  
Software Projects ◽  
Intuitionistic Fuzzy ◽  
Software Quality Evaluation

Abstract Intuitionistic fuzzy sets (IFSs), including member and nonmember functions, have many applications in managing uncertain information. The similarity measures of IFSs proposed to represent the similarity between different types of sensitive fuzzy information. However, some existing similarity measures do not meet the axioms of similarity. Moreover, in some cases, they could not be applied appropriately. In this study, we proposed some novel similarity measures of IFSs constructed by combining the exponential function of membership functions and the negative function of non-membership functions. In this paper, we also proposed a new entropy measure as a stepping stone to calculate the weights of the criteria in the proposed multi-criteria decision making (MCDM) model. The similarity measures used to rank alternatives in the model. Finally, we used this MCDM model to evaluate the quality of software projects.

Fuzzy application in the prediction of axial compressive strength of Portland concrete based on traces and curing time

2021 ◽  
Author(s):  
DENNIS SANTOS TAVARES ◽  
BRUNA CAMPOS AMARAL ◽  
DAVID AUGUSTO RIBEIRO ◽  
TADAYUKI YANAGI JUNIOR ◽  
FRANCISCO CARLOS GOMES ◽  
...  
Keyword(s):  
Compressive Strength ◽  
Construction Industry ◽  
Fuzzy Systems ◽  
Main Property ◽  
Membership Functions ◽  
Curing Time ◽  
Axial Compressive Strength ◽  
Compressive Strength Of Concrete ◽  
Input Variables ◽  
Main Material

Concrete is the main material used in the construction industry and its main property is the axial compressive strength. Usually the prediction of compressive strength is restricted to limited empirical equations and / or laboratory dosages. The objective of this study is to develop fuzzy systems capable of obtaining the axial compressive strength of concrete, from the mixtures and curing time. Several fuzzy systems were developed with Mamdani inference and different defuzzification methods. Triangular membership functions were adopted for the input variables in all systems and triangular functions for the output variables. The developed models were simulated and evaluated using three statistical indexes. The systems with Mamdani inference and centroid, bisector and mom defuzzification proved to be reliable and highly effective. The best performance was obtained by the fuzzy centroid defuzzification system according to the analyses.,

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