Interactive visualization of fuzzy set operations

2010 ◽  
Author(s):  
Yeseul Park ◽  
Jinah Park
Keyword(s):  
Fuzzy Set ◽  
Interactive Visualization ◽  
Set Operations

Disk Diagram: An Interactive Visualization Technique of Fuzzy Set Operations for the Analysis of Fuzzy Data

2010 ◽  
Vol 9 (3) ◽  
pp. 220-232 ◽  
Author(s):  
Yeseul Park ◽  
Jinah Park
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Visual Analytics ◽  
Interactive Visualization ◽  
Data Sets ◽  
Fuzzy Data ◽  
Visualization Technique ◽  
Data Set ◽  
Set Operations ◽  
Data Elements

Fuzzy set refers to the data set which does not have separate, distinct clusters, and they contain data elements whose membership degrees are between 0.0 and 1.0. Many fuzzy sets exist in the real world, and one of the important issues is to make a decision from the fuzzy sets using visual analytics tools by extracting information in the data set intuitively. To analyze the element data in fuzzy sets, the visualization of fuzzy sets needs to show an overview of the data with membership degree and the relationship among the sets. In this article, we suggest an interactive visualization technique of fuzzy set operations, called Disk Diagram, which offers distribution of fuzzy data and two scenarios to allow users to interpret inter-dependency among fuzzy sets. A Disk Diagram enables to depict complexity of fuzzy sets by showing the degree of resemblance between the sets with the layout of star coordinates. This article describes the use of a Disk Diagram with two different data sets such as fuzzy disease set and terror related words set. Lastly, we report the results of heuristic evaluation to show that our technique supports visual perception, usability, and knowledge discovery process in the areas of visual representation and interaction.

PYTHAGOREAN FUZZY MULTI SET AND ITS APPLICATIONS IN FISH FEED FOR INDIAN MAJOR CARP

2020 ◽  
Vol 9 (11) ◽  
pp. 9803-9811
Author(s):  
R. Sophia Porchelvi ◽  
V. Jayapriya
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Fish Feed ◽  
Uncertain Environments ◽  
Pythagorean Fuzzy Set ◽  
Indian Major Carp ◽  
Set Operations ◽  
Basic Set ◽  
Decision Making Problem ◽  
Exponential Distance

Pythagorean fuzzy set is an extension of Intutionistic fuzzy set, which is more capable of expressing and handling the uncertainty under uncertain environments, so that it was broadly applied in various fields. In this paper, we explored the concept of Pythagorean fuzzy multi set (PFMS). We describe some basic set operations of Pythagorean fuzzy multi set and also, we proposed sine exponential distance function. Finally, through an illustrative example it is shown how the proposed distance works in decision-making problem.

An Inference Algorithm for Electronic System Diagnostics at the Block Diagram Level

2006 ◽  
Vol 10 (2) ◽  
pp. 168-172
Author(s):  
Celso Bation Co ◽  
Keyword(s):  
Fuzzy Set ◽  
Block Diagram ◽  
Algorithm Design ◽  
Complete Information ◽  
Electronic System ◽  
Inference Algorithm ◽  
Input Information ◽  
Set Operations

Mathematical processes are designed to enable computers to emulate human inference in troubleshooting. Crisp set operations facilitate the interactive handling of incomplete but precise input information. Fuzzy set operations handle imprecise but complete information. The algorithm design we discuss here is limited to crisp set operations. We use diagnostics at the electronic system block diagram level to illustrate inference algorithm methodology. The algorithm deduces root causes and excludes intermediary causes in its conclusions. It also provides information for anticipating subsequent moves. We also consider results providing no conclusion, as is normally experienced by human troubleshooters under certain conditions.

scholarly journals Fuzzy Set Operations Based on the Theory of Falling Shadows

1993 ◽  
Vol 174 (1) ◽  
pp. 242-255 ◽  
Author(s):  
S.K. Tan ◽  
P.Z. Wang ◽  
E.S. Lee
Keyword(s):  
Fuzzy Set ◽  
Set Operations
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