scholarly journals Fuzzy sets and presheaves

2019 ◽  
Vol 1 ◽  
pp. 3
Author(s):  
John F. Jardine
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
General Framework ◽  
Theoretic Approach ◽  
Data Set

This paper presents a presheaf theoretic approach to the construction of fuzzy sets, which builds on Barr's description of fuzzy sets as sheaves of monomorphisms on a locale. Presheaves are used to give explicit descriptions of limit and colimit descriptions in fuzzy sets on an interval. The Boolean localization construction for sheaves on a locale specializes to a theory of stalks for sheaves and presheaves on an interval.The system V∗(X) of Vietoris-Rips complexes for a data set X is both a simplicial fuzzy set and a simplicial sheaf in this general framework. This example is explicitly discussed through a series of examples.

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.

Complex intuitionistic fuzzy Maclaurin symmetric mean operators and its application to emergency program selection

2021 ◽  
pp. 1-22
Author(s):  
Riaz Ali ◽  
Saleem Abdullah ◽  
Shakoor Muhammad ◽  
Muhammad Naeem ◽  
Ronnason Chinram
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Functions ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Program Selection ◽  
Maclaurin Symmetric Mean ◽  
Complex Intuitionistic Fuzzy Set

Due to the indeterminacy and uncertainty of the decision-makers (DM) in the complex decision making problems of daily life, evaluation and aggregation of the information usually becomes a complicated task. In literature many theories and fuzzy sets (FS) are presented for the evaluation of these decision tasks, but most of these theories and fuzzy sets have failed to explain the uncertainty and vagueness in the decision making issues. Therefore, we use complex intuitionistic fuzzy set (CIFS) instead of fuzzy set and intuitionistic fuzzy set (IFS). A new type of aggregation operation is also developed by the use of complex intuitionistic fuzzy numbers (CIFNs), their accuracy and the score functions are also discussed in detail. Moreover, we utilized the Maclaurin symmetric mean (MSM) operator, which have the ability to capture the relationship among multi-input arguments, as a result, CIF Maclarurin symmetric mean (CIFMSM) operator and CIF dual Maclaurin symmetric mean (CIFDMSM) operator are presented and their characteristics are discussed in detail. On the basis of these operators, a MAGDM method is presented for the solution of group decision making problems. Finally, the validation of the propounded approach is proved by evaluating a numerical example, and by the comparison with the previously researched results.

A fuzzy set theoretic approach to validate simulation models

2006 ◽  
Vol 16 (4) ◽  
pp. 375-398 ◽  
Author(s):  
Jurgen Martens ◽  
Ferdi Put ◽  
Etienne Kerre
Keyword(s):  
Fuzzy Set ◽  
Simulation Models ◽  
Theoretic Approach

Multi-criteria decision making and pattern recognition based on similarity measures for Fermatean fuzzy sets

2021 ◽  
pp. 1-17
Author(s):  
Changlin Xu ◽  
Juhong Shen
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
New Method ◽  
Fuzzy Decision Making ◽  
Multi Criteria Decision Making

 Higher-order fuzzy decision-making methods have become powerful tools to support decision-makers in solving their problems effectively by reflecting uncertainty in calculations better than crisp sets in the last 3 decades. Fermatean fuzzy set proposed by Senapati and Yager, which can easily process uncertain information in decision making, pattern recognition, medical diagnosis et al., is extension of intuitionistic fuzzy set and Pythagorean fuzzy set by relaxing the restraint conditions of the support for degrees and support against degrees. In this paper, we focus on the similarity measures of Fermatean fuzzy sets. The definitions of the Fermatean fuzzy sets similarity measures and its weighted similarity measures on discrete and continuous universes are given in turn. Then, the basic properties of the presented similarity measures are discussed. Afterward, a decision-making process under the Fermatean fuzzy environment based on TOPSIS method is established, and a new method based on the proposed Fermatean fuzzy sets similarity measures is designed to solve the problems of medical diagnosis. Ultimately, an interpretative multi-criteria decision making example and two medical diagnosis examples are provided to demonstrate the viability and effectiveness of the proposed method. Through comparing the different methods in the multi-criteria decision making and the medical diagnosis application, it is found that the new method is as efficient as the other methods. These results illustrate that the proposed method is practical in dealing with the decision making problems and medical diagnosis problems.

Star Neutrosophic Fuzzy Topological Space

2020 ◽  
pp. 77-82
Author(s):  
A.A A.A.Salama ◽  
◽  
◽  
◽  
Hewayda ElGhawalby ◽  
...  
Keyword(s):  
Topological Space ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Space ◽  
New Type

In this paper, we aim to develop a new type of neutrosophic fuzzy set called the star neutrosophic fuzzy set as a generalization to star neutrosophic crisp set defined in by Salama et al.[8], and study some of its properties. Adedd to, we introduce the notion of star neutrosophic fuzzy topological space as a generalization to some topological consepts as star neutrosophic fuzzy closure, and star neutrosophic fuzzy interior. Finally, we extend the concepts of fuzzy topological space, and intuitionistic fuzzy topological space to the case of star neutrosophic fuzzy sets.

scholarly journals Intelligent Information Retrieval Using Hybrid of Fuzzy Set and Trust

2017 ◽  
Vol 10 (2) ◽  
pp. 311-325
Author(s):  
Suruchi Chawla
Keyword(s):  
Information Retrieval ◽  
Fuzzy Set ◽  
Query Expansion ◽  
Information Need ◽  
Data Set ◽  
Search Results ◽  
Intelligent Information Retrieval ◽  
Main Challenge ◽  
Fuzzy Query ◽  
Intelligent Information

The main challenge for effective web Information Retrieval(IR) is to infer the information need from user’s query and retrieve relevant documents. The precision of search results is low due to vague and imprecise user queries and hence could not retrieve sufficient relevant documents. Fuzzy set based query expansion deals with imprecise and vague queries for inferring user’s information need. Trust based web page recommendations retrieve search results according to the user’s information need. In this paper an algorithm is designed for Intelligent Information Retrieval using hybrid of Fuzzy set and Trust in web query session mining to perform Fuzzy query expansion for inferring user’s information need and trust is used for recommendation of web pages according to the user’s information need. Experiment was performed on the data set collected in domains Academics, Entertainment and Sports and search results confirm the improvement of precision.

scholarly journals Convexity of hesitant fuzzy sets based on aggregation functions

2020 ◽  
pp. 45-45
Author(s):  
Pedro Huidobro ◽  
Pedro Alonso ◽  
Vladimír Janis ◽  
Susana Montes
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Fuzzy Optimization ◽  
Hesitant Fuzzy Set ◽  
Hesitant Fuzzy Sets ◽  
Geometric Properties ◽  
Aggregation Functions ◽  
Definition Of

Convexity is one of the most important geometric properties of sets and a useful concept in many fields of mathematics, like optimization. As there are also important applications making use of fuzzy optimization, it is obvious that the studies of convexity are also frequent. In this paper we have extended the notion of convexity for hesitant fuzzy sets in order to fulfill some necessary properties. Namely, we have found an appropriate definition of convexity for hesitant fuzzy sets on any ordered universe based on aggregation functions such that it is compatible with the intersection, that is, the intersection of two convex hesitant fuzzy sets is a convex hesitant fuzzy set and it fulfills the cut worthy property.

scholarly journals Some Operational Computation for Intuitionistic or Pythagorean Fuzzy Set Using C-Programming

2020 ◽  
pp. 123-132
Author(s):  
Jwngsar Moshahary
Keyword(s):  
Fuzzy Sets ◽  
Programming Language ◽  
Fuzzy Set ◽  
Pythagorean Fuzzy Set ◽  
Pythagorean Fuzzy Sets ◽  
C Programming Language ◽  
C Programming

Intuitionistic or pythagorean fuzzy sets are the best tools to deal with uncertainty or ambiguity to solve diverse disciplines of application problems. It is often difficult to compute union, intersection, and complements when it comes to a large number of members contained in the set, also it is difficult to check whether it is a subset or not. Here, we used the C-programming language to overcome the problems, and then it is found that more effective and realistic results have been obtained.

scholarly journals Evidence Theory in Picture Fuzzy Set Environment

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Harish Garg ◽  
R. Sujatha ◽  
D. Nagarajan ◽  
J. Kavikumar ◽  
Jeonghwan Gwak
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Evidence Theory ◽  
Belief Function ◽  
Uncertain Information ◽  
Interval Probability ◽  
Dempster Shafer Theory ◽  
Effective Manner ◽  
Picture Fuzzy Set ◽  
Shafer Theory

Picture fuzzy set is the most widely used tool to handle the uncertainty with the account of three membership degrees, namely, positive, negative, and neutral such that their sum is bound up to 1. It is the generalization of the existing intuitionistic fuzzy and fuzzy sets. This paper studies the interval probability problems of the picture fuzzy sets and their belief structure. The belief function is a vital tool to represent the uncertain information in a more effective manner. On the other hand, the Dempster–Shafer theory (DST) is used to combine the independent sources of evidence with the low conflict. Keeping the advantages of these, in the present paper, we present the concept of the evidence theory for the picture fuzzy set environment using DST. Under this, we define the concept of interval probability distribution and discuss its properties. Finally, an illustrative example related to the decision-making process is employed to illustrate the application of the presented work.

LRE Fault Detection and Isolation Based on Fuzzy Direction Neural Network

2015 ◽  
Vol 727-728 ◽  
pp. 880-883
Author(s):  
Min Chao Huang ◽  
Bao Yu Xing
Keyword(s):  
Neural Network ◽  
Fault Detection ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Rocket Engine ◽  
Fault Detection And Isolation ◽  
Liquid Rocket Engine ◽  
Direction Vector ◽  
Liquid Rocket ◽  
Turbo Pump

A fuzzy directions neural network used for fault detection and isolation (FDI) of a liquid rocket engine (LRE) is presented in this paper. Neural network utilizes fuzzy sets as engine fault classes. Each fuzzy set is an aggregate of fuzzy direction bodies. A fuzzy direction body is described by a direction vector, an included angle and two radii. FDI simulation of the turbo-pump fed liquid rocket engine demonstrates the strong qualities of the fuzzy direction neural network.

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