g-Calculus-Based Compositional Rule of Inference

2006 ◽  
Vol 10 (4) ◽  
pp. 534-541
Author(s):  
Marta Takács ◽  
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Systems ◽  
Fuzzy Numbers ◽  
Approximate Reasoning ◽  
Triangular Fuzzy Numbers

We review a specific case, in which the investigated structure is a real semi-ring with pseudo-operations as a step toward investigating the problem of approximate reasoning in fuzzy systems. We focus on special-type fuzzy sets, i.e. <I>g</I> -generated quasi-triangular fuzzy numbers, and special <I>g</I> -generated t-norms and implication in fuzzy approximate reasoning.

scholarly journals Real-Time Fuzzy Data Processing Based on a Computational Library of Analytic Models

Data ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 59
Author(s):  
Yuriy Kondratenko ◽  
Nina Kondratenko
Keyword(s):  
Data Processing ◽  
Fuzzy Sets ◽  
Real Time ◽  
Fuzzy Numbers ◽  
Fuzzy Arithmetic ◽  
Fuzzy Data ◽  
Triangular Fuzzy Numbers ◽  
Arithmetic Operations ◽  
Automatic Mode ◽  
Analytic Models

This work focuses on fuzzy data processing in control and decision-making systems based on the transformation of real-timeseries and high-frequency data to fuzzy sets with further implementation of diverse fuzzy arithmetic operations. Special attention was paid to the synthesis of the computational library of horizontal and vertical analytic models for fuzzy sets as the results of fuzzy arithmetic operations. The usage of the developed computational library allows increasing the operating speed and accuracy of fuzzy data processing in real time. A computational library was formed for computing of such fuzzy arithmetic operations as fuzzy-maximum. Fuzzy sets as components of fuzzy data processing were chosen as triangular fuzzy numbers. The analytic models were developed based on the analysis of the intersection points between left and right branches of considered triangular fuzzy numbers with different relations between their parameters. Our study introduces the mask for the evaluation of the relations between corresponding parameters of fuzzy numbers that allows to determine the appropriate model from the computational library in automatic mode. The simulation results confirm the efficiency of the proposed computational library for different applications.

scholarly journals Integrated and Differentiated Spaces of Triangular Fuzzy Numbers

2017 ◽  
Vol 59 (1) ◽  
pp. 75-89 ◽  
Author(s):  
Murat Kirişci
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Applied Mathematics ◽  
Possibility Theory ◽  
Triangular Fuzzy Numbers ◽  
Wide Range ◽  
Versatile Tool ◽  
New Space ◽  
Matrix Domains ◽  
Short Time

AbstractFuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Fuzzy sets have be- come popular in every branch of mathematics such as analysis, topology, algebra, applied mathematics etc. Thus fuzzy sets triggered the creation of a wide range of research topics in all areas of science in a short time. In this paper, we use the triangular fuzzy numbers for matrix domains of sequence spaces with infinite matrices. We construct the new space with triangular fuzzy numbers and investigate to structural, topological and algebraic properties of these spaces.

A necessary condition for comparing and ranking of triangular fuzzy numbers on the basis of height-independent ranking techniques

2021 ◽  
Vol 24 (4) ◽  
pp. 269-277
Author(s):  
Alireza Sotoudeh-Anvari
Keyword(s):  
Fuzzy Sets ◽  
Open Problem ◽  
Fuzzy Numbers ◽  
Necessary Condition ◽  
Triangular Fuzzy Numbers ◽  
Ranking Methods ◽  
Effect Analysis ◽  
Suggested Approach ◽  
Signed Distance ◽  
Total Integral

The open problem of comparing fuzzy numbers as one of the most important issues in fuzzy sets has been studied by many researchers. However, this problem has not been solved up to now and perhaps it will never be fully answered. This work proposes a necessary condition for ranking of triangular fuzzy numbers on the basis of some efficient height-independent ranking methods such as centroids, total integral value, signed distance and defuzzification. To the best of our knowledge, this paper provides the first use of a necessary condition in ranking methods. Fortunately, suggested approach is very straightforward, fast and efficient to use in the real problems. To evaluate the suggested approach with the result of existing methods, six examples are presented. Finally, we apply this necessary condition for ranking fuzzy numbers to a fuzzy failure mode and effect analysis (FMEA) problem. The results show that our approach is practical and has reasonable outcome.

Totally Symmetric Type-2 Triangular Fuzzy Numbers

2018 ◽  
Vol 9 (11) ◽  
pp. 1717-1727
Author(s):  
Ajay Minj ◽  
Pathinathan T.
Keyword(s):  
Fuzzy Numbers ◽  
Triangular Fuzzy Numbers

ERP selection using picture fuzzy CODAS method

2021 ◽  
pp. 1-11
Author(s):  
Hacer Yumurtacı Aydoğmuş ◽  
Eren Kamber ◽  
Cengiz Kahraman
Keyword(s):  
Decision Analysis ◽  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Ideal Solution ◽  
Application Area ◽  
Erp System ◽  
Mcdm Method ◽  
Negative Ideal Solution ◽  
Picture Fuzzy Sets ◽  
System Selection

The purpose of this study is to develop an extension of CODAS method using picture fuzzy sets. In this respect, a new methodology is introduced to figure out how picture fuzzy numbers can be applied to CODAS method. COmbinative Distance-based Assessment (CODAS) is a new MCDM method proposed by Ghorabaee et al. Picture fuzzy sets (PFSs) are a new extension of ordinary fuzzy sets for representing human’s judgments having possibility more than two answers such as yes, no, refusal and neutral. Compared with other studies, the proposed method integrates multi-criteria decision analysis with picture fuzzy uncertainty based on Euclidean and Taxicab distances and negative ideal solution. ERP system selection problem is handled as the application area of the developed method, picture fuzzy CODAS. Results indicate that the new proposed method finds meaningful rankings through picture fuzzy sets. Comparative analyzes show that the presented method gives successful and robust results for the solutions of MCDM problems under fuzziness.

scholarly journals The Application of Fuzzy Theory in the Evaluation of Visual Images of Smartphone Rear Cameras

2021 ◽  
Vol 11 (8) ◽  
pp. 3555
Author(s):  
Chien-Hsiung Chen ◽  
Zhongzhen Lin
Keyword(s):  
Factor Analysis ◽  
Fuzzy Numbers ◽  
Fuzzy Theory ◽  
Consumer Perceptions ◽  
Visual Images ◽  
Triangular Fuzzy Numbers ◽  
Potential Consumer ◽  
Comprehensive Comparison ◽  
Different Shapes ◽  
The Relationship

In the present era, technology is developing rapidly. Smartphones play a significant part in people’s lives. However, the research on smartphones mainly focuses on the area of technological realization. The purposes of this study were to examine the relationship between the various rear cameras in smartphones and consumer perceptions, and to understand consumers’ purchasing intentions and preferences. Through the methods of multidimensional scaling (MDS), factor analysis and triangular fuzzy numbers, the visual images of the smartphone rear cameras were analyzed and discussed. The results indicate that the visual images taken by different shapes of rear camera are quite distinct in the categories of innovative and fashionable, and simple and pure, but less distinct in the categories of harmonious and ordered, premium and technical, and superior and valuable. Through a comprehensive comparison, four groups whose images were similar were created. The outcome effectively reflects the potential consumer demands for smartphone rear camera patterns, providing insights for design practices in the smartphone industry.

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