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.

scholarly journals Graphical representations of membership functions of maximum and minimum of two fuzzy numbers using computer program

2012 ◽  
Vol 31 ◽  
pp. 105-115 ◽  
Author(s):  
Shapla Shirin ◽  
Goutam Saha
Keyword(s):  
Computer Program ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Decision Makers ◽  
Graphical Representations ◽  
Fuzzy Logics ◽  
Triangular Fuzzy Numbers ◽  
Different Types ◽  
Analytic Expressions ◽  
Short Time

The set of real numbers R is linearly ordered, but in the fuzzy set theory, this relation is true only for some set of fuzzy numbers where the sets of fuzzy numbers are expressed as the linguistic variables. Different types of Fuzzy machines based on fuzzy logic have been invented where fuzzy logics are described by fuzzy numbers and the fuzzy numbers are needed to compare. Besides these, many techniques are available to assist decision-makers to compare different fuzzy numbers. For these reasons, it is necessary to compute the maximum and the minimum of fuzzy numbers. Till now many researchers introduced different methods for computation, which are done by hand calculation, but these are very disgusting and time consuming to us. In this paper, we presents an algorithm to compute the maximum and the minimum of any two triangular fuzzy numbers, so that one can compare two fuzzy numbers easily in a short time and visualize the analytic expressions and the graphical representations of the maximum and the minimum of any two triangular fuzzy numbers. By using CAS (MATHEMATICA 7.0), the algorithm is implemented in a computer program in order to do these. This algorithm can easily be extended to apply for any type of fuzzy numbers which are comparable. Even it is able to compare more than two fuzzy numbers by comparing the maximum fuzzy number or minimum fuzzy number with another new fuzzy number.DOI: http://dx.doi.org/10.3329/ganit.v31i0.10313GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 31 (2011) 105-115

scholarly journals Fuzzy Cubic Spline Interpolation with Triangular Fuzzy Numbers

2020 ◽  
Vol 8 (5) ◽  
pp. 4164-4166
Keyword(s):  
Fuzzy Numbers ◽  
Spline Interpolation ◽  
Applied Mathematics ◽  
Cubic Spline ◽  
Triangular Fuzzy Numbers ◽  
Best Approximations ◽  
Fuzzy Function ◽  
Novel Approach ◽  
Set Of Points ◽  
Spline Polynomial

In applied mathematics, the salient and engrossing aspect is how to best approximate a function in a given space. In this paper a cubic spline polynomial approximation as best approximations of fuzzy function on a discrete set of points. In this work a novel approach is adopted to show this method using Triangular fuzzy numbers.

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.

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 A Distinctive Symmetric Analyzation of Improving Air Quality Using Multi-Criteria Decision Making Method under Uncertainty Conditions

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1858
Author(s):  
Samayan Narayanamoorthy ◽  
Arumugam Anuja ◽  
Daekook Kang ◽  
Joseph Varghese Kureethara ◽  
Samayan Kalaiselvan ◽  
...  
Keyword(s):  
Decision Making ◽  
Air Quality ◽  
Tamil Nadu ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Number ◽  
Multi Criteria Decision Making ◽  
Triangular Fuzzy Numbers ◽  
Weighting Method ◽  
Wide Range ◽  
Interval Valued

This world has a wide range of technologies and possibilities that are available to control air pollution. Still, finding the best solution to control the contamination of the air without having any impact on humans is a complicated task. This proposal helps to improve the air quality using the multi-criteria decision making method. The decision to improve air quality is a challenging problem with today’s technology and environmental development level. The multi-criteria decision making method is quite often faced with conditions of uncertainty, which can be tackled by employing fuzzy set theory. In this paper, based on an objective weighting method (CCSD), we explore the improved fuzzy MULTIMOORA approach. We use the classical Interval-Valued Triangular Fuzzy Numbers (IVTFNs), viz. the symmetric lower and upper triangular numbers, as the basis. The triangular fuzzy number is identified by the triplets; the lowest, the most promising, and the highest possible values, symmetric with respect to the most promising value. When the lower and upper membership functions are equated to one, we get the normalized interval-valued triangular fuzzy numbers, which consist of symmetric intervals. We evaluate five alternatives among the four criteria using an improved MULTIMOORA method and select the best method for improving air quality in Tamil Nadu, India. Finally, a numerical example is illustrated to show the efficiency of the proposed method.

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
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