A Zadeh′s max-min composition operator for 3-dimensional triangular fuzzy number

2020 ◽  
Vol 39 (3) ◽  
pp. 3783-3793
Author(s):  
Yong Sik Yun
Keyword(s):  
Composition Operator ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Number ◽  
Triangular Fuzzy Numbers ◽  
3 Dimensional ◽  
Definition Of

We generalized triangular fuzzy numbers from ℝ to ℝ 2 . By defining parametric operations between two α-cuts, which are regions, we obtained parametric operations for two triangular fuzzy numbers defined on ℝ 2 . We also generalized triangular fuzzy numbers from ℝ 2 to ℝ 3 . By defining parametric operations between two α-cuts, which are subsets of ℝ 3 , we derived parametric operations for two triangular fuzzy numbers defined on ℝ 3 . For the calculation of Zadeh’s principle operators, the definition of parametric operations between two α-cuts, which are subsets of ℝ 3 , is critical.

scholarly journals New Similarity of Triangular Fuzzy Number and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xixiang Zhang ◽  
Weimin Ma ◽  
Liping Chen
Keyword(s):  
Collaborative Filtering ◽  
Fuzzy Number ◽  
Recommendation System ◽  
Fuzzy Numbers ◽  
Comprehensive Evaluation ◽  
Cloud Model ◽  
Triangular Fuzzy Number ◽  
New Method ◽  
Triangular Fuzzy Numbers

The similarity of triangular fuzzy numbers is an important metric for application of it. There exist several approaches to measure similarity of triangular fuzzy numbers. However, some of them are opt to be large. To make the similarity well distributed, a new method SIAM (Shape’s Indifferent Area and Midpoint) to measure triangular fuzzy number is put forward, which takes the shape’s indifferent area and midpoint of two triangular fuzzy numbers into consideration. Comparison with other similarity measurements shows the effectiveness of the proposed method. Then, it is applied to collaborative filtering recommendation to measure users’ similarity. A collaborative filtering case is used to illustrate users’ similarity based on cloud model and triangular fuzzy number; the result indicates that users’ similarity based on triangular fuzzy number can obtain better discrimination. Finally, a simulated collaborative filtering recommendation system is developed which uses cloud model and triangular fuzzy number to express users’ comprehensive evaluation on items, and result shows that the accuracy of collaborative filtering recommendation based on triangular fuzzy number is higher.

scholarly journals Graphic Representation of a Dimensional Expansion of Triangular Fuzzy Number

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yong Sik Yun
Keyword(s):  
Membership Function ◽  
Fuzzy Number ◽  
Composition Operators ◽  
Triangular Fuzzy Number ◽  
Triangular Fuzzy Numbers ◽  
3 Dimensional ◽  
Plane Passing ◽  
Color Density ◽  
Dimensional Graph ◽  
The Membership Function

We calculate Zadeh’s max-min composition operators for two 3-dimensional triangular fuzzy numbers. We prove that if the 3-dimensional result is limited to 2 dimensions, it is the same as the 2-dimensional result, which is shown as a graph. Since a 3-dimensional graph cannot be drawn, the value of the membership function is expressed with color density. We cut a 3-dimensional triangular fuzzy number by a perpendicular plane passing a vertex, and consider the cut plane as a domain. The value of the membership function for each point on the cut plane is also expressed with color density. The graph expressing the value of the membership function, defined in the plane as a 3-dimensional graph using the z -axis value instead of expressing with color density, is consistent with the results in the 2-dimensional case.

Application of interval-valued triangular fuzzy numbers and their functional to the healthcare problems

Dependability ◽  
2021 ◽  
Vol 21 (1) ◽  
pp. 23-33
Author(s):  
Kapil Naithani ◽  
Rajesh Dangwal
Keyword(s):  
Failure Probability ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Fault Tree Analysis ◽  
Triangular Fuzzy Number ◽  
Triangular Fuzzy Numbers ◽  
Index Method ◽  
Estimate Reliability ◽  
Failure Tree ◽  
Interval Valued

Aim. In healthcare field there exist different types of uncertainty due to medical error generated by human and technologies. In general the crisp value generate loss of precision and inaccuracy about result and therefore the available data is not sufficient to assessed clinical process up to desired degree of accuracy. Therefore fuzzy set theory play as an important and advance role in accuracy of results in healthcare related problems. Methods. Here for more accuracy of result, we use functional fuzzy numbers in this paper. This study uses a new fuzzy fault tree analysis for patient safety risk modelling in healthcare. In this paper we will use level (λ, ρ) interval-valued triangular fuzzy number, their functional, t-norm operation and centre of gravity defuzzification method to evaluate fuzzy failure probability and estimate reliability of system. The effectiveness of these methods is illustrated by an example related to healthcare problems and then we analyse the result obtained with the other existing techniques. Tanaka et al.’s approach has been used to give the rank of basic events of the considered problems. Also, we use functional of fuzzy numbers to analyse the change in fuzzy failure probability. Results. The paper examines the application of the failure tree, t-norm and functional fuzzy numbers in the context of interval-valued triangular fuzzy numbers. The research examined two types of healthcare-specific problems and the corresponding defuzzification techniques for the purpose of reliability analysis using the existing methods. The authors concluded that t-norm is not associated with significant accumulation and identified how a functional fuzzy number affects reliability. Similarly, using the V index method, the least critical events were found for each system.

scholarly journals Computing Cluster Centers of Triangular Fuzzy Numbers using Innovative Metric Distance

2019 ◽  
Vol 8 (11) ◽  
pp. 3378-3381
Keyword(s):  
Fuzzy Number ◽  
Clustering Algorithm ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Number ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy C Means ◽  
Fuzzy C Means Clustering ◽  
Metric Distance ◽  
Matlab Programming ◽  
Computing Cluster

In this paper we compute cluster centers of triangular fuzzy numbers through fuzzy c means clustering algorithm and kernel based fuzzy c means clustering algorithm. An innovative distance between the triangular fuzzy numbers is used and the distance is complete metric on triangular fuzzy numbers. The set of triangular fuzzy numbers and an another set with the same triangular fuzzy numbers by including an outlier or noisy point as an additional triangular fuzzy number are taken to find the cluster centers using MATLAB programming. An example is given to show the effectiveness between the algorithms.

scholarly journals Resilient Supplier Selection Based on Fuzzy BWM and GMo-RTOPSIS under Supply Chain Environment

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Jiawu Gan ◽  
Shuqi Zhong ◽  
Sen Liu ◽  
Dan Yang
Keyword(s):  
Supply Chain ◽  
Fuzzy Number ◽  
Supplier Selection ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Triangular Fuzzy Number ◽  
Random Environments ◽  
Triangular Fuzzy Numbers ◽  
Supply Chain Risk ◽  
Research Gap

Resilient suppliers can reduce supply chain risk, effectively avoid supply chain disruption, and bring profits to enterprises. However, there is no united measuring index system to evaluate the resilient supplier under supply chain environment, and the assessment language sets are usually crisp values. Therefore, in order to fill the research gap, this paper proposes a hybrid method, which combines triangular fuzzy number, the best-worst method (BWM), and the modular TOPSIS in random environments for group decision-making (GMo-RTOPSIS) to solve the above problem. Firstly, the weight of decision-maker is calculated by using fuzzy BWM which can deal with triangular fuzzy numbers. Secondly, triangular fuzzy number is introduced into GMo-RTOPSIS, and combined with fuzzy BWM, alternatives are sorted to select the best resilient supply chain partner. Finally, the feasibility and universality of this method are proved by illustrative examples.

scholarly journals A study on multiplication operation on triangular fuzzy numbers

2021 ◽  
Vol 5 (2) ◽  
pp. 55-62
Author(s):  
Mohamed Ali A ◽  
Maanvizhi P
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Number ◽  
Fuzzy Arithmetic ◽  
Triangular Fuzzy Numbers ◽  
Arithmetic Operations ◽  
Multiplication Operation ◽  
Cut Method ◽  
Standard Approximation ◽  
Basic Content

The arithmetic operations on fuzzy number are basic content in fuzzy mathematics. But still the operations of fuzzy arithmetic operations are not established. There are some arithmetic operations for computing fuzzy number. Certain are analytical methods and further are approximation methods. In this paper we, compare the multiplication operation on triangular fuzzy number between α-cut method and standard approximation method and give some examples.

Ranking of Fuzzy Numbers by using Scaling Method

2019 ◽  
Vol 3 (2) ◽  
pp. 137-143
Author(s):  
Ayad Mohammed Ramadan
Keyword(s):  
Multidimensional Scaling ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Numbers ◽  
Scaling Method ◽  
Ranking Of Fuzzy Numbers ◽  
First Time

In this paper, we presented for the first time a multidimensional scaling approach to find the scaling as well as the ranking of triangular fuzzy numbers. Each fuzzy number was represented by a row in a matrix, and then found the configuration points (scale points) which represent the fuzzy numbers in . Since these points are not uniquely determined, then we presented different techniques to reconfigure the points to compare them with other methods. The results showed the ability of ranking fuzzy numbers

scholarly journals A Novel Approach to Solve Fully Fuzzy Linear Programming Problems with Modified Triangular Fuzzy Numbers

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2937
Author(s):  
Saeid Jafarzadeh Ghoushchi ◽  
Elnaz Osgooei ◽  
Gholamreza Haseli ◽  
Hana Tomaskova
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Number ◽  
Fuzzy Linear Programming ◽  
Fuzzy Decision ◽  
Triangular Fuzzy Numbers ◽  
Novel Approach ◽  
Decision Variables ◽  
Linear Programming Problems ◽  
Fuzzy Solution

Recently, new methods have been recommended to solve fully fuzzy linear programming (FFLP) issues. Likewise, the present study examines a new approach to solve FFLP issues through fuzzy decision parameters and variables using triangular fuzzy numbers. The strategy, which is based on alpha-cut theory and modified triangular fuzzy numbers, is suggested to obtain the optimal fully fuzzy solution for real-world problems. In this method, the problem is considered as a fully fuzzy problem and then is solved by applying the new definition presented for the triangular fuzzy number to optimize decision variables and the objective function. Several numerical examples are solved to illustrate the above method.

scholarly journals Computer-Based Fuzzy Numerical Method for Solving Engineering and Real-World Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Naila Rafiq ◽  
Naveed Yaqoob ◽  
Nasreen Kausar ◽  
Mudassir Shams ◽  
Nazir Ahmad Mir ◽  
...  
Keyword(s):  
Fuzzy Sets ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Numerical Solutions ◽  
Numerical Test ◽  
Real Life ◽  
Triangular Fuzzy Number ◽  
Test Problems

The nonlinear equation is a fundamentally important area of study in mathematics, and the numerical solutions of the nonlinear equations are also an important part of it. Fuzzy sets introduced by Zedeh are an extension of classical sets, which have several applications in engineering, medicine, economics, finance, artificial intelligence, decision-making, and so on. The most special types of fuzzy sets are fuzzy numbers. The important fuzzy numbers are trapezoidal fuzzy and triangular fuzzy numbers, which have several applications. In this research article, we propose an efficient numerical iterative method for estimating roots of fuzzy nonlinear equations, which are based on the special type of fuzzy number called triangular fuzzy number. Convergence analysis proves that the order of convergence of the numerical method is three. Some real-life applications are considered as numerical test problems from engineering, which contain fuzzy quantities in the parametric form. Engineering models include fractional conversion of nitrogen-hydrogen feed into ammonia and Van der Waal’s equation for calculating the volume and pressure of a gas and motion of the object under constant force of gravity. Numerical illustrations are given to show the dominance efficiency of the newly constructed iterative schemes as compared to existing methods in the literature.

scholarly journals A Direct Method to Compare Bipolar LR Fuzzy Numbers

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Reza Ghanbari ◽  
Khatere Ghorbani-Moghadam ◽  
Nezam Mahdavi-Amiri
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Direct Method ◽  
Optimization Algorithms ◽  
Real Life ◽  
New Method ◽  
Triangular Fuzzy Numbers ◽  
Real Life Problem ◽  
A Direct Method

We propose a new method for ordering bipolar fuzzy numbers. In this method, for comparison of bipolar LR fuzzy numbers, we use an extension of Kerre’s method being used in ordering of unipolar fuzzy numbers. We give a direct formula to compare two bipolar triangular fuzzy numbers in O(1) operations, making the process useful for many optimization algorithms. Also, we present an application of bipolar fuzzy number in a real life problem.

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