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 On Computing Cluster Centers of Trapezoidal Fuzzy Numbers

2019 ◽  
Vol 9 (1S3) ◽  
pp. 356-359
Keyword(s):  
Clustering Algorithm ◽  
Fuzzy Numbers ◽  
Trapezoidal Fuzzy Numbers ◽  
Fuzzy C Means ◽  
Fuzzy C Means Clustering ◽  
Metric Distance ◽  
Computing Cluster

In this paper we compute cluster centers of trapezoidal fuzzy numbers through fuzzy c means clustering algorithm and kernel based fuzzy c means clustering algorithm. A new complete metric distance between the trapezoidal fuzzy numbers is used to compute the cluster centers on the set of trapezoidal fuzzy numbers.

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.

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 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.

Drilling Wear Recognition Based on Fuzzy C-Means Clustering Algorithm

2012 ◽  
Vol 538-541 ◽  
pp. 1408-1412
Author(s):  
Ming Xia Yan
Keyword(s):  
Clustering Algorithm ◽  
Fuzzy C Means ◽  
Degree Of Membership ◽  
Fuzzy C Means Clustering ◽  
Clustering And Classification ◽  
Simulation Results ◽  
Severe Degree ◽  
Fuzzy Description ◽  
Matlab Programming ◽  
Wear Modes

Fuzzy c-means clustering algorithm was introduced in detail to classify a set of original sampling data on drilling wear in this paper. Simulation results by Matlab programming show that drill wear modes can be successfully represented by four fuzzy grades after fuzzy clustering and classification. The analysis result indicates that fuzzy description can properly reflect drill wear, FCM can effectively identify different wear modes. It is suggested that the severe degree of membership of wear be used as a criterion for replacement of a drill. This technique is simple and is adaptable to different environment in automatic manufacturing

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.

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