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.

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.

Construction Project Bid Evaluation of Group Decision-Making Model Based on Triangular Fuzzy Number

2013 ◽  
Vol 405-408 ◽  
pp. 3451-3454
Author(s):  
Ming Xuan Zhang ◽  
Dong Lei Zhang
Keyword(s):  
Decision Making ◽  
Membership Function ◽  
Group Decision Making ◽  
Fuzzy Number ◽  
Group Decision ◽  
Comprehensive Evaluation ◽  
Fuzzy Comprehensive Evaluation ◽  
Triangular Fuzzy Number ◽  
Bid Evaluation ◽  
Decision Making Model

A new comprehensive evaluation based on triangular fuzzy number method is put forward in this paper, according to the principle of fuzzy comprehensive evaluation and using trichotomy to determine membership function. And a calculation example is illustrated by using the method presented. The method is a reference to the bid evaluation in the future.

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 A study on product-sum of triangular fuzzy numbers

2021 ◽  
Vol 5 (2) ◽  
pp. 63-67
Author(s):  
Mohamed Ali A ◽  
Rajkumar N
Keyword(s):  
Membership Function ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Numbers ◽  
Triangular Form ◽  
Finite Sum ◽  
The Membership Function

We  study  the  problem:   if  a˜i,   i  ∈  N   are  fuzzy  numbers  of  triangular  form,  then  what is the membership function of the infinite (or finite) sum -˜a1   +  a˜2   +  · · ·   (defined  via  the sub-product-norm convolution)

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 Evaluation of approximate Fuzzy Membership Function using Linguistic Input-an Approached Based on Cubic Spline

2020 ◽  
Vol 1 (2) ◽  
Author(s):  
Stabania Chowdhury ◽  
Rahul Kar
Keyword(s):  
Fuzzy Logic ◽  
Membership Function ◽  
Numerical Data ◽  
Building Blocks ◽  
Cubic Spline ◽  
Triangular Fuzzy Number ◽  
Fuzzy Membership ◽  
Fuzzy Membership Function ◽  
Fuzzy Logic Systems ◽  
The Membership Function

Fuzzy logic systems have found extensive use in system identification, decision making, and pattern recognition problems from industries to academics. The membership functions play a pivotal role in overall role in fuzzy representation, as these are considered as the building blocks of fuzzy set theory and they decide the degree of truth in fuzzy logic. The extraction of the membership function is ambience dependent and thus complication exists in the process of evaluation. In this assessment the main work deals with the derivation of fuzzy membership function where numerical data is available. The numerical cubic spline and defuzzification technique are used here. In this paper we mainly used triangular fuzzy number to construct the membership function. A case study is furnished to emphasize the advantage of adopting the method.

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 Fuzzy-Based Investigation of Challenges for the Deployment of Renewable Energy Power Generation

Energies ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 58
Author(s):  
Shabbiruddin ◽  
Neeraj Kanwar ◽  
Vinay Kumar Jadoun ◽  
Majed A. Alotaibi ◽  
Hasmat Malik ◽  
...  
Keyword(s):  
Power Generation ◽  
Renewable Energy ◽  
Fuzzy Set ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Number ◽  
Decision Makers ◽  
The Other ◽  
Function Shape ◽  
The Membership Function

Studying and analyzing the challenges that the renewable energy sector faces can help evaluate the risks and improve the planning. This research is done by considering the challenges in the implementation of sustainable generation of electricity through RESs in India, based on factors, including technical, financial, involvement, support, and others. The triangular fuzzy number (TFN) method, based on fuzzy logic concept, is used to analyze the challenges in this study. In general, TFN comprises of three numbers, likewise Gaussian fuzzy numbers, trapezoidal fuzzy numbers also exist. The classified sets of numbers are denotations to decision-makers’ perspective or a choice towards the criterion preference. Although alternatives are many to design a fuzzy set depending on elements count, the TFNs are the ones considered as actual representations of a fuzzy number. On the other hand, cases the Gaussian or trapezoidal, are manifestations of fuzzy intervals. Another argument is that the membership function shape corresponding to the number of fuzzy set elements is largely dependent on the study. The challenges identified along with analysis in this paper will help the industry, governments, and policymakers focus and tackle essential issues to facilitate further the deployment of RESs in India towards a more sustainable country.

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.

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