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 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 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.

scholarly journals Calculating the Fuzzy Project Network Critical Path

2012 ◽  
Vol 1 (2) ◽  
pp. 58 ◽  
Author(s):  
Nasser Shahsavari Pour ◽  
Samira Zeynali ◽  
Mansoor Kheradmand
Keyword(s):  
Real World ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Critical Path ◽  
Special Importance ◽  
Activity Time ◽  
Simple Method ◽  
Project Completion ◽  
Project Network ◽  
Ranking Of Fuzzy Numbers

A project network consists of various activities. To determine the length of project time and the amount of the needed sources, the time of project completion must correctly and exactly be calculated, so the critical path is calculated. The activities on this path have no floating. It means that there is no delay on these activities. As a result the calculation of the critical path in a project network has a special importance. In this paper a simple method for calculation the critical path is proposed. Assignment an exact time on any activity in real world is not correct; So the fuzzy and uncertainty theories are used to assigned a length of time on any activities. In the present study the trapezoidal fuzzy numbers are assigned to the length of activity time, and the total time of the project is also a fuzzy number. In addition, to compare the fuzzy numbers, ranking of fuzzy numbers are used. Finally a practical example will show the efficiency of the method.

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

A New Point of View for Fuzzy Numbers and Their Defuzzification

2015 ◽  
Vol 23 (06) ◽  
pp. 909-926 ◽  
Author(s):  
Romà Adillon ◽  
Lambert Jorba
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Graphical Representation ◽  
Point Of View ◽  
Geometrical Approach ◽  
Triangular Fuzzy Numbers ◽  
Trapezoidal Fuzzy Numbers

In this paper we develop a new graphical representation of fuzzy numbers, which we then employ to propose a geometrical approach to their defuzzification. The calculations involved in the proposed method and the resultant representation use Moore's semiplane for intervals and therefore are far simpler than those involved in other approaches. We start by representing triangular and trapezoidal fuzzy numbers in Moore's semiplane. Then we extend this work to any fuzzy number. Although this extension has to be undertaken in [Formula: see text], it preserves all the properties we study for trapezoidal and triangular fuzzy numbers in Moore's semiplane.

scholarly journals Generalization and ranking of fuzzy numbers by relative preference relation

2021 ◽  
Author(s):  
Kavitha Koppula ◽  
Babushri Srinivas Kedukodi ◽  
Syam Prasad Kuncham
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Preference Relation ◽  
Multi Criteria Decision Making ◽  
Fuzzy Preference Relation ◽  
Trapezoidal Fuzzy Numbers ◽  
Relative Preference ◽  
Decision Making Model ◽  
Ranking Of Fuzzy Numbers

AbstractWe define $$2n+1$$ 2 n + 1 and 2n fuzzy numbers, which generalize triangular and trapezoidal fuzzy numbers, respectively. Then, we extend the fuzzy preference relation and relative preference relation to rank $$2n+1$$ 2 n + 1 and 2n fuzzy numbers. When the data is representable in terms of $$2n+1$$ 2 n + 1 fuzzy number, we generalize the FMCDM (fuzzy multi-criteria decision making) model constructed with TOPSIS and relative preference relation. Lastly, we give an example from telecommunications to present the proposed FMCDM model and validate the results obtained.

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 Optimal Saving by Expected Utility Operators

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 17
Author(s):  
Irina Georgescu ◽  
Jani Kinnunen
Keyword(s):  
Utility Function ◽  
Expected Utility ◽  
Potential Risk ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Sufficient Conditions ◽  
Approximation Formula ◽  
Triangular Fuzzy Numbers ◽  
Total Utility ◽  
Optimal Saving

This paper studies an optimal saving model in which risk is represented by a fuzzy number and the total utility function of the model is defined by an expected utility operator. This model generalizes some existing possibilistic saving models and from them, by a particularization, one can obtain new saving models. In the paper, sufficient conditions are set for the presence of potential risk to increase optimal saving levels and an approximation formula for optimal saving is demonstrated. Particular models for a few concrete expected utility operators are analyzed for triangular fuzzy numbers and CRRA-utility functions.

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.

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