Ranking parametric form of fuzzy numbers by defuzzification based on centroids value and ambiguity

2021 ◽  
pp. 1-15
Author(s):  
Devaki Rani Botsa ◽  
Phani Bushan Rao Peddi ◽  
Vikas Boddu
Keyword(s):  
Comparative Study ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
New Method ◽  
Parametric Form ◽  
Ranking Methods ◽  
Process Use ◽  
Generalized Fuzzy Number ◽  
Fuzzy Ranking

This paper proposes a new method to rank the parametric form of fuzzy numbers based on defuzzification. The defuzzification process use centroids, value, ambiguity and decision levels on fuzzy number developed from the parametric form of a generalized fuzzy number. The proposed method avoids reducing function to remove lower alpha levels and can overcome the shortcomings in some of the existing fuzzy ranking methods. The proposed method can effectively rank symmetric fuzzy numbers with the same core and different heights, fuzzy numbers with the same support and different cores, crisp numbers, crisp numbers having the same support and different heights, and fuzzy numbers having compensation of areas. A demonstration of the proposed method through examples and a comparative study with other methods in the literature shows that the proposed method gives effective results.

scholarly journals Fuzzy Risk Analysis for a Production System Based on the Nagel Point of a Triangle

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Handan Akyar
Keyword(s):  
Risk Analysis ◽  
Fuzzy Numbers ◽  
New Method ◽  
Economic Systems ◽  
Triangular Fuzzy Numbers ◽  
Ranking Methods ◽  
Analysis Problem ◽  
Centroid Point ◽  
Fuzzy Risk Analysis ◽  
Fuzzy Ranking

Ordering and ranking fuzzy numbers and their comparisons play a significant role in decision-making problems such as social and economic systems, forecasting, optimization, and risk analysis problems. In this paper, a new method for ordering triangular fuzzy numbers using the Nagel point of a triangle is presented. With the aid of the proposed method, reasonable properties of ordering fuzzy numbers are verified. Certain comparative examples are given to illustrate the advantages of the new method. Many papers have been devoted to studies on fuzzy ranking methods, but some of these studies have certain shortcomings. The proposed method overcomes the drawbacks of the existing methods in the literature. The suggested method can order triangular fuzzy numbers as well as crisp numbers and fuzzy numbers with the same centroid point. An application to the fuzzy risk analysis problem is given, based on the suggested ordering approach.

scholarly journals Evaluating the Efficiency of School Preceptors by Fuzzy Risk Analysis

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Rasoul Saneifard ◽  
Rahim Saneifard
Keyword(s):  
Risk Analysis ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
New Method ◽  
Arithmetic Operations ◽  
Fuzzy Risk Analysis ◽  
Fuzzy Weights

This paper presents a new method for evaluating the efficiency of school preceptors based on fuzzy number arithmetic operations. It uses fuzzy numbers to represent fuzzy grades. The fuzzy weights of criteria are automatically generated from the opinions of evaluators. The simplified fuzzy number arithmetic operations are used for calculating the average of fuzzy numbers. It can evaluate the efficiency of school preceptors in a more flexible and more intelligent manner.

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 New Method for Fuzzy Ranking Based on Possibility and Necessity Measures

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Fuzzy Numbers ◽  
New Method ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Ranking

In this paper, a new method to rank fuzzy numbers is presented. The proposed method based on Possibility and Necessity Measures is called PNM. According to possibility and necessity measures, eight indexes are calculated to extract four rules to rank fuzzy numbers. Also a method to evaluate each rule validation especially when rules’ outcomes yield conflict conclusions is presented. To test PNM performance, some controversial triangular fuzzy numbers are considered. Additionally, four extracted rules are compared with each other and fully analyzed. Furthermore, PNM is compared with other recently proposed methods. Results confirm that PNM is capable to rank a variety of fuzzy numbers and their images with any selected bandwidths, interval and any degree of closeness

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 Numerical Solution of Uncertain Beam Equations Using Double Parametric Form of Fuzzy Numbers

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Smita Tapaswini ◽  
S. Chakraverty
Keyword(s):  
Differential Equation ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Initial Conditions ◽  
Triangular Fuzzy Number ◽  
Fuzzy Differential Equation ◽  
Beam Equation ◽  
Parametric Form ◽  
Beam Equations ◽  
A New Technique

Present paper proposes a new technique to solve uncertain beam equation using double parametric form of fuzzy numbers. Uncertainties appearing in the initial conditions are taken in terms of triangular fuzzy number. Using the single parametric form, the fuzzy beam equation is converted first to an interval-based fuzzy differential equation. Next, this differential equation is transformed to crisp form by applying double parametric form of fuzzy number. Finally, the same is solved by homotopy perturbation method (HPM) to obtain the uncertain responses subject to unit step and impulse loads. Obtained results are depicted in terms of plots to show the efficiency and powerfulness of the methodology.

scholarly journals An Approach to solve Hexagonal Fuzzy Assignment Problem using Modified Best Candidate Method and Comparative Study with Existing Methods

YMER Digital ◽  
2021 ◽  
Vol 20 (11) ◽  
pp. 208-221
Author(s):  
M Maragatham ◽  
◽  
Suzane Raj L ◽  
Keyword(s):  
Comparative Study ◽  
Assignment Problem ◽  
Fuzzy Numbers ◽  
New Method ◽  
Optimal Solutions ◽  
Numerical Example ◽  
Systematic Procedure ◽  
Fuzzy Cost ◽  
Ranking Technique

The objective of fuzzy assignment problem is to find the least assignment fuzzy cost (maximum fuzzy profit) of workers with varying degree of skills to job. To attain the objective in this article, an approach involving modified best candidate method has been used to solve Hexagonal fuzzy assignment problem. To order the hexagonal fuzzy numbers Robust’s Ranking technique is applied. We examine a numerical example by using new method and compute by existing two methods. Also we compare the optimal solutions among this new method and two existing method .The proposed method is a systematic procedure, easy to apply for solving fuzzy assignment problem.

A New Centroids Method for Ranking of Trapezoid Fuzzy Numbers

2014 ◽  
Vol 68 (1) ◽  
Author(s):  
Lazim Abdullah ◽  
Fateen Najwa Azman
Keyword(s):  
Decision Making ◽  
Euclidean Distance ◽  
Fuzzy Numbers ◽  
New Method ◽  
Important Process ◽  
Ranking Methods ◽  
Satisfactory Solution ◽  
Centroid Method ◽  
Straightforward Calculation ◽  
Numerical Example

Ranking fuzzy numbers has become an important process in decision making. Many ranking methods have been proposed thus far and one of the commonly used is centroid of trapezoid. However, there is still no agreement on the method that can always provide a satisfactory solution to every situation. This paper aims to propose a new method of centroid using the circumcenter. The calculation for the circumcenter is derived from the trapezoidal fuzzy numbers and a series of the proposed steps. The proposed method offers a straightforward calculation by considering the centroid in each part of trapezoid to obtain a new centroid which eventually becomes the circumcenter. The Euclidean distance is used to calculate the ranking function from the circumcenter of centroids and the original point. A numerical example is given to illustrate the proposed method. At the end of this paper, a comparison of centroid method between the proposed method and other methods is presented.

A human-intuitive fuzzy ranking approach with spread and skewness factors

2021 ◽  
pp. 1-15
Author(s):  
Farnaz Sabahi ◽  
Mohammad-R. Akbarzadeh–T.
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Computational Approach ◽  
Fuzzy Ranking ◽  
Image Ranking ◽  
Ranking Problems ◽  
Definition Of

It would be hard to deny the importance of fuzzy number ranking in fuzzy-based applications. The definition of fuzzy ranking, however, evades an easy description due to the overlapping of fuzzy sets. While many researchers have addressed this subject, close examination reveals that their results suffer from one or more shortcomings such as image-ranking problems or ranking two equally embedded fuzzy numbers with the same centroid and different spreads. This paper proposes a new fast and straightforward computational approach to ranking fuzzy numbers that aims to overcome such problems. The proposed approach considers several important factors such as spread, skewness and center, in addition to human intuition. Further, the proposed ranking approach involves a composition of these factors as demonstrated in the several examples provided and in comparison with other existing approaches.

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