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.

scholarly journals Ranking Fuzzy Numbers by Centroid Method

2014 ◽  
Vol 8 (3) ◽  
Author(s):  
Fateen Najwa Azman ◽  
Lazim Abdullah
Keyword(s):  
Numerical Calculation ◽  
Decision Process ◽  
Fuzzy Numbers ◽  
New Method ◽  
Centroid Method ◽  
Generalized Fuzzy Numbers

Ranking fuzzy numbers are one of the important tools in decision process. There are many methods that have been proposed by a number of researchers but most of the methods are nondiscriminating and counterintuitive. Thus, proposing a new method for ranking fuzzy numbers are very prominent. The main objective of this paper is to get better ranking results to rank generalized fuzzy numbers than existing method. This paper reviews the centroid method in ranking fuzzy numbers by several researchers. A new calculation of centroid method will be proposed in this paper. At the end of the paper, a numerical calculation and a comparison of centroid method between the proposed method and other researchers’ method will be showed to check on its consistency.

A New Method for Ranking Intuitionistic Fuzzy Numbers

2011 ◽  
Vol 2 (1) ◽  
pp. 43-49 ◽  
Author(s):  
Cui-Ping Wei ◽  
Xijin Tang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Ranking Method ◽  
New Method ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Additional Information ◽  
Intuitionistic Fuzzy ◽  
Possibility Degree

In this paper the ranking method for intuitionistic fuzzy numbers is studied. The authors first define a possibility degree formula to compare two intuitionistic fuzzy numbers. In comparison with Chen and Tan’s score function, the possibility degree formula provides additional information for the comparison of two intuitionistic fuzzy numbers. Based on the possibility degree formula, the authors give a possibility degree method to rank intuitionistic fuzzy numbers, which is used to rank the alternatives in multi-criteria decision making problems.

scholarly journals Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
P. Phani Bushan Rao ◽  
N. Ravi Shankar
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Satisfactory Result ◽  
Fuzzy Numbers ◽  
New Method ◽  
Triangular Fuzzy Numbers ◽  
Distance Method ◽  
Fuzzy Environment ◽  
Index Of Optimism

Ranking fuzzy numbers are an important aspect of decision making in a fuzzy environment. Since their inception in 1965, many authors have proposed different methods for ranking fuzzy numbers. However, there is no method which gives a satisfactory result to all situations. Most of the methods proposed so far are nondiscriminating and counterintuitive. This paper proposes a new method for ranking fuzzy numbers based on the Circumcenter of Centroids and uses an index of optimism to reflect the decision maker's optimistic attitude and also an index of modality that represents the neutrality of the decision maker. This method ranks various types of fuzzy numbers which include normal, generalized trapezoidal, and triangular fuzzy numbers along with crisp numbers with the particularity that crisp numbers are to be considered particular cases of fuzzy numbers.

Decision making method for evaluating logistics companies based on the ordered representation of the polygonal fuzziness1

2020 ◽  
Vol 39 (3) ◽  
pp. 3151-3166
Author(s):  
Xiaoping Li ◽  
Yujie Tao ◽  
Yanhong Li
Keyword(s):  
Decision Making ◽  
Euclidean Distance ◽  
Fuzzy Numbers ◽  
Decision Matrix ◽  
Arithmetic Average ◽  
Weighted Arithmetic ◽  
Relative Closeness ◽  
Negative Ideal Solution ◽  
Arbitrary Precision ◽  
Polygonal Fuzzy Numbers

A polygonal fuzzy numbers can describe fuzzy information by means of finite ordered real numbers. It not only overcomes the complexity of traditional fuzzy number operations, but also keeps some good properties of trapezoidal fuzzy numbers, and it can approximate general fuzzy numbers with arbitrary precision. In this paper, a weighted arithmetic average operator is defined by the ordered representation and its operations of the polygonal fuzzy numbers, and a new Euclidean distance for measuring the polygonal fuzzy numbers is given. Secondly, in view of cost attribute and benefit attributes, the polygonal fuzzy decision matrix is normalized, and the weighted Euclidean distance is used to solve the positive (negative) ideal solution and the relative closeness of the decision matrix, and then a new decision method is given. Finally, the effectiveness of the proposed decision-making method is illustrated by an example of the evaluation of logistics companies by shopping websites.

scholarly journals A new method for ranking fuzzy numbers and its application to group decision making

2014 ◽  
Vol 38 (4) ◽  
pp. 1563-1582 ◽  
Author(s):  
Feng Zhang ◽  
Joshua Ignatius ◽  
Chee Peng Lim ◽  
Yajun Zhao
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
New Method

Interval Rough Neutrosophic TOPSIS Strategy for Multi-Attribute Decision Making

2020 ◽  
pp. 98-118
Author(s):  
Rumi Roy ◽  
Surapati Pramanik ◽  
Tapan Kumar Roy
Keyword(s):  
Decision Making ◽  
Euclidean Distance ◽  
Hamming Distance ◽  
Ideal Solution ◽  
Numerical Example ◽  
New Strategy ◽  
Order Preference ◽  
Multi Attribute Decision Making ◽  
Ranking Order ◽  
Negative Ideal Solution

In this chapter, the authors present a new strategy for multi-attribute decision making in interval rough neutrosophic environment. They define Hamming distance and Euclidean distance between interval rough neutrosophic numbers. They also define interval rough neutrosophic relative positive ideal solution (IRNRPIS) and interval rough neutrosophic relative negative ideal solution (IRNRNIS). Then the ranking order of the alternatives is obtained by the technique for order preference by similarity to ideal solution (TOPSIS) strategy. Finally, a numerical example is provided to demonstrate the applicability and effectiveness of the proposed interval rough neutrosophic TOPSIS strategy.

A New Method for Ranking Intuitionistic Fuzzy Numbers

2013 ◽  
pp. 45-51
Author(s):  
Cui-Ping Wei ◽  
Xijin Tang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Ranking Method ◽  
New Method ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Additional Information ◽  
Intuitionistic Fuzzy ◽  
Possibility Degree

In this paper the ranking method for intuitionistic fuzzy numbers is studied. The authors first define a possibility degree formula to compare two intuitionistic fuzzy numbers. In comparison with Chen and Tan’s score function, the possibility degree formula provides additional information for the comparison of two intuitionistic fuzzy numbers. Based on the possibility degree formula, the authors give a possibility degree method to rank intuitionistic fuzzy numbers, which is used to rank the alternatives in multi-criteria decision making problems.

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 A Hybrid Technique for Order Preference in Decision-Making

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Ismat Beg ◽  
Tabasam Rashid
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
New Method ◽  
Hybrid Technique ◽  
Ideal Solution ◽  
Laboratory Technique ◽  
Decision Making Problem ◽  
Classical Technique ◽  
Order Preference ◽  
Interaction Phenomena

We propose a hybrid technique by merging fuzzy version of the classical technique for order preference by similarity to ideal solution and decision-making trial and evaluation laboratory technique for trapezoidal fuzzy numbers, where interaction phenomena among the decision-making problem and weights are taken into account. The feasibility of this new method is demonstrated by applying it to an example.

A NEW METHOD FOR RANKING TRIANGULAR FUZZY NUMBERS

2012 ◽  
Vol 20 (05) ◽  
pp. 729-740 ◽  
Author(s):  
EMRAH AKYAR ◽  
HANDAN AKYAR ◽  
SERKAN ALİ DÜZCE
Keyword(s):  
Decision Making ◽  
Risk Analysis ◽  
Fuzzy Numbers ◽  
New Method ◽  
Triangular Fuzzy Numbers ◽  
Application Systems ◽  
Systems Control

The ranking and comparing of fuzzy numbers have important practical uses, such as in risk analysis problems, decision-making, optimization, forecasting, socioeconomic systems, control and certain other fuzzy application systems. Several methods for ranking fuzzy numbers have been widely-discussed though most of them have shortcomings. In this paper, we present a new method for ranking triangular fuzzy numbers based on their incenter and inradius. The proposed method is much simpler and more efficient than other methods in the literature. Some comparative examples are also given to illustrate the advantages of the proposed method.

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