A MODIFICATION OF THE INDEX OF LIOU AND WANG FOR RANKING FUZZY NUMBER

2007 ◽  
Vol 15 (04) ◽  
pp. 411-424 ◽  
Author(s):  
M. SOCORRO GARCIA ◽  
M. TERESA LAMATA
Keyword(s):  
Satisfactory Result ◽  
Coefficient Of Variation ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Mean Value ◽  
Weighted Mean ◽  
Numerical Examples ◽  
Centroid Point ◽  
Ranking Fuzzy Number ◽  
Index Of Optimism

Different methods have been proposed for ranking fuzzy numbers. These include methods based on distances, centroid point, coefficient of variation, and weighted mean value. However, there is still no method that can always give a satisfactory result to every situation; some are counterintuitive and not discriminating. This paper presents an approach for ranking fuzzy numbers with integral value that is an extension of the index of Liou and Wang. This method, that is independent of the type of membership function used, can rank more than two fuzzy numbers simultaneously. This ranking method use an index of optimism to reflect the decision maker's optimistic attitude, but rather it also contains an index of modality that represents the neutrality of the decision maker. The approach is illustrated with numerical examples.

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.

Ranking Fuzzy Numbers Based on the Mean and Fuzzy Degree of Fuzzy Number

2012 ◽  
Vol 220-223 ◽  
pp. 2102-2108
Author(s):  
Gui Xiang Wang ◽  
Guang Tao Zhou
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Numerical Examples ◽  
Novel Approach ◽  
The Mean ◽  
Fuzzy Degree ◽  
Comparative Results ◽  
Ranking Index

In this paper, a novel approach to ranking fuzzy numbers based on the mean and the fuzzy degree of fuzzy number is proposed. In the approach, a new ranking index that is comprehensive consideration of the mean and the fuzzy degree of fuzzy number is constructed, and then the properties of the ranking index are given. Moreover, to compare the proposed approach with the existing approaches, numerical examples are given. The comparative results illustrate that the approach proposed in this paper is better and has simpler calculations.

scholarly journals A New Distance Measure and Ranking Method for Generalized Trapezoidal Fuzzy Numbers

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
T. Allahviranloo ◽  
M. A. Jahantigh ◽  
S. Hajighasemi
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Distance Measure ◽  
Ranking Method ◽  
Trapezoidal Fuzzy Numbers ◽  
Approximate Approach ◽  
Centroid Point ◽  
Generalized Trapezoidal Fuzzy Numbers

This study presents an approximate approach for ranking fuzzy numbers based on the centroid point of a fuzzy number and its area. The total approximate is determined by convex combining of fuzzy number’s relative and its area that is based on decision maker’s optimistic perspectives. The proposed approach is simple in terms of computational efforts and is efficient in ranking a large quantity of fuzzy numbers. A group of examples by Bortolan and Degani (1985) demonstrate the accuracy and applicability of the proposed approach. Finally by this approach, a new measure is introduced between two fuzzy numbers.

scholarly journals A New Method for Defuzzification and Ranking of Fuzzy Numbers Based on the Statistical Beta Distribution

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
A. Rahmani ◽  
F. Hosseinzadeh Lotfi ◽  
M. Rostamy-Malkhalifeh ◽  
T. Allahviranloo
Keyword(s):  
Beta Distribution ◽  
Granular Computing ◽  
Fuzzy Numbers ◽  
Mean Value ◽  
Human Reasoning ◽  
Fuzzy Information ◽  
Numerical Examples ◽  
Novel Method ◽  
The Mean ◽  
Ranking Of Fuzzy Numbers

Granular computing is an emerging computing theory and paradigm that deals with the processing of information granules, which are defined as a number of information entities grouped together due to their similarity, physical adjacency, or indistinguishability. In most aspects of human reasoning, these granules have an uncertain formation, so the concept of granularity of fuzzy information could be of special interest for the applications where fuzzy sets must be converted to crisp sets to avoid uncertainty. This paper proposes a novel method of defuzzification based on the mean value of statistical Beta distribution and an algorithm for ranking fuzzy numbers based on the crisp number ranking system on R. The proposed method is quite easy to use, but the main reason for following this approach is the equality of left spread, right spread, and mode of Beta distribution with their corresponding values in fuzzy numbers within(0,1)interval, in addition to the fact that the resulting method can satisfy all reasonable properties of fuzzy quantity ordering defined by Wang et al. The algorithm is illustrated through several numerical examples and it is then compared with some of the other methods provided by literature.

scholarly journals Quadrilateral Fuzzy Number

2018 ◽  
Vol 7 (4.10) ◽  
pp. 1018
Author(s):  
Pathinathan T ◽  
Santhoshkumar S
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Numerical Examples ◽  
Practical Applications ◽  
Algebraic Properties

Fuzzy numbers are used to represent uncertainty. Various types of fuzzy numbers are used in practical applications. In this paper we define Perfect Pentagonal Fuzzy Number (PPFN), Quadrilateral Fuzzy Number (QNF) and Left skewed Quadrilateral Fuzzy Number and Right skewed Quadrilateral Fuzzy Number. We study their algebraic properties with numerical examples.  

scholarly journals Methods in Ranking Fuzzy Numbers: A Unified Index and Comparative Reviews

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Thanh-Lam Nguyen
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Fuzzy Data ◽  
Weighted Mean ◽  
Consistency Property ◽  
Left And Right ◽  
Computational Simplicity ◽  
Accurate Matching ◽  
Unified Index ◽  
Image Pattern

Fuzzy set theory, extensively applied in abundant disciplines, has been recognized as a plausible tool in dealing with uncertain and vague information due to its prowess in mathematically manipulating the knowledge of imprecision. In fuzzy-data comparisons, exploring the general ranking measure that is capable of consistently differentiating the magnitude of fuzzy numbers has widely captivated academics’ attention. To date, numerous indices have been established; however, counterintuition, less discrimination, and/or inconsistency on their fuzzy-number rating outcomes have prohibited their comprehensive implementation. To ameliorate their manifested ranking weaknesses, this paper proposes a unified index that multiplies weighted-mean and weighted-area discriminatory components of a fuzzy number, respectively, called centroid value and attitude-incorporated left-and-right area. From theoretical proof of consistency property and comparative studies for triangular, triangular-and-trapezoidal mixed, and nonlinear fuzzy numbers, the unified index demonstrates conspicuous ranking gains in terms of intuition support, consistency, reliability, and computational simplicity capability. More importantly, the unified index possesses the consistency property for ranking fuzzy numbers and their images as well as for symmetric fuzzy numbers with an identical altitude which is a rather critical property for accurate matching and/or retrieval of information in the field of computer vision and image pattern recognition.

scholarly journals A New Distance Measure for Trapezoidal Fuzzy Numbers

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
M. J. Ebadi ◽  
M. Suleiman ◽  
Fudziah Bt. Ismail ◽  
A. Ahmadian ◽  
M. R. Balooch Shahryari ◽  
...  
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Distance Measure ◽  
Trapezoidal Fuzzy Numbers ◽  
Metric Properties ◽  
Centroid Point ◽  
Complete Discussion ◽  
First Time

We propose a new distance measure for the space of all trapezoidal fuzzy numbers using centroid point and left/right spread of trapezoidal fuzzy numbers. Moreover, the metric properties of suggested distance measure are investigated. Indeed, we show that for two arbitrary trapezoidal fuzzy numbers if the distance between centroid points and also the distance between left spreads and right spreads go to zero, then two given fuzzy numbers are equal. Consequently, we complete discussion about the relation between fuzzy number and its centroid which is the firstly discussed by Hadi-Vencheh and Allame (2010). To the best of our knowledge, this is first time in the literature that such metric is applied by centroid point.

scholarly journals A Study On Reliability Using Pendant, Hexant, Octant Fuzzy Numbers

2021 ◽  
Author(s):  
P. Jini Varghese ◽  
G. Michael Rosario
Keyword(s):  
Fuzzy Number ◽  
Comparative Research ◽  
Fuzzy Numbers ◽  
Integration Method ◽  
Centroid Method ◽  
Distance Method ◽  
Numerical Examples ◽  
Signed Distance ◽  
Mathematical Operations

The weaving machine’s reliability is assessed using newly introduced fuzzy numbers. The fuzzy numbers introduced in this study give a better method to improve the reliability than other techniques. Pendant Fuzzy Number, Hexant Fuzzy Number, and Octant Fuzzy Number are all introduced in this present study. Pendant Fuzzy Number, Hexant Fuzzy Number, and Octant Fuzzy Number,α-cuts are defined, as well as their mathematical operations. The numerical examples are utilised to conduct a comparative research of reliability using various Fuzzy Numbers, and their defuzzification is accomplished using various ways such as Signed Distance method, Graded Mean Integration Method and Centroid Method. The purpose of this study is to discover the most reliable value for a weaving machine.

scholarly journals Intuitionistic decagonal fuzzy number and its arithmetic operations

2017 ◽  
Vol 7 (1) ◽  
pp. 51-58
Author(s):  
RAJKUMAR A ◽  
JOSE PARVIN PRAVEENA N ◽  
DHANUSH C
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Accuracy Function ◽  
Arithmetic Operations ◽  
Numerical Examples ◽  
Addition And Subtraction

This paper introduced a new conception Intuitionistic Decagonal fuzzy Number and defines fundamental arithmetic operations like addition, subtraction. Numerical examples for addition and subtraction between two Intuitionistic Decagonal fuzzy Numbers are given.Score function and accuracy function are also defined.

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