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 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.

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

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 A Theoretical Development of Distance Measure for Intuitionistic Fuzzy Numbers

2010 ◽  
Vol 2010 ◽  
pp. 1-25 ◽  
Author(s):  
Debashree Guha ◽  
Debjani Chakraborty
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Theoretical Development ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy Numbers ◽  
Metric Properties ◽  
Intuitionistic Fuzzy

The objective of this paper is to introduce a distance measure for intuitionistic fuzzy numbers. Firstly the existing distance measures for intuitionistic fuzzy sets are analyzed and compared with the help of some examples. Then the new distance measure for intuitionistic fuzzy numbers is proposed based on interval difference. Also in particular the type of distance measure for triangle intuitionistic fuzzy numbers is described. The metric properties of the proposed measure are also studied. Some numerical examples are considered for applying the proposed measure and finally the result is compared with the existing ones.

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 Multiattribute Group Decision Making with Unknown Decision Expert Weights Information in the Framework of Interval Intuitionistic Trapezoidal Fuzzy Numbers

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zongcai Jiang ◽  
Yan Wang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Distance Measure ◽  
Group Decision ◽  
Fuzzy Decision ◽  
Decision Matrix ◽  
Trapezoidal Fuzzy Numbers ◽  
Overall Evaluation ◽  
The Given

The aim of this paper is to investigate an approach to multiattribute group decision making with interval intuitionistic trapezoidal fuzzy numbers, in which the decision expert weights are unknown. First, we introduce a distance measure between two interval intuitionistic trapezoidal fuzzy matrixes, and based on the distance between individual matrix and extreme matrix, as well as the average matrix, we obtain the decision expert weights. Second, we utilize the interval intuitionistic trapezoidal fuzzy weighted geometric (IITFWG) operator and the interval intuitionistic trapezoidal fuzzy ordered weighted geometric (IITFOWG) operator to aggregate all individual interval intuitionistic trapezoidal fuzzy decision matrices into a collective interval intuitionistic trapezoidal fuzzy decision matrix and then derive the group overall evaluation values of the given alternatives. Finally, an illustrative example of emergency alternatives selection is given to demonstrate the effectiveness and superiority of the proposed method.

scholarly journals Metric Properties between Trapezoidal Intuitionistic Fuzzy Numbers

2019 ◽  
Vol 8 (3) ◽  
pp. 3951-3954
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Interval Numbers ◽  
New Approach ◽  
Intuitionistic Fuzzy Numbers ◽  
Metric Properties ◽  
Intuitionistic Fuzzy ◽  
Metric Distance ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

Generally ranking of fuzzy number is more essential for convertion of fuzzy number to crisp one. In this manuscript, a new approach to rank the trapezoidal intuitionistic fuzzy numbers using cuts is established. The metric distance of the interval numbers is extended to trapezoidal intuitionistic fuzzy numbers. By using both the ranking of trapezoidal intuitionistic fuzzy numbers and cuts there is abundant scope of investigating the numerical problems in optimization.

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