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 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 Reliability Estimation of a Network Structure Using Generalized Trapezoidal Fuzzy Numbers

2021 ◽  
Vol 51 (1) ◽  
pp. 225-241
Author(s):  
Amit Kumar ◽  
Pooja Dhiman
Keyword(s):  
System Reliability ◽  
Fuzzy Numbers ◽  
Test System ◽  
Reliability Estimation ◽  
Trapezoidal Fuzzy Numbers ◽  
Level Of Satisfaction ◽  
Degree Of Satisfaction ◽  
Fuzzy Logic Method ◽  
Context Specific ◽  
Generalized Trapezoidal Fuzzy Numbers

Abstract Classical sets are used commonly to consider reliability. Because of the uncertainty in the data (which considered in the present paper) classical sets fail to describe the reliability accurately. Uncertainty leads to fluctuation in the actual situation of the structure. Fuzzy logic method attempts to test system reliability with the benefit of membership function. Within this context, specific problems of reasoning-based approaches are studied, explored and correlated with standard reliability approaches. In this paper Generalized Trapezoidal Fuzzy numbers (GTrFN) are used to assess the structure's fuzzy reliability. The reliability of each event is assigned with different level of satisfaction and some improved operations on the generalized trapezoidal fuzzy numbers (GTrFN) are used to calculate the fuzzy boundaries for the resultant reliability of the final event along with the degree of satisfaction. Also the results are compared to demonstrate the application of the improved operations on Generalized Trapezoidal Fuzzy Numbers (GTrFN). The obtained results converge to more precise interval values as compare to the vague fuzzy number.

scholarly journals New Ranking Method For Fuzzy Numbers By Their Expansion Center

2014 ◽  
Vol 4 (3) ◽  
pp. 181-187 ◽  
Author(s):  
Zhenyuan Wang ◽  
Li Zhang-Westmant
Keyword(s):  
Decision Making ◽  
Data Analysis ◽  
Real Axis ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Ranking Method ◽  
Important Criterion ◽  
Real Numbers ◽  
Numerical Index ◽  
The Membership Function

Abstract Based on the area between the curve of the membership function of a fuzzy number and the horizontal real axis, a characteristic as a new numerical index, called the expansion center, for fuzzy numbers is proposed. An intuitive and reasonable ranking method for fuzzy numbers based on this characteristic is also established. The new ranking method is applicable for decision making and data analysis in fuzz environments. An important criterion of the goodness for ranking fuzzy numbers, the geometric intuitivity, is also introduced. It guarantees coinciding with the natural ordering of the real numbers.

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