A New Distance Measure for Trapezoidal Fuzzy Numbers
Open Access
- 15 April 2013
- journal article
- research article
- Published by Hindawi Limited in Mathematical Problems in Engineering
- Vol. 2013, 1-4
- https://doi.org/10.1155/2013/424186
Abstract
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.Keywords
This publication has 14 references indexed in Scilit:
- Trapezoidal approximation and aggregationFuzzy Sets and Systems, 2011
- The revised method of ranking LR fuzzy number based on deviation degreeExpert Systems with Applications, 2010
- On the relation between a fuzzy number and its centroidComputers & Mathematics with Applications, 2010
- A new approach for ranking of trapezoidal fuzzy numbersComputers & Mathematics with Applications, 2009
- Ranking fuzzy numbers by distance minimizationApplied Mathematical Modelling, 2007
- Ranking of fuzzy numbers by sign distanceInformation Sciences, 2006
- On the centroids of fuzzy numbersFuzzy Sets and Systems, 2006
- Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metricFuzzy Sets and Systems, 2004
- Numerical solutions of fuzzy differential and integral equationsFuzzy Sets and Systems, 1999
- Metrics and orders in space of fuzzy numbersFuzzy Sets and Systems, 1998