New Distance Measure for Atanassov’s Intuitionistic Fuzzy Sets and Its Application in Decision Making
1
School of Business, Nankai University, Tianjin 300071, China
2
College of Air and Missile Defense, Air Force Engineering University, Xi’an 710051, China
3
College of Air Traffic Control and Navigation, Air Force Engineering University, Xi’an 710051, China
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(10), 429; https://doi.org/10.3390/sym10100429
Received: 5 September 2018 / Revised: 15 September 2018 / Accepted: 19 September 2018 / Published: 22 September 2018
The intuitionistic fuzzy set introduced by Atanassov has greater ability in depicting and handling uncertainty. Intuitionistic fuzzy measure is an important research area of intuitionistic fuzzy set theory. Distance measure and similarity measure are two complementary concepts quantifying the difference and closeness of intuitionistic fuzzy sets. This paper addresses the definition of an effective distance measure with concise form and specific meaning for Atanassov’s intuitionistic fuzzy sets (AIFSs). A new distance measure for AIFSs is defined based on a distance measure of interval values and the transformation from AIFSs to interval valued fuzzy sets. The axiomatic properties of the new distance measure are mathematically investigated. Comparative analysis based in numerical examples indicates that the new distance measure is competent to quantify the difference between AIFSs. The application of the new distance measure is also discussed. A new method for multi-attribute decision making (MADM) is developed based on the technique for order preference by similarity to an ideal solution method and the new distance measure. Numerical applications indicate that the developed MADM method can obtain reasonable preference orders. This shows that the new distance measure is effective and rational from both mathematical and practical points of view.
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Keywords:
Atanassov’s intuitionistic fuzzy sets; distance measure; similarity measure; decision making
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MDPI and ACS Style
Ke, D.; Song, Y.; Quan, W. New Distance Measure for Atanassov’s Intuitionistic Fuzzy Sets and Its Application in Decision Making. Symmetry 2018, 10, 429. https://doi.org/10.3390/sym10100429
AMA Style
Ke D, Song Y, Quan W. New Distance Measure for Atanassov’s Intuitionistic Fuzzy Sets and Its Application in Decision Making. Symmetry. 2018; 10(10):429. https://doi.org/10.3390/sym10100429
Chicago/Turabian StyleKe, Di; Song, Yafei; Quan, Wen. 2018. "New Distance Measure for Atanassov’s Intuitionistic Fuzzy Sets and Its Application in Decision Making" Symmetry 10, no. 10: 429. https://doi.org/10.3390/sym10100429
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