Open AccessA Comparative Analysis on Geometric Measure in Intuitionistic Fuzzy Set and Interval-Valued Intuitionistic Fuzzy Set
Author(s) -
A. Mamani,
M. Suganya
Publication year - 2019
Publication title -
international journal of scientific research in science, engineering and technology
Language(s) - English
Resource type - Journals
eISSN - 2395-1990
pISSN - 2394-4099
DOI - 10.32628/ijsrset1384150
Subject(s) - mathematics , fuzzy mathematics , fuzzy number , fuzzy set , fuzzy classification , discrete mathematics , fuzzy set operations , hamming distance , algebra over a field , measure (data warehouse) , defuzzification , fuzzy logic , pure mathematics , artificial intelligence , computer science , data mining
Intuitionistic Fuzzy set (IFS) was proposed in early 80’s. It is a well known theory. As a developer in Fuzzy Mathematics, interval – valued Intuitionistic Fuzzy sets (IVIFS) were developed afterwards by Gargo and Atanssov. It has a wide range of applications in the field of Optimization and algebra. There are many distance measure in Fuzzy such as Hamming, Normalized Hamming, Euclidean, Normalized Euclidean, Geometric, Normalized Geometric etc… to calculate the distance between two fuzzy numbers. In this paper, the comparison between Geometric distance measure in Intuitionistic Fuzzy set and interval – valued Intuitionistic Fuzzy sets is explored. The step-wise conservation of Intuitionistic Fuzzy set and interval – valued Intuitionistic Fuzzy sets is also proposed. This type of comparative analysis shows that the distance between Intuitionistic Fuzzy set and interval – valued Intuitionistic Fuzzy sets varies slightly due to boundaries of interval – valued Intuitionistic Fuzzy sets.