TY - JOUR
ID - 5225
TI - Several new results based on the study of distance measures of intuitionistic fuzzy sets
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Chen, C.
AU - Deng, X.
AD - School of Mathematics, South China University of Technology, Guangzhou, 510640, China
Y1 - 2020
PY - 2020
VL - 17
IS - 2
SP - 147
EP - 163
KW - Intuitionistic fuzzy set
KW - distance measure
KW - inclusion relation
KW - hesitancy degree
KW - characteristic function
DO - 10.22111/ijfs.2020.5225
N2 - It is doubtless that intuitionistic fuzzy set (IFS) theory plays an increasingly important role in solving the problems under uncertain situation. As one of the most critical members in the theory, distance measure is widely used in many aspects. Nevertheless, it is a pity that part of the existing distance measures has some drawbacks in practical significance and accuracy. To make up for their drawbacks and pursue more accuracy and effectiveness, in this paper, we propose a new inclusion relation of IFSs and a new definition called strict distance measure. Based on this new relation, an analysis is given to point out that the common shortcoming of Hamming distance measure and Euclidean distance measure is the mishandling of hesitancy degree. Therefore, the role of hesitancy degree in distance measure is studied deeply and then three strict distance measures are put forward to overcome the above shortcoming. In addition, a novel definition called the characteristic function of distance measure is defined to describe the character of strict distance measure. On this basis, a theorem is presented to illustrate the inevitability of the occurrence of unrecognized result in pattern recognition problems in some special cases. This theorem also shows that the problem cannot be entirely attributed to distance measures. In view of this condition, we provide an appropriate solution. Compared with other existing distance measures in some examples, the superiorities of our improved distance measures are demonstrated to be more effective and more significant.
UR - https://ijfs.usb.ac.ir/article_5225.html
L1 - https://ijfs.usb.ac.ir/article_5225_c3b0df3eaa33f2919b05d4fd2ec17961.pdf
ER -