A new vector valued similarity measure for intuitionistic fuzzy sets based on OWA operators

Document Type: Research Paper

Authors

1 Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, 610054, China

2 School of Computer and Information Sciences,Southwest University, Chongqing 400715, China

Abstract

Plenty of researches have been carried out, focusing on the measures of distance, similarity, and correlation between intuitionistic fuzzy sets (IFSs).
However, most of them are single-valued measures and lack of potential for efficiency validation.
In this paper, a new vector valued similarity measure for IFSs is proposed based on OWA operators.
The vector is defined as a two-tuple consisting of the similarity measure and uncertainty measure, in which the latter is the uncertainty of the former.
OWA operators have the ability to aggregate all values in the universe of discourse of IFSs, and to determine the weights according to specific applications.
A framework is built to measure similarity between IFSs.
A series of definitions and theorems are given and proved to satisfy the corresponding axioms defined for IFSs.
In order to illustrate the effectiveness of the proposed vector valued similarity measure,
a classification problem is used as an application.

Keywords


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Testing set
Setosa Versicolor Virginica
S U S U S U
1 0.4630 0.7269 0.9157 0.5196 0.9157 0.4093
2 0.3707 0.8097 0.7603 0.4020 0.9286 0.2440
3 0.3207 0.7155 0.7110 0.3604 0.8794 0.2246
4 0.3544 0.8971 0.8050 0.3597 0.9131 0.2859
5 0.4092 0.8203 0.8618 0.4314 0.9696 0.3469
6 0.4084 0.8089 0.7992 0.4473 0.9677 0.2702
7 0.4197 0.7298 0.7626 0.4020 0.9303 0.2303
8 0.3427 0.6289 0.6254 0.2150 0.7939 0.0945
9 0.2417 0.7542 0.6923 0.2549 0.8004 0.2318
10 0.5055 0.6615 0.8974 0.5881 0.8729 0.4655
11 0.4136 0.8157 0.7550 0.3828 0.9225 0.2170
12 0.3906 0.8567 0.8421 0.4111 0.9498 0.3350
13 0.3614 0.5925 0.6451 0.2352 0.8136 0.1065
14 0.4549 0.7390 0.9077 0.4978 0.8732 0.3780
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17 0.4633 0.7429 0.8068 0.4400 0.9745 0.2508
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19 0.3886 0.7662 0.7305 0.3650 0.8980 0.2085
20 0.3647 0.7958 0.7551 0.4093 0.9235 0.2498
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