A Novel Similarity Measure Based on Generalized Score Function For Interval-valued Intuitionistic Fuzzy Sets With Applications

Abstract

Although there are more and more studies on dealing with uncertainty and vagueness of information, there exist still some basic flaws related to distinguishing and comparing them. Most of the existing methods are based on the distance and entropy measures. However, more and more counterintuitive measures have been revealed and published in the literature. In this paper, a novel similarity measure for interval-valued intuitionistic fuzzy sets is proposed based on the generalized score function, which is in turn constructed from the generalized p-norm knowledge measure. The generalized p-norm knowledge measure for interval-valued intuitionistic fuzzy sets incorporates the amount of knowledge and fuzziness of information that provides reasonable measurements regardless of the representation norm. Based on the generalized knowledge measure and score function, the novel similarity measure can incorporate the significance (importance) of information making it more intuitive in comparing them, especially the ill-defined ones with the same amount of approving and disapproving information. The superiority of the proposed methods is shown by comparing with some existing measures in some numerical examples. Furthermore, it is also applied to deal with pattern recognition and medical diagnosis problems, that proves to be more flexible and adequate for dealing with uncertain and vague information.