Abstract
This paper introduces a new Multi-interval-valued fuzzy sets (MIVFSs) model, in which the membership degrees of an alternative to given a set are represented by multiple interval values within the [0, 1] range along with their respective counting numbers. Then, the related concepts, order strategies, and some basic operational rules of multi-interval-valued fuzzy elements are investigated. Afterwards, several information measures including distance, similarity, and interval projection are further developed. Building upon this foundation, we designed two multiple-attribute decision-making (MADM) ranking methods in the multi-interval-valued fuzzy information system. To illustrate the practical application of our model, we provide a numerical example involving linguistic information, addressing the issue of ranking doctors in online healthcare. Through a comparative analysis, we demonstrate the effectiveness and practicality of the proposed model in handling MADM problems.
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