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Top1. Introduction
The multi-attribute group decision making (MAGDM) is to fuse preferences depicted through some decision makers about evaluation attributes for alternatives (Li, 2007; Fu et al. 2020). The problem of MAGDM can be seen everywhere in daily life (Tong et al.,2022; Zheng er al.,2023; Chao et al.,2021). For example, people are concerned about the choice of nursing homes, the choice of cruise ships (Cao et al.,2022) or the choice of sustainable suppliers (Xu et al.,2019). In the traditional MAGDM, the evaluation attributes belong to a mutually independent state. Due to the advent of social media, the environment of MAGDM becomes complicated, which makes the evaluation attributes have a certain degree of uncertainty, resulting in a certain relationship between evaluation attributes. Therefore, how to build a new MAGDM method with multi-evaluation attributes correlation is the key problem addressed in this paper.
One of the key issues is to deal with the correlation between multiple evaluation attributes (Ju et al.,2020; Chen et al. 2020; Li et al., 2020). In the traditional process of MAGDM, the weights of evaluation attributes are subjectively given or objectively obtained. This indicates that these evaluation attributes are independent of each other. However, Due to the advent of social media, the environment of MAGDM becomes more and more complex and uncertain, which makes the evaluation attributes have some correlation with each other (Marichal & Roubens, 2000; She et al.,2021; Teng& Liu, 2021). For example, the evaluation attributes in nursing homes include living environment, hardware facilities and the literacy of accompanying personnel. The living environment can reflect the good attitude of the caregivers to work, and the high-quality caregivers also show that their serious attitude in work makes the living environment of the elderly comfortable. This indicates that there is a positive relationship between the evaluation attributes of nursing homes.
Choquet integral is an effective way to solve the interaction between multiple evaluation attributes (Teng& Liu, 2021; Wang et al.,2018; Byüközkan et al.,2021]. For example, Teng et al. (2021) designed a generalized Choquet integral to explore the correlation between evaluation attributes in MAGDM. At the same time, the Pythagorean fuzzy number based Choquet integral is proposed to discuss the interaction between multiple evaluation attributes (Byüközkan et al.,2021). These Choquet integral methods can not preserve the initial preferences of each decision maker in the merging of all preference fusion, while fuzzy numbers with interval valued functions can deal with this problem well (Dubois & Prade, 1980; Qiu,2021; Qiu &Yu, 2023; Li et al.,2018; 2020; Fei et al.,2018; Nan,2014). In the traditional Choquet integral, the multiple evaluation attributes are local interaction, only some attributes coalitions are considered. In order to consider all attribute coalitions, hence, the fuzzy joint Choquet integral based on an interval-valued function is put forward to deal with the correlation between multiple evaluation attributes in this paper.