# Linguistic Interval-Valued Spherical Fuzzy Soft Set and Its Application in Decision Making
The main advantage of the fuzzy soft set is that it can solve MADM better when fuzzy data arise in the form of approximations by different parameters. Hence, more and more scholars studied and proposed new hybrid models, such as the interval-valued fuzzy soft set [23], spherical fuzzy soft set [24], intertemporal hesitant fuzzy soft set [25], possibility fermatean fuzzy soft set [26], generalized interval-valued intuitionistic fuzzy soft set [27] and so on [28; 29; 30]. These hybrid models effectively combine the description of imprecise and ambiguous data by different fuzzy sets with the advantage of the soft set as parametrization tools, and achieve promising results in some tasks, such as MADM [31; 32; 33; 34], parameter reduction [35; 36; 37], approximate reasoning [38; 39] and so on [40]. The geometric representations of the intuitionistic fuzzy set, Pythagorean fuzzy set, picture fuzzy set, spherical fuzzy, linguistic interval-valued spherical fuzzy set and LIVSFSS are given in Figure 1.  
The purpose of this paper is to propose a new hybrid model: the linguistic interval-valued spherical fuzzy soft set (LIVSFSS), which can not only achieve the preferences of decision makers by using linguistic terms and provide a greater degree of freedom for the decision makers, but also captures fuzzy information better in the form of approximations by different parameters under MADM. Hence, we first define the basic concepts of LIVSFSS. Then, we discuss various operational laws and the proofs of properties about LIVSFSS, such as the \"AND\" operation, the \"OR\" operation, the possibility operation, the necessity operation and so on. Subsequently, we redefine the linguistic weighted choice value and the linguistic soft weighted overall choice value after analyzing the decision-making algorithms based on different interval-valued fuzzy soft set models. Finally, we propose the MADM algorithm and the parameter reduction algorithm. Furthermore, we illustrate the algorithms' rationality and effectiveness by examples and comparative analysis. The main contributions of this paper are summarized as follows. 1. LIVSFSS is proposed for the first time by combining the linguistic interval-valued spherical fuzzy set with the soft set, and its basic concepts, operations and properties are discussed. 2. In order to solve MADM problems and consider the influence of the parameter weight, the linguistic weighted choice value and the linguistic soft weighted overall choice value are redefined by analyzing other models. Then the MADM algorithm and parameter reduction algorithm are proposed. 3. We apply the MADM algorithm and parameter reduction algorithm to examples and compare them with some existing algorithms to illustrate their rationality and effectiveness. The remainder of this paper is organized as follows. In Section 2, we recall the basic concepts required for this paper. In Section 3, we introduce the proposed concepts and operations of LIVSFSS. In Section 4, we introduce the multi-attribute decision-making algorithm and parameter reduction algorithm based on LIVSFSS. The conclusions and directions for future work are outlined in Section 5.