## 1 Introduction
[24] introduced TODIM technique for finding the best alternative in decision making problems, where the information occurred in the form of PF numbers. [PERSON] [25] introduced many aggregation operators such as interaction weighted averaging and weighted geometric operators. Using PF information, [PERSON] & [PERSON] [26] developed the power aggregation operators to deal with an MAGDM problem. [PERSON] et al. [27] launched the induced generalized OWA operators for PF information. [PERSON] et al. [28] developed the LINMAP technique to track the best investment company in railway projects using PF information. [PERSON] [29] developed a multi-objective optimization based on ratio analysis (MOORA) with PF set information and applied it to MAGDM problem. To solve an MAGDM problem with partially known weight information, [PERSON] [30] introduced an improved score function, where the preferences of the attribute are taken in the form of IVPF sets. Hamacher operations [31], including Hamacher product and sum, are good alternatives to the algebraic product and sum, respectively [32]. In last few years, many researchers discussed the Hamacher aggregation operators and their applications [33; 34]. [PERSON] & [PERSON] [35] developed the concept of 2-tuple linguistic processing model based on the symbolic translation model, and also showed that the 2-tuple linguistic information processing manner can effectively avoid the loss and distortion of information. A group decision-making model was proposed by [PERSON] et al. [36], to manage a non homogeneous information. For choosing the appropriate agile manufacturing system, [PERSON] [37] developed a 2-tuple fuzzy linguistic processing model. The TOPSIS technique are extended by [PERSON] [38] for MAGDM problem with 2-tuple linguistic information. [PERSON] & [PERSON] [39] proposed the efficient algorithm for DFMEA combining 2-tuple and the OWA operator. Bonferroni mean operators are extended by [PERSON] & [PERSON] [40] for the 2-tuple linguistic information. The dependent interval 2-tuple linguistic aggregation operators are proposed by [PERSON] et al. [41] for MAGDM. [PERSON] et al. [42] proposed an algorithm for the MAGDM problems, using the interval 2-tuple linguistic information and Choquet integral aggregation operators. To study the application of MAGDM on the supplier selection [PERSON] [43] defined the 2-tuple linguistic Muirheadmean operators. A consensus-reaching model for the 2-tuple linguistic MAGDM was proposed by [PERSON] et al. [44], where the weight information was incomplete. The notion of spherical fuzz set (SFS) was first time introduced by [PERSON] et al. [45], and defined some aggregation operators for MADM problem with the spherical fuzzy information. [PERSON] et al. [46] defined the extended TOPSIS method to spherical fuzzy TOPSIS and an illustrative example is presented for multi-criteria decision making problem. Basically, spherical fuzzy set is the extended form of picture fuzzy set and Pythagorean fuzzy set. In the SF set, all the membership grades are satisfying the condition \(0\leq\left(\mu_{\Re}(r)\right)^{2}+\left(\eta_{\Re}(r)\right)^{2}+\left(\
u_{ \Re}(r)\right)^{2}\leq 1\) instead of \(0\leq\mu_{\Re}(r)+\eta_{\Re}(r)+\
u_{\Re}(r)\leq 1\) as in picture fuzzy set. [PERSON] et al. [47] defined linguistic spherical fuzzy set, combining the idea of linguistic fuzzy set and spherical fuzzy set. [PERSON] et al. [48] defined some spherical fuzzy aggregation operators, using Dombi operation, discussed their application on decision making, and also discussed the representation of spherical fuzzy t-norm and t-conorm in [49]. Due to the motivation and inspiration of the above discussion in this article we introduce the notion of 2-tuple spherical fuzzy linguistic sets, each element of which is composed of linguistic postive, neutral, and negative membership grades. We introduce the aggregation techniques for 2-tuple spherical fuzzy linguistic numbers.