# Multiple Attribute Decision-Making Method Using Linguistic Cubic Hesitant Variables
## 1 Introduction  
Decision making (DM) theory and methods is an important research field [1; 2; 3; 4], while linguistic DM is a critical topic in DM theory and methods since using linguistic terms and arguments, such as \"good\" and \"very good\", for the assessment of the objective world is very fitting for human thinking and expressing habits. In particular, human linguistic expression has precedence over the numerical value expression regarding qualitative attributes in the DM process. Firstly, the concept of a linguistic variable (LV) was presented for its approximate reasoning application [5]. Then, a linguistic DM problem was solved using linguistic arguments [6; 7]. Next, various linguistic aggregation operators were introduced for (group) DM problems [8; 9; 10; 11; 12]. In the interval/uncertain linguistic setting, various aggregation operators of interval/uncertain LVs were presented for uncertain linguistic DM problems [13; 14; 15; 16; 17]. Under determinate and indeterminate linguistic situations, the linguistic cubic variable (LCV) that consists of its interval/uncertain LV and its certain LV was presented as the linguistic extension of a cubic set in [18] and the weighted aggregation operators of LCVs [19; 20] were proposed for DM problems with LCV information. On the one hand, a neutrosophic linguistic number (NLN), which is considered as a changeable interval linguistic number depending on its indeterminacy, and the weighted aggregation operators of NLNs were introduced for group DM problems with NLN information [21], and then the linguistic neutrosophic uncertain number(LNUN) that consists of the truth, falsity, and indeterminacy NLNs, and its weighted aggregation operators was introduced for group DM problems with LNUN information [22]. On the other hand, the linguistic neutrosophic variable/number (LNV/LNN) that consists of the truth, falsity, and indeterminacy LVs and the aggregation operators of LNVs [23; 24; 25] was presented, and then the correlation coefficients and cosine measures of LNVs [26; 27] were introduced for (group) DM problems under truth, falsity, and indeterminacy linguistic environments. Based on the hybrid idea of both an interval LNV and a single-valued LNV, a linguistic neutrosophic cubic variable (LNCV) and some aggregation operators of LNCs [28; 29] were proposed for DM problems with LNCV information. Furthermore, the single-valued linguistic neutrosophic interval linguistic number (SVLNILN) that is composed of both its interval LV (its uncertain linguistic argument) and its single-valued LNV (its confident argument) and the weighted aggregation operators of SVLNILNs were proposed for DM problems with SVLNILN information [30]. Regarding decision makers' hesitancy in the NLN DM process, the expected value and similarity measure of hesitant NLNs based on the objective extension method of the least common multiple number/cardinality (LCMN/LCMC) [31] were introduced for multi-attribute DM (MADM) problems with hesitant NLN information. Furthermore, the similarity measures of hesitant LNVs based on the LCMN extension method [32] were presented for MADM problems with hesitant LNN information. However, DM information composed of an interval linguistic value (an uncertain linguistic part) and a hesitant linguistic set (HLS) (a hesitant linguistic part) exists in some DM problems due to decision makers' uncertainty and hesitancy regarding an evaluated object.