## 1 Introduction
Following this, [PERSON] and [PERSON] [13] demonstrated that linearization-based limits are provided by the extended Gilmore-Lawler bounding strategy for binary quadratic problems. The authors of the same paper established that the bound derived via the first level reformulation linearization approach is also a type of linearization-based bound. Recently, using an extended formulation for the minimum spanning tree problem, [PERSON] and [PERSON] [14] derived a series of relaxations for the QMST with increased complexity. The aforementioned research on QMST is viewed as an optimization problem with one objective function, where the linear and quadratic weights are in conjunction. [PERSON] et al. [15] investigated the contrasting characteristics of linear and quadratic weights. In this case, the authors have broken down the problem into two distinct minimization objectives for linear and quadratic weights. Their research suggests a Pareto local search algorithm for a bi-objective QMST that takes into account the quadratic weights for any two neighboring edges. The accuracy of parameters associated with decision-making problems is frequently compromised due to several variables, including inadequate data, limited input sources, the dynamic nature of input parameters, and measurement inaccuracy, among others. Therefore, a multitude of academics has proposed several advanced theories, including the probability theory, fuzzy set theory ([PERSON] [16]), rough set theory ([PERSON] [17]), and uncertainty theory ([PERSON] [18]), in order to analyze and represent useful information that is hidden inside imprecise or ill-defined data. The literature has several instances where these ideas have been implemented, as demonstrated by [PERSON] et al. [19], [PERSON] et al. [20], [PERSON] and [PERSON] [21], [PERSON] et al. [22] and [PERSON] et al. [23]. The investigation of stochastic MST has been conducted by researchers in response to the problem of uncertain MST ([PERSON] and [PERSON] [24]; [PERSON] and [PERSON] [25]). There exist several noteworthy scholarly publications pertaining to fuzzy MST, including works by [PERSON] and [PERSON] [26], [PERSON] et al. [27], and [PERSON] et al. [28]. Conversely, a limited number of studies have concentrated on QMST with uncertain parameters, as opposed to uncertain MST. Up till now, only three research studies have focused on the practical use of the QMST problem in an uncertain setting. The problem was solved by [PERSON] and [PERSON] [29] using a genetic algorithm. This research is regarded as an introductory study on QMST with fuzzy parameters. Afterwards, [PERSON] et al. [30] developed a QMST that incorporated uncertain variables representing linear and quadratic weights. Using the rough-fuzzy hybrid paradigm, [PERSON] et al. [20] conducted research on the multi-objective QMST problem. Considering the existing research on QMST within the uncertain paradigm, it is evident that a multi-objective QMST problem, under the framework of uncertainty theory ([PERSON] [18]), is yet to be addressed in the literature. Therefore, the present study emphasizes the following contributions to address the observed lacuna:  
1. A multi-objective uncertain adjacent quadratic minimum spanning tree (mUAQMSTP), where the linear and quadratic weights are treated as uncertain variables. 2. This study uses the chance-constrained programming (CCP) approach to model the mUAQMSTP. 3. The deterministic equivalent of the CCP for the proposed mUAQMSTP is subsequently solved using the global criterion method ([PERSON] [31]), a classical technique in multi-objective programming. Additionally, two multi-objective evolutionary algorithms (MOEAs) are employed: (a) non-dominated sorting algorithm II (NSGAII) ([PERSON] et al. [32]) and (b) duplicate elimination non-dominated sorting evolutionary algorithm (DENSEA) ([PERSON] et al. [33]). The subsequent section within the article is delineated as shown below. Section 2 covers the fundamental concepts that are crucial for this research.