# Enhancing Sensor Data Imputation: OWA-Based Model Aggregation for Missing Values
###### Abstract
Many methods have been invented for missing data imputation; some of these studies are based on a priori-estimated parameters for the model, such as in [14], and others do not require estimated parameters, such as clustering algorithms and the Choquet integral (ChI). In addition, [PERSON] [15] offered a method for calculating the weights of the ordered weighted averaging (OWA) operator using a set of samples that contain the aggregated data required. The present study aims to investigate the problem of OWA aggregation of a set of variables interconnected and constrained by a series of linear inequalities. In his paper, [PERSON] suggests a linear programming (LP) model to solve such a problem. Meanwhile, another study introduced a linear objective programming strategy to estimate the OWA weights depending on a specified level of \"orness\", as described in [16]. The following line discusses fuzzy aggregation and fuzzy set theory. A group of operators named the fuzzy induced generalized hybrid averaging (FIGHA) operator, the fuzzy generalized hybrid averaging (FGA) operator, and the quasi-FHA operator were proposed by [PERSON] and [PERSON] in [17]. These operators have the advantage of being flexible, meaning they can incorporate a wide variety of fuzzy aggregation operators. This makes them suitable for various applications, including situations with decision-making challenges. Ref. [18] introduces a new practical operator based on the concept of least mean square errors. The new OWA operator may obtain the OWA weights utilizing fuzzy inference and weight judgments from decision-makers (DMs). Moreover, missing-value imputation approaches can also be categorized based on techniques that are used for approximating those values. Consequently, imputation methods can be classified into two types [19]. The first type includes approaches in which missing values can be predicted using statistical or mathematical methods. These approaches are very simple, as the mean value of the features can replace the missing data values. However, using such methods can potentially introduce bias into the estimations [20; 21]. Some methods are sophisticated, where more advanced statistical tools are used. The second type includes famous machine learning techniques that have been heavily used in the literature lately. The methods included in this category involve the creation of a model or a fusion of multiple models that acquire knowledge from a substantial amount of data. A well-trained model can make accurate predictions, which helps in accurately imputing missing values. The methods that come under this category could use neural networks [22; 23], support vector machines [24], or nearest-neighbor-based strategies [25]. In addition, the current state of machine learning approaches has limitations or deficiencies in complexity and expense, such as the artificial neural network method. In this work, we propose a new OWA-based missing data imputation method. It is a simple and effectively trained model that obtains a prediction capacity of absent values using a quadratic optimization technique. This methodology assumes that the given data can be represented as an additive input vector that follows a Gaussian distribution. Specifically, we assume that the mean of this distribution is zero and the covariance matrix is deterministic. Without losing generality, this assumption is typical in data aggregation applications. The covariance of the random variables is assumed to be a deterministic matrix, e.g., an identity matrix. Some values in the data points are randomly chosen as missing values. This approach proposes an OWA operator to impute the missing values in the dataset. In particular, a realization dataset was used to evaluate the proposed method. The rest of the sections of the paper are organized as follows. In Section 2, we clarify the detailed methodology of the proposed approach, which includes the description of the modeling of the measurements, the dataset type, and the learning strategy.