# Enhancing Sensor Data Imputation: OWA-Based Model Aggregation for Missing Values
###### Abstract  
Due to some limitations in the data collection process caused either by human-related errors or by collection electronics, sensors, and network connectivity-related errors, the important values at some points could be lost. However, a complete dataset is required for the desired performance of the subsequent applications in various fields like engineering, data science, statistics, etc. An efficient data imputation technique is desired to fill in the missing data values to achieve completeness within the dataset. The fuzzy integral is considered one of the most powerful techniques for multi-source information fusion. It has a wide range of applications in many real-world decision-making problems that often require decisions to be made with partially observable/available information. To address this problem, algorithms impute missing data with a representative sample or by predicting the most likely value given the observed data. In this article, we take a completely different approach to the information fusion task in the ordered weighted averaging (OWA) context. In particular, we empirically explore for different distributions how the weights/importance of the missing sources are distributed across the observed inputs/sources. The experimental results on the synthetic and real-world datasets demonstrate the applicability of the proposed methods. missing data imputation; quadratic programming; OWA operators; data aggregation; measurement learning +
Footnote †: journal: _Future Internet_  
be complete and consistent so that their relevance is not questionable and can provide important information about related phenomena [7]. Different data mining techniques, such as classification, time series analysis, regression, etc., could produce insight into the data. The performance of such methods cannot be optimized if some critical data points are missing. Thus, maintaining the relevance of the collected data is essential. As stated in [8], the various scenarios involving missing data can be classified into three distinct forms: missing at random (MAR), missing completely at random (MCAR), and missing not at random (MNAR). Suppose the missing values are assumed according to be of type MAR. In that case, these values can be estimated using another technique (i.e., the approach in which values of the missing sample are ignored). MCAR-type missing data indicate that any missing observation is unrelated to the data values of the other variables or the available data values [9]. When missing data values are considered as MNAR-type, the values related to a variable are missed due to the nature of the variable itself. Practically, MCAR-type missing data occur very rarely. Among these three, MAR-type data is a reliable assumption. In this case, data are considered to be MAR-type as long as the data meet the requirement of not depending on the value of another variable. To achieve an effective imputation of missing values, it is crucial to model the mechanism through which these values are calculated accurately. The assumption of data missing at random (MAR) is generally acknowledged and commonly used in various approaches, as defined in [10]. The primary emphasis of previous investigations was the efficacy and precision of the suggested methodologies in restoring randomly absent values for individual values. The model's design to impute missing data is considered an essential problem of great practical importance in many fields, such as machine learning [11]. Missing data imputation and identification of the active aggregation have recently become a topic of interest in research to increase knowledge aggregation in practical applications [12]. In the end, despite the many research studies conducted to solve this task, particularly the imputation of missing data in practical applications such as collecting information from sensors, it is still challenging due to many limitations [13].