Soft Computing Evaluation Logic

2.8Penalty‐Controlled Missingness‐Tolerant Aggregation

Aggregation of degrees of truth or degrees of fuzzy membership using GL aggregation structures assumes the availability of all input data. Unfortunately, in many applications some inputs are missing. In this chapter, we present an aggregation process that controllably tolerates missing data [DUJ12a]. The aggregation process is implemented in the context of LSP evaluation criteria. Using the presented method, the aggregators automatically reconfigure themselves so that only the available data are aggregated. Consequently, evaluation decisions can be based on incomplete data. A typical example of missing data in online real estate and missingness‐tolerant aggregation can be found in Section 4.2.4, where we use an evaluation engine based on methodology presented in subsequent sections.

2.8.1 Missing Data in Evaluation Problems

The problem of missing data is ubiquitous in statistical analysis [ALL01, LIT87, HOW07, HOW09]. Statisticians usually differentiate three types of “missingness.” If the attributes a₁, …, a_n are used to compute an indicator , then the probability p_i that an attribute a_i is missing can be constant and independent of the values of a₁, …, a_n. Such an attribute is missing completely at random (denoted MCAR). If p_i does not depend on a_i but it can depend on , then this form of missingness is missing at random ...