Soft Computing Evaluation Logic

3.5Canonical Aggregation Structures

All aggregation structures must have logic justification. In other words, some aggregation structures are logically correct and some can be logically incorrect. Consequently, the design of aggregation structures is not an arbitrary procedure—it must follow justifiable patterns and design rules. In this chapter, we present basic design rules for logic aggregation structures used in LSP criteria.

Logic aggregation structures usually consist of combining the GCD, standard negation , CPA and DPA. Theoretically, aggregation structures can have arbitrary configuration and parameters. However, some aggregation structures have regular and recognizable forms and are frequently encountered in evaluation models. These structures can be called canonical aggregation structures (CAS) and include the following:

• Conjunctive CAS with increasing andness
• Disjunctive CAS with increasing orness
• Aggregated mandatory/optional and sufficient/optional CAS
• Distributed mandatory/optional and sufficient/optional CAS
• Mandatory/desired/optional and sufficient/desired/optional CAS

3.5.1 Conjunctive CAS with Increasing Andness

For each aggregator, we can define its shadow as the set of input attributes that affect the output of the aggregator. This concept is illustrated in Fig. 3.5.1 and can also be used for aggregation structures that are not regular trees, because ...