Soft Computing Evaluation Logic

2.6Partial Absorption: A Fundamental Asymmetric Aggregator

Growing old is mandatory, growing wise is optional.

The most important simple aggregator in GL is GCD, and the most important compound aggregator is the partial absorption (PA). Introductory presentations of PA can be found in many places in this book: PA was introduced as Pattern 11 and Pattern 12 in section 2.1.2, then as a basic idempotent GL aggregator in Section 2.1.9, as the origin of the concept of multipolarity in Section 2.2.4, and as a model of heterogeneous annihilators in definitions 2.4.26 and 2.4.27 of Section 2.4.1. In this chapter we study PA in more detail, focusing on its analytic forms and implementation options.

Mixing mandatory and optional requirements is the most frequent type of asymmetric logic aggregation based on heterogeneous annihilators. It is present in almost all evaluation problems. For example, when people select the location of their home they usually aggregate components such as distance from work (for parents), distance from school (for children), distance from entertainment, shopping, hospitals, post office, etc. These individual criteria are usually partitioned into two groups: mandatory and optional. The low distances from work and school are frequently interpreted as mandatory requirements, while the low distances from the post office or entertainment facilities may be optional (desired, but not mandatory). This asymmetry means that a home that is too far from school will ...