Soft Computing Evaluation Logic

2.3Andness and Orness

A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.

—David Hilbert

The goal of this chapter is to present the three most important forms of andness/orness: local andness, mean local andness, and global andness. We analyze and compare these indicators from the standpoint of their computational properties and usability in decision models.

The GCD aggregator (graded conjunction/disjunction, Section 2.1.7) is the most important GL aggregator. It is a model of simultaneity and substitutability, characterized by two complementary indicators: andness and orness. Andness (or conjunction degree) is a metric of similarity between GCD and the full conjunction. It is denoted . Similarly, orness (or disjunction degree) is a metric of similarity between GCD and the full disjunction. It is denoted , and it is a complement of andness: . The basic concepts of andness and orness are introduced in section 2.2.2 (P₁₂). The history of development of these concepts is presented in section 2.1.12.

2.3.1 A General Definition of Andness/Orness

Fig. 2.3.1 is suitable to explain ...