ABSTRACT
This chapter is a continuation of the study of fuzzy connectives, and tnorms, t-conorms and negations will still play a basic role in the topics discussed. We begin with fuzzy implications, a topic that has applications in data fusion. The theory we develop for averaging operators puts into context several phenomena observed in Chapter 5, and sheds new light on the important family of Frank t-norms. The section on powers of t-norms provides a definition of the r-th power of a t-norm, and characterizes those automorphisms of the unit interval that are such powers. Powers of t-norms have played an important role in the development of t-norm theory, for example, in proving the existence of generators. The sensitivity of a connective is a measure of its robustness, and that section illustrates various such measures. Copulas are important objects in joint distribution theory in statistics, and have some connections with t-norms. This connection is explored briefly in the last section.
