A survey of weak connectives and the preservation of their properties by aggregations

The aim of this paper is to choose diverse definitions of generalized logical connectives and to present them in a coherent order, from the weakest to the richest. Such a rich list of notions allows us to consider the problem of admissible aggregations in the presented classes of unary and binary operations. This gives a contribution to the discussion of tolerance analysis in soft computing, decision making, approximate reasoning, and fuzzy control. First, we present a short survey of the development of MV-logic's connectives. Next, we discuss postulates used for generalized logical connectives. Finally, we describe families of weak connectives and indicate the preservation of their properties by some aggregation functions.