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

Authors:
Józef Drewniak;Anna Król
Affiliations:
Institute of Mathematics, University of Rzeszów, 35-310 Rzeszów, ul. Rejtana 16a, Poland;Institute of Mathematics, University of Rzeszów, 35-310 Rzeszów, ul. Rejtana 16a, Poland
Venue:
Fuzzy Sets and Systems
Year:
2010

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Abstract

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.