On the use of Hamacher’s t-norms family for information aggregation

Abstract

Combination of pieces of information issued from different sources plays a central role in several engineering as well as academic applications. The challenge that was usually addressed in these topics is how to deal with uncertainty and imperfection pervading the different sources of knowledge as well as with conflictual pieces of information. The theory of t-norms and t-conorms have been intensively investigated by many authors (see, for instance [E.P. Klement, R. Mesiar, E. Pap, Triangular Norms, Kluwer Academic Publisher, Dordrecht, 2000]) because of their appealing properties to model and manage the basic combination modes referring to a conjunctive and a disjunctive modes. Hamacher’s family of t-norms [E.P. Klement, R. Mesiar, E. Pap, Triangular Norms, Kluwer Academic Publisher, 2000] offers a special interest because it supplies a wide class of t-norm operators ranging from the probabilistic product to the weakest t-norm. Dubois and Prade [Data Fusion in Robotics and Machine Intelligence, Academic Press, New York; Contr. Eng. Practice 2 (1994) 812] have proposed an interesting setting for dealing with conflict based on the adaptiveness property that allows a gradual moving from a conjunctive mode to a disjunctive mode as soon as the conflict increases. This paper attempts to capture the basic ideas of the adaptiveness in order to build new combination rules based on Hamacher’s family. Particularly, certainty based qualification [R.R. Yager, Expert systems using fuzzy logic, in: R.R.Yager, L. Zadeh (Eds.), Intelligent Systems, Kluwer Academic Publisher, 1992, 27] will be reviewed and, accordingly, two families of rules will be put forward and compared to the adaptive rule of Dubois’ and Prade’s.