ON THE FUZZY SET THEORY AND AGGREGATION FUNCTIONS: HISTORY AND SOME RECENT ADVANCES

Document Type: Research Paper

Authors

1 Department of Mathematics and Descriptive Geometry, Fac. of Civil Engineering,, Slovak University of Technology in Bratislava,, Radlinskeho 11, 810 05 Bratislava, Slovakia

2 Institute IAM, Fac. of Chemical and Food Technology,, Slovak University of Technology in Bratislava,, Radlinskeho 9, 812 37 Bratislava, Slovakia

Abstract

Several fuzzy connectives, including those proposed by Lotfi
Zadeh, can be seen as linear extensions of the Boolean connectives from the
scale $\{0,1\}$ into the scale $[0,1]$. We discuss these extensions, in particular,
we focus on the dualities arising from the Boolean dualities. These
dualities allow to transfer the results from some particular class of extended Boolean functions, e.g., from
conjunctive functions, into some other distinguished classes, e.g., into fuzzy
implications. We also stress the role of aggregation functions in fuzzy set
theory. Then we continue with several recent advances and new directions in
aggregation theory. In particular, we discuss some generalizations of
monotonicity, additivity and maxitivity issues. Finally, some applications of
aggregation functions are sketched.

Keywords


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