Mesiar, R., Kolesarova, A. (2018). ON THE FUZZY SET THEORY AND AGGREGATION FUNCTIONS: HISTORY AND SOME RECENT ADVANCES. Iranian Journal of Fuzzy Systems, 15(7), 1-12. doi: 10.22111/ijfs.2018.4278

R. Mesiar; A. Kolesarova. "ON THE FUZZY SET THEORY AND AGGREGATION FUNCTIONS: HISTORY AND SOME RECENT ADVANCES". Iranian Journal of Fuzzy Systems, 15, 7, 2018, 1-12. doi: 10.22111/ijfs.2018.4278

Mesiar, R., Kolesarova, A. (2018). 'ON THE FUZZY SET THEORY AND AGGREGATION FUNCTIONS: HISTORY AND SOME RECENT ADVANCES', Iranian Journal of Fuzzy Systems, 15(7), pp. 1-12. doi: 10.22111/ijfs.2018.4278

Mesiar, R., Kolesarova, A. ON THE FUZZY SET THEORY AND AGGREGATION FUNCTIONS: HISTORY AND SOME RECENT ADVANCES. Iranian Journal of Fuzzy Systems, 2018; 15(7): 1-12. doi: 10.22111/ijfs.2018.4278

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

^{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.

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