Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations

The convergence of a series of fuzzy sets was examined via Zadeh’s Extension Principle by M. Stojaković and Z. Stojaković [M. Stojaković, Z. Stojaković, Addition and series of fuzzy sets, Fuzzy Sets and Systems 83 (1996), 341–346]. Since the utilization of this approach is quite difficult in practice, we prefer the idea of using the sum of the series of λλ-level sets. The main purpose of the present paper is to determine the αα-, ββ- and γγ-duals of the classical sets of sequences of fuzzy numbers and is to give the necessary and sufficient conditions on an infinite matrix of fuzzy numbers transforming one of the classical sets to the another one.