Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations. (English) Zbl 1189.15003
Summary: The convergence of a series of fuzzy sets was examined via Zadeh’s Extension Principle by M. Stojaković and Z. Stojaković [Fuzzy Sets Syst. 83, No. 3, 341–346 (1996; Zbl 0879.46050)]. Since the utilization of this approach is quite difficult in practice, we prefer the idea of using the sum of the series of \(\lambda \)-level sets. The main purpose of the present paper is to determine the \(\alpha -\), \(\beta \)- and \(\gamma \)-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.
Keywords:
set of the sequences of fuzzy numbers; \(\alpha \)-dual; \(\beta \)-dual; \(\gamma \)-dual and matrix transformationsCitations:
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