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The goal of this paper is to introduce a novel soft hyperstructure called multi-fuzzy soft hyperstructure. We investigate the notion of multi-fuzzy soft hypermodules and some of their structural properties are discussed. We discuss the behavior image and inverse image of a multi-fuzzy soft set under the multi-fuzzy soft function. According to Zadeh's extension principle, we prove that the image and inverse image of a multi-fuzzy soft hypermodules are further multi-fuzzy soft hypermodule. [ABSTRACT FROM AUTHOR]

Many effective tools in fuzzy soft set theory have been proposed to handle various complicated problems in different fields of our real life, especially in decision making. Molodtsov's soft set theory has been regarded as a newly emerging mathematical tool to deal with uncertainty and vagueness. Lattice ordered multi-fuzzy soft set ( L M F S S ) has been applied in forecasting process. However, similarity measure is not used in this application. In our research, similarity measure of L M F S S is proposed to calculate the similarity between two L M F S S s . Moreover, some of its properties are introduced and proved. Finally, an application of L M F S S in decision making using similarity measure is analysed. [ABSTRACT FROM AUTHOR]