| Summary: | 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 (<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">L</mi><mspace width="-2.84526pt"></mspace><mi mathvariant="script">M</mi><mspace width="-2.84526pt"></mspace><mi mathvariant="script">F</mi><mspace width="-2.84526pt"></mspace><mi mathvariant="script">S</mi><mspace width="-2.84526pt"></mspace><mi mathvariant="script">S</mi></mrow></semantics></math></inline-formula>) has been applied in forecasting process. However, similarity measure is not used in this application. In our research, similarity measure of <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">L</mi><mspace width="-2.84526pt"></mspace><mi mathvariant="script">M</mi><mspace width="-2.84526pt"></mspace><mi mathvariant="script">F</mi><mspace width="-2.84526pt"></mspace><mi mathvariant="script">S</mi><mspace width="-2.84526pt"></mspace><mi mathvariant="script">S</mi></mrow></semantics></math></inline-formula> is proposed to calculate the similarity between two <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">L</mi><mspace width="-2.84526pt"></mspace><mi mathvariant="script">M</mi><mspace width="-2.84526pt"></mspace><mi mathvariant="script">F</mi><mspace width="-2.84526pt"></mspace><mi mathvariant="script">S</mi><mspace width="-2.84526pt"></mspace><mi mathvariant="script">S</mi><mi>s</mi></mrow></semantics></math></inline-formula>. Moreover, some of its properties are introduced and proved. Finally, an application of <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">L</mi><mspace width="-2.84526pt"></mspace><mi mathvariant="script">M</mi><mspace width="-2.84526pt"></mspace><mi mathvariant="script">F</mi><mspace width="-2.84526pt"></mspace><mi mathvariant="script">S</mi><mspace width="-2.84526pt"></mspace><mi mathvariant="script">S</mi></mrow></semantics></math></inline-formula> in decision making using similarity measure is analysed.
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