On the extension of nullnorms and uninorms to fuzzy truth values

In this work, by applying Zadeh's extension principle, we extend type-1 proper nullnorms and proper uninorms to fuzzy truth values. The definitions of type-2 nullnorms and uninorms are introduced. We mainly discuss in which subalgebras of fuzzy truth values extended proper nullnorms and proper uninorms are type-2 nullnorms and uninorms, respectively.