Fuzzy N-Continuous And N-Bounded Linear Operators And Wigner-Type Theorem In Fuzzy N-Normed Linear Spaces

In this paper,we will study the types of fuzzy n-continuous and n-bounded linear operators in fuzzy n-normed linear spaces and their relations.Moreover,we introduce Wigner-Type theorem to fuzzy n-normed linear spaces by the study of n-normed linear spaces.In the first chapter,we introduce the historical background and development status of fuzzy n-normed linear spaces,which should be paid attention to the B-S fuzzy normed linear spaces.On the basis of such spaces,we introduce the fuzzy n-normed linear spaces and the ?-n-norm which induced by fuzzy n-norm.Finally,we introduce the 2-fuzzy n-normed linear spaces on all fuzzy sets.In the second chapter,we define three types of fuzzy strongly,weakly and sequentially n-continuous linear operators.We prove that if T is St-f-n-continuous,then T is Sq-f-n-continuous.We also show that T is f-n-continuous if and only if T is Sq-f-n-continuous.Furthermore,strongly and weakly fuzzy n-bounded linear operators are defined,and the relationship between them is proved by examples.In the third chapter,we mainly study Wigner-Type theorem on fuzzy n-normed linear spaces.Based on the existing conclusions of the Wigner-type theorem obtained in n-normed linear spaces [11],and combined with the special properties of fuzzy n-normed spaces,we give a proof of Wigner-Type theorem in fuzzy n-normed linear spaces to show that for n ?3,every mapping which preserves two fuzzy n-norms one and zero is phase-equivalent to a linear fuzzy n-isometry.