ویراساینس.
سند علمی

Atomic Decompositions of Fuzzy Normed Linear Spaces for Wavelet Applications

Sorin Nadaban, Ioan Dzitac

چکیده

Wavelet analysis is a powerful tool withmodern applications as diverse as: image processing, signal processing, data compression, data mining, speech recognition, computer graphics, etc. The aim of this paper is to introduce the concept of atomic decomposition of fuzzy normed linear spaces, which play a key role in the development of fuzzy wavelet theory. Atomic decompositions appeared in applications to signal processing and sampling theory among other areas. First we give a general definition of fuzzy normed linear spaces and we obtain decomposition theorems for fuzzy norms into a family of semi-norms, within more general settings. The results are both for Bag–Samanta fuzzy norms and for Katsaras fuzzy norms. As a consequence, we obtain locally convex topologies induced by this types of fuzzy norms. The results established in this paper, constitute a foundation for the development of fuzzy operator theory and fuzzy wavelet theory within this more general frame.

اسناد مشابه

  • fuzzy reflexivity of felbin's type fuzzy normed linear spaces and fixed point theorems in such spaces

    مقاله۲۰۱۱iranian journal of fuzzy systemst. bag, s. k. samanta

    an idea of fuzzy reexivity of felbin's type fuzzy normed linear spaces is introduced and its properties are studied. concept of fuzzy uniform normal structure is given and using the geometric properties of this concept xed point theorems are proved in fuzzy normed linear spaces.

  • on approximate cauchy equation in felbin's type fuzzy normed linear spaces

    مقاله۲۰۱۳iranian journal of fuzzy systemsi. sadeqi, f. moradlou, m. salehi

    n this paper we study the hyers-ulam-rassias stability of cauchyequation in felbin's type fuzzy normed linear spaces. as a resultwe give an example of a fuzzy normed linear space such that thefuzzy version of the stability problem remains true, while it failsto be correct in clas

  • A Note on Generalized Intuitionistic Fuzzy Normed Linear Space

    سند علمی۲۰۱۱T. K. Samanta

    s In respect of the de finition of intuitionistic fuzzy n-norm [9] , the definition of generalised intuitionistic fuzzy ψ norm ( in short GIFψN ) is introduced over a linear space and there after a few results on generalized intuitionistic fuzzy ψ normed linear space and finite d

  • ON APPROXIMATE CAUCHY EQUATION IN FELBIN'S TYPE FUZZY NORMED LINEAR SPACES

    مقاله۲۰۱۳Iranian Journal of Fuzzy SystemsI. Sadeqi, F. Moradlou, M. Salehi

    n this paper we study the Hyers-Ulam-Rassias stability of Cauchyequation in Felbin's type fuzzy normed linear spaces. As a resultwe give an example of a fuzzy normed linear space such that thefuzzy version of the stability problem remains true, while it failsto be correct in clas

  • FUZZY REFLEXIVITY OF FELBIN'S TYPE FUZZY NORMED LINEAR SPACES AND FIXED POINT THEOREMS IN SUCH SPACES

    مقاله۲۰۱۱Iranian Journal of Fuzzy SystemsT. Bag, S. K. Samanta

    An idea of fuzzy reexivity of Felbin's type fuzzy normed linear spaces is introduced and its properties are studied. Concept of fuzzy uniform normal structure is given and using the geometric properties of this concept xed point theorems are proved in fuzzy normed linear spaces.

  • a comparative study of fuzzy norms of linear operators on a fuzzy normed linear spaces

    مقالهjournal of mathematical modelingmorteza saheli, morteza saheli

    in the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operator