On Paranormed Type Fuzzy Real Valued Class of Sequences2ℓF(p)

Abstract

Abstract. In this article we introduce the fuzzy real valued double sequence spaces 2 l F ( p ) where p = ( p nk ) is a double sequence of bounded strictly positive numbers. Westudy their different properties like completeness , solidness , symmetricity, convergencefree etc. We prove some inclusion results also. 1. IntroductionThe concept of fuzzy sets was introduced by Zadeh [19] in 1965. The poten-tial of the notion of fuzzy set was realized by different scientific groups and manyresearchers. The concept of fuzziness has been applied in various fields such ascybernetics, artificial intelligence, expert system and fuzzy control, pattern recog-nition, operation research, decision making, image analysis, projectiles, probabilitytheory, agriculture, weather forecasting, etc.Using the notion of fuzzy real numbers, different types of fuzzy real-valued sequencespaces have been introduced and studied by Nanda [5], Nuray and Savas [6], Tripa-thy and Dutta ([10], [11], [12]), Tripathy and Borgohain [18], Tripathy and Baruah([8], [9]), Tripathy and Sarma [15], Choudhary and Tripathy [2] and many others.The initial works on double sequences of real or complex terms is found in Bromwich[1]. The notion of regular convergence of double sequences of real or complex termsis introduced by Hardy [2]. Tripathy and Sarma ([13], [14]) studied different typesof double sequence spaces, while Tripathy and Dutta ([10], [11], [12]) introducedand investigated different types of double sequence spaces.The notion of paranormed sequence spaces is pity old. Different classes of para-normed sequence spaces have been introduced and studied by Choudhary and Tri-pathy [2], Tripathy and Sen[16], Tripathy[7]. Tripathy and Sen [17] have character-ized some matrix classes involving some paranormed sequence spaces, those unify