Sequence Space m(M, φ)Fof Fuzzy Real Numbers Defined by Orlicz Functions with Fuzzy Metric

Abstract

Abstract. The sequence space m(M,φ) F of fuzzy real numbers is introduced. Someproperties of this sequence space like solidness, symmetricity, convergence-free etc. arestudied. We obtain some inclusion relations involving this sequence space. 1. IntroductionThe concept of fuzzy set theory was introduced by L.A. Zadeh in the year 1965.Later on different classes of sequences of fuzzy numbers have been investigated byEsi [2], Nuray and Savas [6], Syau [9], Tripathy and Baruah ([13], [14], [15]), Tripa-thy and Borgohain [16], Tripathy and Dutta ([17], [18]), Tripathy and Sarma [20]and many others.An Orlicz function is a function M : [0,∞) → [0,∞), which is continuous,non-decreasing and convex with M(0) = 0,M(x) >0,for x>0 and M(x) → ∞, asx→ ∞.If the convexity of the Orlicz function is replaced by M(x+y) ≤ M(x)+M(y),then this function is called as modulus function.Remark. An Orlicz function satisfies the inequality M(λx) ≤ λM(x) for all λwith0 <λ<1.Sargent [8] introduced the crisp set sequence space m(φ) and studied someproperties of this space. Later on it was studied from the sequence space point ofview and some matrix classes were characterized with one member as m(φ) by Rathand Tripathy [7], Tripathy [10] and others. In this article we introduce the spacem(M,φ)