Thai Journal of Mathematics Volume 15 (2017) Number 2 : 503–515 http://thaijmath.in.cmu.ac.th ISSN 1686-0209 Asymptotically Equivalent Generalized Difference Sequences of Fuzzy Real Numbers Defined by Orlicz Function Amar Jyoti Dutta Department of Mathematics Pragjyotish College (A/U Gauhati University) Bharalumukh, Santipur, Guwahati-781009, Assam, India e-mail : amar iasst@yahoo.co.in Abstract : The aim of this article is to introduce the classes of strong Δ m - lacunary asymptotically equivalent, Δ m -lacunary asymptotically statistically equiv- alent, strong Δ m -almost asymptotically equivalent sequences of fuzzy real numbers in terms of Orlicz function. We have established some relations between the classes of the sequences. Keywords : asymptotically equivalent; lacunary; statistically convergent; fuzzy real number; Ces` aro summable; Orlicz function. 2010 Mathematics Subject Classification : 40A05; 40C05; 46D25. 1 Introduction and Preliminaries Marouf [1] introduced the idea of asymptotically equivalent sequences and asymptotic regular matrices and thereafter Patterson [2] extends these concepts by introducing asymptotically statistically equivalent analog and natural regu- larity conditions for nonnegative summability matrices. Savas [3, 4] introduced and studied the concepts of asymptotically equivalent and λ-statistical conver- gence and generalized the idea of I -asymptotically lacunary statistical equivalent sequences. Recently Esi and Esi [5] introduced the idea of asymptotically S Δ λ,L (F )- Copyright c  2017 by the Mathematical Association of Thailand. All rights reserved.