Palestine Journal of Mathematics Vol. 9(1)(2020) , 174–186 © Palestine Polytechnic University-PPU 2020 Some New Classes of Multiplier Ideal Convergent Triple Sequence Spaces of Fuzzy Numbers Defined by Orlicz Functions Sangita Saha, Ayhan Esi and Santanu Roy Communicated by Fuad Kittaneh MSC 2010 Classifications: 40A05, 40A30, 40D25. Keywords and phrases: Multiplier sequence, Ideal convergence, Fuzzy numbers, Triple sequences, normal, monotone, symmetric, convergence free, sequence algebra. Abstract In this article, some new classes of multiplier ideal convergent triple sequence spaces of fuzzy numbers defined by an Orlicz function and a multiplier sequence are introduced. The multiplier problem is characterized.We also make an effort to prove some algebraic and topological properties such as closed property, completeness, solid, monotone, symmetric, se- quence algebra, convergence free etc. of these spaces. Moreover some inclusion relation between these spaces are established. 1 Introduction The fuzzy set theory extended the basic mathematical concept of a set. After the pioneering work done on fuzzy set theory by Zadeh [35] in 1965, a huge number of research papers have been appeared on fuzzy theory and its applications as well as fuzzy analogues of the classical theo- ries. Fuzzy set theory is a powerful hand set for modeling, uncertainty and vagueness in various problems arising in the field of science and engineering. Several mathematicians have discussed various aspects of the theory and applications of fuzzy sets such as fuzzy topological spaces, similarity relations and fuzzy orderings, fuzzy measures of fuzzy events, fuzzy mathematical programming. In fact the fuzzy set theory has become an active area of research in science and engineering for the last half century. While studying fuzzy topological spaces, we face many situations where we need to deal with convergence of fuzzy numbers. Using the notion of fuzzy real numbers, different types of fuzzy real-valued sequence spaces have been introduced and studied by several mathematicians. Matloka [12] introduced bounded and convergent sequences of fuzzy numbers and studied some of their properties. Nanda [13] studied the sequences of fuzzy numbers and showed that the set of all convergent sequences of fuzzy numbers forms a complete metric space. The summability theory of multiple sequences was studied by Agnew [1] and he derived cer- tain theorems for double sequences. At the initial stage, the different types of notions of triple sequences were introduced and investigated by Sahiner et al. [20] and Sahiner and Tripathy [21]. Recently statistical convergence of triple sequences on probabilistic normed space was in- troduced by Savas and Esi [24]. Later on, Esi [5] has introduced statistical convergence of triple sequences in topological groups. More works on triple sequences are found in Kumar et. al. [9], Dutta et. al. [3], Tripathy and Goswami [28], Nath and Roy [14-16], Saha et. al. [18], Saha and Roy [19] and so on. The notion of ideal convergence depends on the structure of the ideal I of the subset of the set of natural numbers. The concept of ideal convergence for single sequences was introduced by Kostyrko, Salat and Wilczyaski [8] in 2000-2001. Later on it was further developed by Salat et al. [22-23], Tripathy and Sen [32], Tripathy and Tripathy [34], Kumar et. al. [9], Das et al. [2], Tripathy and Hazarika [29] and many others. An Orlicz function M is a function M : [0, ∞) → [0, ∞) such that it is continuous, non- decreasing and convex with M (0)= 0,M (x) > 0 for x > 0 and M (x) →∞ as x →∞.