9 Notes on Intuitionistic Fuzzy Sets ISSN 1310–4926 Vol. 20, 2014, No. 1, 9–19 Non-linear arithmetic operation on generalized triangular intuitionistic fuzzy numbers Sankar Prasad Mondal * and Tapan Kumar Roy Department of Mathematics, Bengal Engineering and Science University Shibpur,Howrah–711103, West Bengal, India * Corresponding author (email:sankar.res07@gmail.com) Abstract: In this paper we discussed some nonlinear arithmetic operation on generalized triangular intuitionistic fuzzy numbers. Some examples and an application are given. Keywords: Fuzzy set, Intuitionistic fuzzy number. AMS Classification: 03E72, 03E75, 26E50. 1 Introduction Zadeh [1] and Dubois and Prade [2] were the first who introduced the conception based on fuzzy number and fuzzy arithmetic. Generalizations of fuzzy sets theory [1] is considered to be one of Intuitionistic fuzzy set (IFS). Out of several higher-order fuzzy sets, IFS was first introduced by Atanassov [3] have been found to be suitable to deal with unexplored areas. The fuzzy set considers only the degree of belongingness and non-belongingness. Fuzzy set theory does not incorporate the degree of hesitation (i.e., degree of non-determinacy defined as, ͳ− sum of membership function and non-membership function. To handle such situations, Atanassov [4] explored the concept of fuzzy set theory by intuitionistic fuzzy set (IFS) theory. The degree of acceptance in Fuzzy Sets is only considered, otherwise IFS is characterized by a membership function and a non-membership function so that the sum of both values is less than one [4]. Basic arithmetic operations of TIFNs is defined by Deng-Feng Li in [5] using membership and non-membership values. Basic arithmetic operations of TIFNs such as addition, subtraction and multiplication are defined by Mahapatra and Roy in [6], by considering the six tuple number itself and division by A. Nagoorgani and K. Ponnalagu [7]. Now-a-days, IFSs are being studied extensively and being used in different fields of Science and Technology. Amongst the all research works mainly on IFS we can include Atanassov [4, 8–11], Atanassov and Gargov [12], Szmidt and Kacprzyk [13], Buhaescu [14], Ban [15], Deschrijver and Kerre [16], Stoyanova [17], Cornelis et al. [18], Buhaesku [19], Gerstenkorn and Manko [20], Stoyanova and Atanassov [21], Stoyanova [22], Mahapatra and Roy [23], Hajeeh [24], Persona et al. [25], Prabha et al. [26], Nikolaidis and Mourelatos [27], Kumar et al.[28] and Wang [29], Shaw and Roy [30], Adak et al.[31], A.Varghese and S. Kuriakose [32].