Abstract—In general fuzzy sets are used to analyze the fuzzy system reliability. Here intuitionistic fuzzy set theory for analyzing the fuzzy system reliability has been used. To analyze the fuzzy system reliability, the reliability of each component of the system as a triangular intuitionistic fuzzy number is considered. Triangular intuitionistic fuzzy number and their arithmetic operations are introduced. Expressions for computing the fuzzy reliability of a series system and a parallel system following triangular intuitionistic fuzzy numbers have been described. Here an imprecise reliability model of an electric network model of dark room is taken. To compute the imprecise reliability of the above said system, reliability of each component of the systems is represented by triangular intuitionistic fuzzy numbers. Respective numerical example is presented. Keywords—Fuzzy set, Intuitionistic fuzzy number, System reliability, Triangular intuitionistic fuzzy number. I. INTRODUCTION T is well known that the conventional reliability analysis using probabilities has been found to be inadequate to handle uncertainty of failure data and modeling. To overcome this problem, the concept of fuzzy [1] approach has been used in the evaluation of the reliability of a system. In [2] Kaufmann et al. pointed out that the discipline of the reliability engineering encompasses a number of different activities, out of which the reliability modeling is the most important activity. For a long period of time efforts have been made in the design and development of reliable large-scale systems. In that period of time considerable work has been done by researchers to build a systematic theory of reliability based on the probability theory. In [3] Cai et al. pointed out that there are two fundamental assumptions in the conventional reliability theory, i.e. (a) Binary state assumptions: the system is precisely defined as functioning or failing. (b) Probability assumptions: the system behaviour is fuzzy characterized in the context of probability measures. Because of the inaccuracy and uncertainties of data, G.S. Mahapatra is with the Mathematics Department, Bengal Engineering and Science University, Shibpur, P.O.-B. Garden, Howrah-711103, India (phone: +919433135327; fax: +91-33-26682916; e- mail:g_s_mahapatra@yahoo.com). T.K. Roy is with the Mathematics Department, Bengal Engineering and Science University, Shibpur, P.O.-B. Garden, Howrah-711103, India (phone: +919432658432; fax: +91-33-26682916; e-mail: roy_t_k@yahoo.co.in). the estimation of precise values of probability becomes very difficult in many systems. In [4], Cai et al introduced system failure engineering and its use of fuzzy methodology. In [5], Chen presented a method for analyzing the fuzzy system reliability using fuzzy number arithmetic opaerations. In [6], Cheng et al. used interval of confidence for analyzing the fuzzy system reliability. In [7], Singer presented a fuzzy set approach for fault tree and the reliability analysis. Verma [8] presented the dynamic reliability evaluation of the deteriorating system using the concept of probist reliability as a triangular fuzzy number. Intuitionistic fuzzy set (IFS) is one of the generalizations of fuzzy sets theory [9]. Out of several higher-order fuzzy sets, IFS first introduced by Atanassov [10] have been found to be compatible to deal with vagueness. The concept of IFS can be viewed as an appropriate/alternative approach to define a fuzzy set in case where available information is not sufficient for the definition of an imprecise concept by means of a conventional fuzzy set. In fuzzy sets the degree of acceptance is considered only but IFS is characterized by a membership function and a non-membership function so that the sum of both values is less than one [11]. Presently intuitionistic fuzzy sets are being studied and used in different fields of science. Among the works on these sets, Atanassov [12-14], Atanassov and Gargov [15], Szmidt and Kacrzyk [16], Buhaescu [17], Gerstenkorn and Manko [18], Stojona and Atanassov [19], Stoyanova [20], Deschrijver and Kerre [21] can be mentioned. With best of our knowledge, Burillo [22] proposed definition of intuitionistic fuzzy number and studied perturbations of intuitionistic fuzzy number and the first properties of the correlation between these numbers. Mitchell [23] considered the problem of ranking a set of intuitionistic fuzzy numbers to define a fuzzy rank and a characteristic vagueness factor for each intuitionistic fuzzy number. Here intuitionistic fuzzy number (IFN) is presented according to the approach of presentation of fuzzy number. Arithmetic operations of proposed IFN are evaluated. This paper is organized as follows: Section 2 presents basic concept of intuitionistic fuzzy sets and intuitionistic fuzzy number. Section 3 presents arithmetic operations between two triangular intuitionistic fuzzy numbers. Section 4 presents expressions for finding the fuzzy reliability of a series and a parallel system using arithmetic operations on triangular intuitionistic fuzzy numbers. Section 5 presents the intuitionitic fuzzy success tree of imprecise reliability of a Reliability Evaluation using Triangular Intuitionistic Fuzzy Numbers Arithmetic Operations G. S. Mahapatra, and T. K. Roy I World Academy of Science, Engineering and Technology International Journal of Computer and Information Engineering Vol:3, No:2, 2009 350 International Scholarly and Scientific Research & Innovation 3(2) 2009 scholar.waset.org/1307-6892/10400 International Science Index, Computer and Information Engineering Vol:3, No:2, 2009 waset.org/Publication/10400