{"title":"Reliability Evaluation using Triangular Intuitionistic Fuzzy Numbers Arithmetic Operations","authors":"G. S. Mahapatra, T. K. Roy","volume":26,"journal":"International Journal of Computer and Information Engineering","pagesStart":350,"pagesEnd":358,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10400","abstract":"In general fuzzy sets are used to analyze the fuzzy\r\nsystem reliability. Here intuitionistic fuzzy set theory for analyzing\r\nthe fuzzy system reliability has been used. To analyze the fuzzy\r\nsystem reliability, the reliability of each component of the system as\r\na triangular intuitionistic fuzzy number is considered. Triangular\r\nintuitionistic fuzzy number and their arithmetic operations are\r\nintroduced. Expressions for computing the fuzzy reliability of a\r\nseries system and a parallel system following triangular intuitionistic\r\nfuzzy numbers have been described. Here an imprecise reliability\r\nmodel of an electric network model of dark room is taken. To\r\ncompute the imprecise reliability of the above said system, reliability\r\nof each component of the systems is represented by triangular\r\nintuitionistic fuzzy numbers. Respective numerical example is\r\npresented.","references":"[1] T. Onisawa and J. Kacprzyk, Reliability and safety under fuzziness 1sted:\r\nPhysica Verlag, (1995).\r\n[2] A. Kaufmann and M. M. Gupta, Fuzzy mathematical models in\r\nengineering and management science, North-Holland, Amstredam,\r\n(1988).\r\n[3] K. Y. Cai, C. Y. Wen and M. L. Zhang, Fuzzy variables as a basis for a\r\ntheory of fuzzy reliability in the possibility context, Fuzzy Sets and\r\nSystems, 42 (1991), 142-145.\r\n[4] K. Y. Cai, C. Y. Wen and M. L. Zhang, Fuzzy states as a basis for a\r\ntheory of fuzzy reliability, Microelectronic Reliability, 33 (1993), 2253-\r\n2263.\r\n[5] C. H. Cheng and D. L. Mon, Fuzzy system reliability analysis by interval\r\nof confidence, Fuzzy Sets and Systems, 56 (1993), 29-35.\r\n[6] S. M. Chen, Fuzzy system reliability analysis using fuzzy number\r\narithmetic operations, Fuzzy Sets and Systems, 64 (1994), 31-38.\r\n[7] D. Singer, A fuzzy set approach to fault tree and reliability analysis,\r\nFuzzy Sets and Systems, 34 (1990), 145-155.\r\n[8] A. K. Verma; A. Srividya; Rajesh Prabhu Gaonkar, Fuzzy dynamic\r\nreliability evaluation of a deteriorating system under imperfect repair,\r\nInternational Journal of Reliability, Quality and Safety Engineering, 11\r\n(4) 2004, 387-398.\r\n[9] L. A. Zadeh, Fuzzy sets, Information Control, 8 (1965), 338-353.\r\n[10] K.T. Atanassov, Intuitionistic fuzzy sets, VII ITKR-s Session, Sofia\r\n(deposed in Central Science-Technical Library of Bulgarian Academy of\r\nScience, 1697\/84), 1983 (in Bulgarian).\r\n[11] K.T. Atanassov, Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1986;\r\n20: 87-96.\r\n[12] K.T. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets and\r\nSystems 33(1) (1989) 37-46.\r\n[13] K.T. Atanassov, Intuitionistic Fuzzy Sets, Physica-Verlag, Heidelberg,\r\nNew York, 1999.\r\n[14] K.T. Atanassov, Two theorems for Intuitionistic fuzzy sets. Fuzzy Sets\r\nand Systems, 2000; 110: 267-269.\r\n[15] K.T. Atanassov, G. Gargov, Interval-valued intuitionistic fuzzy sets,\r\nFuzzy Sets and Systems, 31 (3) (1989) 343-349.\r\n[16] E. Szmidt, J. Kacrzyk, Distances between intuitionistic fuzzy sets, Fuzzy\r\nSets and Systems, 114 (3) (2000) 505-518.\r\n[17] T. Buhaesku, On the convexity of intuitionistic fuzzy sets, Itinerant\r\nseminar on functional equations, approximation and convexity, Cluj-\r\nNapoca (1988) 137-144.\r\n[18] T. Gerstenkorn and J. Manko, Correlation of intuitionistic fuzzy sets,\r\nFuzzy Sets and Systems, 44 (1991), 39-43.\r\n[19] D. Stoyanova and K.T. Atanassov, Relations between operators, defined\r\nover intuitionistic fuzzy sets, IM-MFAIS, 1 1990, 46-49, Sofia,\r\nBulgaria.\r\n[20] D. Stoyanova, More on Cartesian product over intuitionistic fuzzy sets,\r\nBUSEFAL 54 (1993) 9-13.\r\n[21] G. Deschrijver, E.E. Kerre, On the relationship between intuitionistic\r\nfuzzy sets and some other extensions of fuzzy set theory, Journal of\r\nFuzzy Mathematics, 10 (3) (2002) 711-724.\r\n[22] P. Burillo, H.Bustince, V. Mohedano, Some definition of intuitionistic\r\nfuzzy number, Fuzzy based expert systems, fuzzy Bulgarian enthusiasts,\r\nSeptember 28-30, 1994, Sofia, Bulgaria.\r\n[23] H. B. Mitchell, Ranking-Intuitionistic Fuzzy Numbers, International\r\nJournal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12 (3)\r\n2004, 377-386.\r\n[24] B. S. Dhillon, Human reliability and error in transportation systems -\r\n(Springer series in reliability engineering), Springer-Verlag, London,\r\n2007.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 26, 2009"}