Reliability Evaluation using Triangular Intuitionistic Fuzzy Numbers Arithmetic Operations

Authors: G. S. Mahapatra, T. K. Roy

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, Systemreliability, Triangular intuitionistic fuzzy number.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1075166

References:

[1] T. Onisawa and J. Kacprzyk, Reliability and safety under fuzziness 1sted: Physica Verlag, (1995).
[2] A. Kaufmann and M. M. Gupta, Fuzzy mathematical models in engineering and management science, North-Holland, Amstredam, (1988).
[3] K. Y. Cai, C. Y. Wen and M. L. Zhang, Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context, Fuzzy Sets and Systems, 42 (1991), 142-145.
[4] K. Y. Cai, C. Y. Wen and M. L. Zhang, Fuzzy states as a basis for a theory of fuzzy reliability, Microelectronic Reliability, 33 (1993), 2253- 2263.
[5] C. H. Cheng and D. L. Mon, Fuzzy system reliability analysis by interval of confidence, Fuzzy Sets and Systems, 56 (1993), 29-35.
[6] S. M. Chen, Fuzzy system reliability analysis using fuzzy number arithmetic operations, Fuzzy Sets and Systems, 64 (1994), 31-38.
[7] D. Singer, A fuzzy set approach to fault tree and reliability analysis, Fuzzy Sets and Systems, 34 (1990), 145-155.
[8] A. K. Verma; A. Srividya; Rajesh Prabhu Gaonkar, Fuzzy dynamic reliability evaluation of a deteriorating system under imperfect repair, International Journal of Reliability, Quality and Safety Engineering, 11 (4) 2004, 387-398.
[9] L. A. Zadeh, Fuzzy sets, Information Control, 8 (1965), 338-353.
[10] K.T. Atanassov, Intuitionistic fuzzy sets, VII ITKR-s Session, Sofia (deposed in Central Science-Technical Library of Bulgarian Academy of Science, 1697/84), 1983 (in Bulgarian).
[11] K.T. Atanassov, Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1986; 20: 87-96.
[12] K.T. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets and Systems 33(1) (1989) 37-46.
[13] K.T. Atanassov, Intuitionistic Fuzzy Sets, Physica-Verlag, Heidelberg, New York, 1999.
[14] K.T. Atanassov, Two theorems for Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 2000; 110: 267-269.
[15] K.T. Atanassov, G. Gargov, Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31 (3) (1989) 343-349.
[16] E. Szmidt, J. Kacrzyk, Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems, 114 (3) (2000) 505-518.
[17] T. Buhaesku, On the convexity of intuitionistic fuzzy sets, Itinerant seminar on functional equations, approximation and convexity, Cluj- Napoca (1988) 137-144.
[18] T. Gerstenkorn and J. Manko, Correlation of intuitionistic fuzzy sets, Fuzzy Sets and Systems, 44 (1991), 39-43.
[19] D. Stoyanova and K.T. Atanassov, Relations between operators, defined over intuitionistic fuzzy sets, IM-MFAIS, 1 1990, 46-49, Sofia, Bulgaria.
[20] D. Stoyanova, More on Cartesian product over intuitionistic fuzzy sets, BUSEFAL 54 (1993) 9-13.
[21] G. Deschrijver, E.E. Kerre, On the relationship between intuitionistic fuzzy sets and some other extensions of fuzzy set theory, Journal of Fuzzy Mathematics, 10 (3) (2002) 711-724.
[22] P. Burillo, H.Bustince, V. Mohedano, Some definition of intuitionistic fuzzy number, Fuzzy based expert systems, fuzzy Bulgarian enthusiasts, September 28-30, 1994, Sofia, Bulgaria.
[23] H. B. Mitchell, Ranking-Intuitionistic Fuzzy Numbers, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12 (3) 2004, 377-386.
[24] B. S. Dhillon, Human reliability and error in transportation systems - (Springer series in reliability engineering), Springer-Verlag, London, 2007.