Fuzzy system reliability evaluation using time-dependent intuitionistic fuzzy set

In general, fuzzy sets are used to analyse the system reliability. In this article, the concept of fuzzy set is extended by the idea of intuitionistic fuzzy set (IFS) and a new general procedure is proposed to construct the membership and non-membership functions of the fuzzy reliability using time-dependent IFS. Here, failure rate function of the system is represented by a triangular intuitionistic fuzzy number (IFN). Also, using proposed approach, membership and non-membership functions of fuzzy reliability of series and parallel systems are constructed, where the failure rate of each component is taken as a time-dependent triangular IFN. The major advantage of using IFS over fuzzy sets is that IFS separate the positive and negative evidences for membership of an element in the set. Numerical examples are given to illustrate the proposed approach.

[1]  Deng-Feng Li,et al.  Multiattribute decision making models and methods using intuitionistic fuzzy sets , 2005, J. Comput. Syst. Sci..

[2]  Kai-Yuan Cai,et al.  Coherent Systems in Profust Reliability Theory , 1995 .

[3]  Hong-Zhong Huang,et al.  Reliability assessment for fuzzy multi-state systems , 2010, Int. J. Syst. Sci..

[4]  Kai-Yuan Cai,et al.  Fuzzy states as a basis for a theory of fuzzy reliability , 1993 .

[5]  Ching-Hsue Cheng,et al.  Fuzzy system reliability analysis by interval of confidence , 1993 .

[6]  Kai-Yuan Cai,et al.  Street-lighting lamps replacement: a fuzzy viewpoint , 1990 .

[7]  Shyi-Ming Chen.  FUZZY SYSTEM RELIABILITY-ANALYSIS USING FUZZY NUMBER ARITHMETIC OPERATIONS (VOL 64, PG 31, 1994) , 1994 .

[8]  Ravindra Arora,et al.  IEEE Press Series on Power Engineering , 2011 .

[9]  Ching-Hsue Cheng,et al.  Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly , 2006, Microelectron. Reliab..

[10]  Shyi-Ming Chen,et al.  Analyzing Fuzzy System Reliability Using Vague Set Theory , 2003 .

[11]  Cai Kaiyuan,et al.  Posbist reliability behavior of typical systems with two types of failure , 1991 .

[12]  Basil K. Papadopoulos,et al.  L-fuzzy Sets and Intuitionistic Fuzzy Sets , 2007, Computational Intelligence Based on Lattice Theory.

[13]  Przemyslaw Grzegorzewski,et al.  Distances and orderings in a family of intuitionistic fuzzy numbers , 2003, EUSFLAT Conf..

[14]  Ming-Hung Shu,et al.  Fault-tree analysis for liquefied natural gas terminal emergency shutdown system , 2009, Expert Syst. Appl..

[15]  K. Atanassov,et al.  Intuitionistic fuzzy Prolog , 1993 .

[16]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[17]  Cai Kaiyuan,et al.  Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context , 1991 .

[18]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[19]  T. Onisawa,et al.  Reliability and Safety Analyses under Fuzziness , 1995 .

[20]  D. Singer.  A fuzzy set approach to fault tree and reliability analysis , 1990 .

[21]  Ching-Hsue Cheng,et al.  The reliability of general vague fault-tree analysis on weapon systems fault diagnosis , 2006, Soft Comput..

[22]  Li Dengfeng,et al.  New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions , 2002, Pattern Recognit. Lett..

[23]  Dengfeng Li,et al.  New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions , 2002, Pattern Recognit. Lett..

[24]  Humberto Bustince,et al.  Vague sets are intuitionistic fuzzy sets , 1996, Fuzzy Sets Syst..

[25]  Ranjit Biswas,et al.  An application of intuitionistic fuzzy sets in medical diagnosis , 2001, Fuzzy Sets Syst..

[26]  I. M. Aliev,et al.  Fuzzy system reliability analysis using dependent fuzzy set , 2004 .

[27]  Ching-Hsue Cheng,et al.  A general and easy computational method for functions of fuzzy numbers , 1995 .