International Journal of Soft Computing and Engineering (IJSCE)
ISSN: 2231-2307, Volume-7 Issue-4, September 2017
1
Retrieval Number: C3035077317/2017©BEIESP
Published By:
Blue Eyes Intelligence Engineering
& Sciences Publication
Abstract: The aim of this paper is investigates the reliability
characteristics of systems using generalized intuitionistic fuzzy
exponential lifetime distribution, in which the lifetime parameter
is assumed to be generalized intuitionistic fuzzy number.
Generalized intuitionistic fuzzy reliability, generalized
intuitionistic fuzzy hazard function, generalized intuitionistic
fuzzy mean time to failure and their
-cut have been
discussed when systems follow generalized intuitionistic fuzzy
exponential lifetime distribution. Further, reliability analysis of
the series and parallel systems has been done.
Index Terms: generalized intuitionistic fuzzy number (GIFN),
-cut, generalized intuitionistic fuzzy distribution,
generalized intuitionistic fuzzy reliability.
I. INTRODUCTION
After the introduction of fuzzy sets by Zadeh (1965), many
researchers used the concept of fuzzy set to deal with
uncertainty in reliability analysis. For example: Singer
(1990), Cia et al. (1993), Chen (1994), Mong et al. (1994),
Pandey and Tyagi (2007), Pandey et al. (2009), Baloui
Jamkhaneh (2011), Baloui Jamkhaneh (2014) and etc.
Atanassov (1986) introduced concept intuitionistic fuzzy sets
(IFS) as a generalization of fuzzy sets. Intuitionistic fuzzy
sets theory is a useful tool in modeling real life problems,
wherein hesitation between belongingness and
non-belongingness cannot be ruled out. Burillo et al. (1994)
proposed the definition of intuitionistic fuzzy number (IFN).
Mahapatra and Roy (2009) presented triangular intuitionistic
fuzzy number (TIFN) and used it for reliability evaluation.
Mahapatra and Mahapatra (2010) presented intuitionistic
fuzzy fault tree using arithmetic operation of trapezoidal
intuitionistic fuzzy number (TrIFN) which are evaluated
based on (α,β)-cuts method. Pandey et al. (2011) describes a
novel approach, based on intuitionistic fuzzy set theory for
reliability analysis of series and parallel network. Kumar et
al. (2011) developed a new approach for analyzing the fuzzy
system reliability of series and parallel systems using
intuitionistic fuzzy set theory. Kumar and Yadav (2011)
presented a new method for fuzzy system reliability analysis
based on arithmetic operations of different types of
intuitionistic fuzzy numbers. Sharma (2012) presented the
reliability of a system using IFS. Garg et al. (2013) predicted
the behavior of an industrial system under imprecise and
vague environment. To handle the uncertainty in the data,
they used IFS theory rather than fuzzy set theory. Also Garg
and Rani (2013) presented a technique for computing the
membership functions of the intuitionistic fuzzy set (IFS) in
reliability analyzed by utilizing imprecise, uncertain and
vague data. Bohra and singh (2015) used intuitionistic fuzzy
Revised Version Manuscript Received on July 13, 2017
Prof. E. Baloui Jamkhaneh, Department of Statistics, Qaemshahr
Branch, Islamic Azad University, Qaemshahr, Iran; E-mail:
e_baloui2008@yahoo.com
Rayleigh distribution in evaluating the systems reliability.
Kumar and Singh (2015) presented fuzzy system reliability
using intuitionistic fuzzy Weibull lifetime distribution.
Kumar and Singh (2017) investigated the applications of
generalized trapezoidal intuitionistic fuzzy number in fuzzy
reliability theory.
Baloui Jamkhaneh and Nadarajah (2015) considered new
generalized intuitionistic fuzzy sets (GIFS
B
) and introduced
some operators over GIFS
B
. Shabani and Baloui Jamkhaneh
(2014) introduced a new generalized intuitionistic fuzzy
number (GIFN
B
) based on generalization of the IFS. The
main objective of this paper is to evaluated systems reliability
using generalized intuitionistic fuzzy exponential
distribution, in which the parameter of the exponential
distribution is taken as a generalized intuitionistic fuzzy
number related to Shabani and Baloui Jamkhaneh (2014).
The originality of this study comes from the fact that, there
were no previous works in generalized intuitionistic fuzzy
distributions. This paper is organized as follows: In Section 2,
we briefly introduce generalized intuitionistic fuzzy
numbers. In Section 3 define generalized intuitionistic fuzzy
distribution. In Section 4, generalized intuitionistic fuzzy
reliability is introduced. In Section 5, generalized
intuitionistic fuzzy reliability of series and parallel system is
calculated. The paper is concluded in Section 6.
II. PRELIMINARIES
A. Generalized Intuitionistic Fuzzy Number
Definition1. (Baloui Jamkhaneh, Nadarajah (2015)) Let be
a non empty set. A generalized intuitionistic fuzzy sets
(
) in , is defined as an object of the form
where the functions
and
, denote the degree of membership
and degree of non membership functions of A respectively,
and
for each and
.
Definition2. (Shabani, Baloui Jamkhaneh (2014)) In special
case, generalized L-R type intuitionistic fuzzy number A can
be described as any
of the real line whose
membership function
and non-membership function
are defined as follows
,
System Reliability using Generalized Intuitionistic
Fuzzy Exponential Lifetime Distribution
E. Baloui Jamkhaneh