A Study On Reliability Using Pendant, Hexant, Octant Fuzzy Numbers
The weaving machine’s reliability is assessed using newly introduced fuzzy numbers. The fuzzy numbers introduced in this study give a better method to improve the reliability than other techniques. Pendant Fuzzy Number, Hexant Fuzzy Number, and Octant Fuzzy Number are all introduced in this present study. Pendant Fuzzy Number, Hexant Fuzzy Number, and Octant Fuzzy Number,α-cuts are defined, as well as their mathematical operations. The numerical examples are utilised to conduct a comparative research of reliability using various Fuzzy Numbers, and their defuzzification is accomplished using various ways such as Signed Distance method, Graded Mean Integration Method and Centroid Method. The purpose of this study is to discover the most reliable value for a weaving machine.
Zadeh LA, Fuzzy sets,Information and control 8 (1965), 338–353.
Panda DC, A new method for evaluation of fuzzy reliability of multistage interconnection. International Journal of Research and Reviews in Applied Sciences 3:14–20, (2016).
He Q, Yabing ZHA, Zhang R, Sun Q, Liu T, Reliability analysis for multi-state system based on triangular fuzzy variety subset Bayesian networks. EksploatNiezawodnosc- Maintenance and Reliability 19:152–165 (2017).
Mahapatra GS, Roy TK, Reliability of components using interval nonlinear programing. Electronic Journal of Applied Statistical Analysis 5:151–163 (2012).
Jamkhaneh EB, An evaluation of the systems reliability using fuzzy lifetime distribution. Journal of applied mathematics Islamic Azad University of Lahijan 7:73–80 (2011).
Hussian MA, Amin EA, Fuzzy reliability estimation for exponential distribution using ranked set sampling. International Journal of Contemporary Mathematical Sciences 12:31–42 (2017).
Alive IM, Kara Z, Fuzzy system reliability analysis using time dependent fuzzy set. Control and Cybernetics Journal 33 653-662 (2004).
Dong YG, Chen XZ, Cho HD, Kwon JW, Simulation of fuzzy reliability indexes, Journal of Mechanical Science and Technology 17:492–500, (2003).
Wu HC, Fuzzy reliability estimation using Bayesian approach. Computers and Industrial Engineering, 46:467–493, (2004).
Sharma MK, Possibility and Probability aspect to fuzzy reliability analysis of a network system. Global Journal of Pure and Applied Mathematics, 13; 3641–3655, (2017).
Kumar G, Bajaj RK, Intuitionistic fuzzy reliability of K-out-of-N: G system using statistical confidence interval, International Journal of Applied Information Systems 7:1–7, (2014).
Chaube S, Singh SB, Fuzzy reliability of two-stage weighted-k-out-of-n systems with common components, International Journal of Mathematical Engineering and Management Sciences 1:41–51, (2016).
Lee HM, Fuh CF, Su JS, Fuzzy parallel system reliability analysis based on level (λ,ρ)
interval-valued fuzzy numbers, International Journal of Innovative Computing Information and Control 8:5703–5713, (2012).
Kumar M, Yadav SP, A novel approach for analyzing fuzzy system reliability using different types of intuitionistic fuzzy failure rates of components, ISA Transactions 51:288–297, (2012).
Kumar M, Yadav SP, Kumar S, Fuzzy system reliability evaluation using time-independent intuitionistic fuzzy set, International Journal of Systems Science 44:50–66, (2013).
Razak KA, Rajakumar K, A study on fuzzy reliability measures, Applied Mathematical Sciences 7:3335–3343, (2013).
Rao KD, Kushwaha HS, Verma AK, Srividya A, Anew uncertainty importance measure in fuzzy reliability analysis, International Journal of Performability Engineering 5:219–226, (2009).
Xu X, Mithra J, Distribution system reliability evaluation using credibility theory, International Journal of Engineering Science and Technology 2:107-118, (2010)
Rezvani S, Multiplication Operation on Trapezoidal Fuzzy numbers, Journal of Physical Sciences, vol no-15, 17–26 (2011).
Praveen Prakash A and Geetha Lakshmi M, A Trident Fuzzy Number and its Arithmetic Operations, International Journal of Innovative Research in Computer and Communication Engineering, vol no-4(10) (2016).
Rama B and Michael Rosario G, Inventory model with penalty cost and shortage cost using trident fuzzy numbers, International Journal of Artificial Intelligence and Soft Computing, vol no-7–issue 1, pp. 59–85, 2019.
Rama B and Michael Rosario G, Quadrant Fuzzy Number and its Arithmetic Operations, Journal of Computer and Mathematical Sciences, vol no-10(7), 1466–1475 July 2019.
Nagoorgani A, A new operation on triangular fuzzy number for solving fuzzy linear programming problem, Applied Mathematical Sciences, 6, 525–532 (2012).
Avinash J. Kamble, Some Notes on Pentagonal Fuzzy Numbers, International Journal of Mathematical Archive, Vol no-13(2), 113–121, (2017).
Menaka G, Ranking of Octagonal Intuitionistic Fuzzy Numbers, IOSR Journal of Mathematics, vol 13 issue 3 Ver. II, pp. 63–71, (2017).
Rezvani S, “Ranking generalized exponential trapezoidal fuzzy numbers based on variance”, Applied Mathematics and Computation, (2015).
HesamoddinTahami and HengamehFakhravar “A Fuzzy Inventory Model Considering Imperfect Quality Items with Receiving Reparative Batch and Order”, European Journal of Engineering Research and Science, (2020).
RituparnaPakhira, Uttam Ghosh and Susmita Sarkar “Study of Memory Effect in a Fuzzy EOQ Model with No Shortage”, International Journal of Intelligent Systems and Applications, (2019).
SankarPrasadMondal, Manimohan Mandal and Debasish Bhattacharya. “Non-linear interval valued fuzzy numbers and their application in difference equations”, Granular Computing, (2017).
Michael Rosario G and Dhanalakhmi A, “Intuitionistic Fuzzy Equations and its Application on Reliability Evaluation”, ‘International Journal of Advanced Technology Engineering and Science’, Volume 03, Number 03, March (2015).
Srinath LS, Reliability Engineering, Fourth Edition, Affiliated East-West Press Private Limited – (2016) (Text Book).
Charles E. Ebeling, An Introduction to Reliability and Maintainability Engineering, McGraw Hill Education India private Limited – (2017).
Jini Varghese P and Michael Rosario G, Fuzzy reliability evaluation of weaving machine in textile industry, International Journal of Mathematical Archieve, vol. 9. no. 1, ISSN 2229-5046, (2018).
Jini Varghese P and Michael Rosario G, some arithmetic operations in trapezoidal Fuzzy numbers and intuitionistic trapezoidal Fuzzy numbers, Journal of Applied Science and Computations, vol. 5, issue 122018, 40–49, (2019).
Jini Varghese P and Michael Rosario G. “Fuzzy Probist System Reliability of Weaving Machine in Textile Industry”, IOP Conference Series: Materials Science and Engineering, (2021).