[Home ] [Archive]   [ فارسی ]  
:: Main :: About :: Current Issue :: Archive :: Search :: Submit :: Contact ::
Main Menu
Home::
Journal Information::
Articles archive::
For Authors::
For Reviewers::
Registration::
Ethics Considerations::
Contact us::
Site Facilities::
::
Search in website

Advanced Search
..
Receive site information
Enter your Email in the following box to receive the site news and information.
..
Indexing and Abstracting



 
..
Social Media

..
Licenses
Creative Commons License
This Journal is licensed under a Creative Commons Attribution NonCommercial 4.0
International License
(CC BY-NC 4.0).
 
..
Similarity Check Systems


..
:: Volume 18, Issue 1 (8-2024) ::
JSS 2024, 18(1): 0-0 Back to browse issues page
Fuzzy Order Statistics Based on α-Value and Some of Its Applications in Reliability
Mahdieh Mozafari , Mohammad Khanjari Sadegh * , Mohammad Ghasem Akbari , Gholamreza Hesamian
Abstract:   (1104 Views)
In this paper, fuzzy order statistics are expressed based on the concept of α-value, and some of its applications in reliability have been examined. For this purpose, if the lifetime distribution of the system components is known, some of the reliability criteria of the $i$th order statistic using the definition of a fuzzy random variable based on the α-value have been investigated. Also, if the lifetime distribution of the components is unknown or only the fuzzy observations of the lifetime of the components are available, the empirical distribution function of the fuzzy data is used to estimate the reliability based on ordinal statistics, and examples are provided to illustrate the results.
Keywords: α-value, Fuzzy order statistics, Lifetime distribution, Reliability, Scale fuzzy random variable.
Full-Text [PDF 948 kb]   (512 Downloads)    
Type of Study: Research | Subject: Fuzzy Statistics
Received: 2023/06/21 | Accepted: 2024/08/31 | Published: 2024/06/4
References
1. Taheri, S., Akbari, M. Q. and Hesamian, G. (1402), Moving Average Modeling based on α-Value of Fuzzy Random Variables, Journal of Statistical Sciences, Accepted for publication.
2. Mozafari, M., Khanjari Sadegh, M., Akbari, M. Q. and Hesamian, G. (1401), Concepts of Reliability in Fuzzy Environment, Journal of Statistical Sciences, 17, 157-175.
3. Aiche‎, ‎F‎. ‎and Dubois‎, ‎D‎. ‎(2010)‎, ‎An Extension of Stochastic Dominance to Fuzzy Random Variables‎, ‎Computational Intelligence for Knowledge-Based Systems Design‎: ‎Lecture Notes in Computer Science, 6178‎, ‎159-168‎. [DOI:10.1007/978-3-642-14049-5_17]
4. ‎Akbari‎, ‎M‎. ‎G‎. ‎and Rezaei‎, ‎A‎. ‎H‎. ‎(2009)‎, ‎Order Statistics using Fuzzy Random Variables‎, ‎Statistics and Probability Letters, ‎79‎, ‎1031-1037‎. [DOI:10.1016/j.spl.2008.12.009]
5. ‎Brunelli‎, ‎M‎. ‎and Mezei‎, ‎J‎. ‎(2013), How Different are Ranking Methods for Fuzzy Numbers? A Numerical Study‎, International Journal of Approximate Reasoning, 54‎, ‎627-639‎. ‎ [DOI:10.1016/j.ijar.2013.01.009]
6. Hesamian‎, ‎G‎. ‎R‎. ‎and Chachi‎, ‎J‎. ‎(2015)‎, ‎Two-Sample Kolmogorov-Smirnov Fuzzy Test for Fuzzy Random Variables‎, Statistical Papers‎, 56‎, ‎61-82‎. [DOI:10.1007/s00362-013-0566-2]
7. ‎Hesamian‎, ‎G.‎, ‎Akbari‎, ‎M‎. ‎G‎. ‎and ‎Yaghoobpoor, ‎R. ‎(2018), ‎Quality ‎Control ‎Process ‎Based ‎on ‎Fuzzy ‎Random ‎Variables, IEEE Transactions on Fuzzy Systems, 27, ‎671-685.‎ [DOI:10.1109/TFUZZ.2018.2866811]
8. Hesamian‎, ‎G.‎, ‎Akbari‎, ‎M‎. ‎G‎. ‎and Zendehdel‎, ‎J‎. ‎(2019)‎, ‎Location and Scale Fuzzy Random Variables‎, International Journal of Systems Science‎, ‎229-241‎. [DOI:10.1080/00207721.2019.1701131]
9. ‎Hesamian‎, ‎G. ‎(2022)‎, ‎Fuzzy Statistical Inferences Based on Fuzzy Random Variables ‎, Taylor & Francis Group, DOI: 10.1201/9781003248644‎. [DOI:10.1201/9781003248644]
10. Jiang‎, ‎C‎. ‎and Chen‎, ‎C‎. ‎(2003)‎, ‎A Numerical Algorithm of Fuzzy Reliability‎, Reliability Engineering and System Safety, 80‎, ‎299-307‎. [DOI:10.1016/S0951-8320(03)00055-3]
11. ‎Kwakernaak‎, ‎H‎. ‎(1978)‎, ‎Fuzzy Random Variables-I‎. ‎Definition and Theorem‎, Information Sciences‎, 15‎, ‎1-29‎. [DOI:10.1016/0020-0255(78)90019-1]
12. ‎Kwakernaak‎, ‎H‎. ‎(1979)‎, ‎Fuzzy Random Variables-II‎. ‎Algorithms and Examples for the Discrete Case‎, Information Sciences, 17‎, ‎253-278‎. [DOI:10.1016/0020-0255(79)90020-3]
13. ‎Piriyakumar‎, ‎E.L‎. ‎and Renganathan‎, ‎N‎. ‎(2001)‎,‎ ‎Stochastic Ordering of Fuzzy Random Variables‎, Information and Management Sciences, 12‎, ‎29-40‎.
14. ‎Puri‎, ‎M‎. ‎L‎. ‎and Ralescu‎, ‎D‎. ‎A‎. ‎(1986)‎, ‎Fuzzy Random Variables‎, ‎Journal of Mathematical Analysis and Applications, 114‎, ‎409-422‎. [DOI:10.1016/0022-247X(86)90093-4]
15. ‎Saeidi‎, ‎A‎. ‎R.‎, ‎Akbari‎, ‎M‎. ‎G‎. ‎and Doostparast‎, ‎M‎. ‎(2014)‎, ‎Hypotheses Testing with the Two Parameter Pareto Distribution on the Basis of Records in Fuzzy Environment‎, Kybernetika‎, 50‎, ‎744-757‎. [DOI:10.14736/kyb-2014-5-0744]
16. ‎Sedra‎, ‎A‎. ‎and Smith‎, ‎K‎. ‎(2004)‎, ‎Microelectronic Circuits‎, United Kingdom‎: ‎Oxford University Press‎.
17. ‎Yao‎, ‎J.S‎. ‎and Wu‎, ‎K‎. ‎(2000)‎, ‎Ranking Fuzzy Numbers Based on Decomposition Principle and Signed Distance‎, ‎Fuzzy Sets and Systems, 116‎, ‎275-288‎. [DOI:10.1016/S0165-0114(98)00122-5]
18. ‎Zadeh‎, ‎L‎. ‎A‎. ‎(1965)‎, ‎Fuzzy Sets‎, Information Control, 8‎, ‎338-356‎. [DOI:10.1016/S0019-9958(65)90241-X]
19. ‎Zarei‎, ‎R.‎, ‎Amini‎, ‎M.‎, ‎Rezaei Roknabadi‎, ‎A‎. ‎H‎. ‎and Akbari‎, ‎M‎. ‎G‎. ‎(2012)‎, ‎Some Fuzzy Stochastic Orderings for Fuzzy Random Variables‎, Fuzzy Optim Decis Making, 110‎, ‎209-225‎. [DOI:10.1007/s10700-012-9121-1]
20. ‎Zarei‎, ‎R.‎, ‎Amini‎, ‎M‎. ‎and Rezaei Roknabadi‎, ‎A‎. ‎H‎. ‎(2015)‎, ‎Fuzzy Stochastic Ordering for C-Fuzzy Random Variables and its Applications, Soft Comput, 19‎, ‎179-188‎. [DOI:10.1007/s00500-014-1241-9]
21. ‎Zendehdel‎, ‎J.‎, ‎Z‎arei‎, R. and ‎Akbari‎, ‎M‎. ‎G. ‎(2022)‎, ‎A Novel Approach for Modeling System Reliability Characteristics in an Imprecise Environment‎, Journal of Mathematical Modeling‎, 10, ‎449-465.‎
Send email to the article author

Add your comments about this article
Your username or Email:

CAPTCHA



XML   Persian Abstract   Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Mozafari M, Khanjari Sadegh M, Akbari M G, Hesamian G. Fuzzy Order Statistics Based on α-Value and Some of Its Applications in Reliability. JSS 2024; 18 (1)
URL: http://jss.irstat.ir/article-1-854-en.html


Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Volume 18, Issue 1 (8-2024) Back to browse issues page
مجله علوم آماری – نشریه علمی پژوهشی انجمن آمار ایران Journal of Statistical Sciences

Persian site map - English site map - Created in 0.06 seconds with 43 queries by YEKTAWEB 4700