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Journals / Hacettepe Journal of Mathematics and Statistics / 2012 / Cilt: 41 - Sayı: 1

[0,1]-Fuzzy $beta$-rank functions

Xiu XIN
Huan LIAN
Pages
59–65
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

A [0, 1]-fuzzy $alpha$ -rank function on E is equivalent to a [0, 1]-fuzzy $beta$ -rank function on E.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the concepts of [0, 1]-fuzzy $beta$ -rank function and [0, 1]- fuzzy $alpha$ -rank function are presented.
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Key Findings & Data:The set of all closed and perfect [0, 1]-matroids (i.e. closed Goetschel-Voxman fuzzy matroids) on E and that of all [0, 1]-fuzzy $beta$ -rank functions on E are in one-to-one correspondence.
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Conclusion & Impact:A [0, 1]-fuzzy $alpha$ -rank function on E is equivalent to a [0, 1]-fuzzy $beta$ -rank function on E.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, the concepts of [0, 1]-fuzzy $beta$ -rank function and [0, 1]- fuzzy $alpha$ -rank function are presented. The set of all closed and perfect [0, 1]-matroids (i.e. closed Goetschel-Voxman fuzzy matroids) on E and that of all [0, 1]-fuzzy $beta$ -rank functions on E are in one-to-one correspondence. A [0, 1]-fuzzy $alpha$ -rank function on E is equivalent to a [0, 1]-fuzzy $beta$ -rank function on E.

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Cite This Article

XIN, X., LIAN, H. (2022). [0,1]-Fuzzy $beta$-rank functions. Hacettepe Journal of Mathematics and Statistics, Cilt: 41 - Sayı: 1, 59–65. https://ajindex.com/articles/530497

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References (9)

  1. Goetschel, R. and Voxman, W. Fuzzy matroids, Fuzzy Sets and Systems 27, 291-302, 1988
  2. Hsueh, I. -C. On fuzzication of matroids, Fuzzy Sets and Systems 53, 319-327, 1993
  3. Huang, H.L. and Shi, F.-G. L-fuzzy numbers and their properties, Information Sciences 178, 1141-1151, 2008
  4. Novak, L. A. On fuzzy independence set systems, Fuzzy Sets and Systems 91, 365-374, 1997
  5. Novak, L. A. On Goetschel and Voxman fuzzy matroids, Fuzzy Sets and Systems 117, 407-412, 2001
  6. Shi, F. -G. L-fuzzy relation and L-fuzzy subgroup, Journal of Fuzzy Mathematics 8, 491-499, 2000
  7. Shi, F.-G. A new approach to the fuzzification of matroids, Fuzzy Sets and Systems 160, 696-705, 2009
  8. Shi, F.-G. (L,M)-fuzzy matroids, Fuzzy Sets and Systems 160, 2387-2400, 2009
  9. Xin, X. and Shi, F. -G. Rank functions for closed and perfect [0,1] matroids, Hacet. J. Math. Stat. 39(1), 31-39, 2010.