Classical mathematics deals with only two conclusions: true and false. But fuzzy logic is a multiple-valued logic in which the truth values of variables might be any real number between 0 and 1. L. A. Zadeh developed the idea of fuzzy logic in 1965 to investigate the haziness and lack of concentration in information found in mathematics. The notion of the fuzzy set has been successfully applied in studying the different classes of sequence spaces. In recent years, many researchers have replaced these mathematical structures of real or complex numbers with fuzzy numbers and interval numbers and have investigated many results. This study aims to analyze the sequence space bVFp(X) for 1≤p<∞ of p- bounded variation of fuzzy real numbers and it is extended to the p- bounded variation of the difference sequence space bVFp(ΔmX) of fuzzy real numbers. The proposed study will be based on a dry lab review. It will be based on existing theories that are already proven and established. On the promise of the existing theories, we will study some new results with their different properties. To study the different properties, we will introduce a new metric on bVFp(ΔmX). Moreover, we shall explore some of the inclusion relations with respect to p and q.
| Published in | Pure and Applied Mathematics Journal (Volume 11, Issue 3) |
| DOI | 10.11648/j.pamj.20221103.12 |
| Page(s) | 47-50 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2022. Published by Science Publishing Group |
Fuzzy Real Numbers, Fuzzy Set, Fuzzy Sequence, Difference Sequence of Fuzzy Real Numbers
| [1] | A. Baruah, and B. C. Tripathy, New type of difference sequence spaces of fuzzy real numbers. Mathematical Modeling and Analysis. 14 (2009) 391-397. |
| [2] | B. Achyutananda and T. Binod Chandra, N¨orlund and Riesz mean of sequences of fuzzy real numbers. Applied Mathematics Letters. 23 (2010) 651- 655. |
| [3] | C. Basudev, and T. Binod Chandra, On fuzzy real-valued lFp sequences. In Proc. International Conf. 8th Joint Con. Inf. Sci. (10th International Conf. on Fuzzy Theory and Technology. (2005) 184-190. |
| [4] | N. R. Das, and C. Ajanta, Boundedness of fuzzy real-valued sequences. Bull. Cal. Math. Soc. 90 (1998) 35-44. |
| [5] | D. Paritosh Chandra, Fuzzy normed linear sequence space bVFp. Proyecciones (Antofagasta, on line). 37 (2018) 389-403. |
| [6] | E. Mikail., S. Ekrem. and A. Hifsi, On some difference sequence spaces of fuzzy numbers. Soft Computer 20 (2016) 4395-4401. |
| [7] | E. Mikail, and R. Çolak, On some generalized difference sequence spaces. Soochow Journal of Mathematics. 21 (1995) 377-386. |
| [8] | J. Tanweer, A note on multiordered fuzzy difference sequence spaces. Filomat. 32 (2018) 2867-2874. |
| [9] | H. Kizmaz, On certain sequence spaces. Canadian Mathematical Bulletin. 24 (1981) 169-176. |
| [10] | M. Matloka, Sequence of fuzzy numbers. Busefal. 28 (1986) 28-37. |
| [11] | S. Nanda, (1989), On sequences of fuzzy numbers. Fuzzy Sets and System. 33, 123-126. |
| [12] | C.. Rifat, A. Hssi and E. Mikail., Generalized difference sequences of fuzzy numbers. Chaos, Solution, and Fractions. 40 (2009) 1109-1117. |
| [13] | Ö. Talo, F. Bassar, On the space bVFp of sequences of p-bounded variation of fuzzy numbers. Acta. Math. Sin.-English Ser. 24 (2008) 1205-1212. |
| [14] | T. Binod Chandra and D. Paritosh Chandra, On the sequence of fuzzy number sequence bVFp. Songklanakarin J. Sci. Technol. 41 (2019) 11–14. |
| [15] | T. Binod Chandra, & A. Esi, A new type of difference sequence spaces. Int. J. Sci. Technol. 1 (2006) 11-14. |
| [16] | B. Yuan, & K. George, Fuzzy sets and fuzzy logic: theory and applications. PHI New Delhi. (1995) 443-455. |
| [17] | L. A. Zadeh, Is there a need for fuzzy logic?. Information Sciences. 178 (2008) 2751–2779. |
APA Style
Gyan Prasad Paudel, Narayan Prasad Pahari, Sanjeev Kumar. (2022). Generalized Form of p-Bounded Variation of Sequences of Fuzzy Real Numbers. Pure and Applied Mathematics Journal, 11(3), 47-50. https://doi.org/10.11648/j.pamj.20221103.12
ACS Style
Gyan Prasad Paudel; Narayan Prasad Pahari; Sanjeev Kumar. Generalized Form of p-Bounded Variation of Sequences of Fuzzy Real Numbers. Pure Appl. Math. J. 2022, 11(3), 47-50. doi: 10.11648/j.pamj.20221103.12
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.pamj.20221103.12,
author = {Gyan Prasad Paudel and Narayan Prasad Pahari and Sanjeev Kumar},
title = {Generalized Form of p-Bounded Variation of Sequences of Fuzzy Real Numbers},
journal = {Pure and Applied Mathematics Journal},
volume = {11},
number = {3},
pages = {47-50},
doi = {10.11648/j.pamj.20221103.12},
url = {https://doi.org/10.11648/j.pamj.20221103.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20221103.12},
abstract = {Classical mathematics deals with only two conclusions: true and false. But fuzzy logic is a multiple-valued logic in which the truth values of variables might be any real number between 0 and 1. L. A. Zadeh developed the idea of fuzzy logic in 1965 to investigate the haziness and lack of concentration in information found in mathematics. The notion of the fuzzy set has been successfully applied in studying the different classes of sequence spaces. In recent years, many researchers have replaced these mathematical structures of real or complex numbers with fuzzy numbers and interval numbers and have investigated many results. This study aims to analyze the sequence space bVFp(X) for 1≤pFp(ΔmX) of fuzzy real numbers. The proposed study will be based on a dry lab review. It will be based on existing theories that are already proven and established. On the promise of the existing theories, we will study some new results with their different properties. To study the different properties, we will introduce a new metric on bVFp(ΔmX). Moreover, we shall explore some of the inclusion relations with respect to p and q.},
year = {2022}
}
TY - JOUR T1 - Generalized Form of p-Bounded Variation of Sequences of Fuzzy Real Numbers AU - Gyan Prasad Paudel AU - Narayan Prasad Pahari AU - Sanjeev Kumar Y1 - 2022/07/12 PY - 2022 N1 - https://doi.org/10.11648/j.pamj.20221103.12 DO - 10.11648/j.pamj.20221103.12 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 47 EP - 50 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20221103.12 AB - Classical mathematics deals with only two conclusions: true and false. But fuzzy logic is a multiple-valued logic in which the truth values of variables might be any real number between 0 and 1. L. A. Zadeh developed the idea of fuzzy logic in 1965 to investigate the haziness and lack of concentration in information found in mathematics. The notion of the fuzzy set has been successfully applied in studying the different classes of sequence spaces. In recent years, many researchers have replaced these mathematical structures of real or complex numbers with fuzzy numbers and interval numbers and have investigated many results. This study aims to analyze the sequence space bVFp(X) for 1≤pFp(ΔmX) of fuzzy real numbers. The proposed study will be based on a dry lab review. It will be based on existing theories that are already proven and established. On the promise of the existing theories, we will study some new results with their different properties. To study the different properties, we will introduce a new metric on bVFp(ΔmX). Moreover, we shall explore some of the inclusion relations with respect to p and q. VL - 11 IS - 3 ER -
Email: