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. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Fuzzy Real Numbers, Fuzzy Set, Fuzzy Sequence, Difference Sequence of Fuzzy Real Numbers
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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
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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 -
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