A Method to Improve the Multiplicative Inconsistency Preserving the Preference Information of Every Element of an Intuitionistic Fuzzy Preference Relation

Hyonil Oh; Gukchol Ri; Yungil Kim; Cholju Kim

doi:doi:10.11648/j.ajist.20240802.11

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A Method to Improve the Multiplicative Inconsistency Preserving the Preference Information of Every Element of an Intuitionistic Fuzzy Preference Relation

Hyonil Oh^*

, Gukchol Ri, Yungil Kim, Cholju Kim

Published in American Journal of Information Science and Technology (Volume 8, Issue 2)

Received: 12 April 2024 Accepted: 23 May 2024 Published: 24 May 2024

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Abstract

In general, almost intuitionistic fuzzy preference relations (IFPRs) provided by experts are multiplicutively inconsistent because of the complexity of a problem, lack of correct or sufficient knowledge about the problem domain, the ambiguity inherent in human thinking and so forth on. To solve this subject, we propose a method to improve the multiplicative inconsistency preserving the preference information of every element of an initial IFPR. For this, we formulate a formula that straightforwardly calculates the multiplicative consistent IFPR preserving the preference information of every element of the IFPR. Based on it, the necessary and sufficient results for the IFPR to be multiplicatively consistent are derived. By using the results, a consistency testing matrix and a consistency index that can select the most inconsistent elements in the IFPR are constructed and a method that revises them by a proper intuitionitic fuzzy numbers for improving inconsistency as well as preserving the initial preference information is proposed. Then, it is proved that the consistency index converges into zero. As a result, an acceptable consistent IFPR that preserves the preference information of every element and saves a lot of elements of the initial IFPR is constructed. In addition, this method needs a few calculations in comparison with previous methods to improve multiplicative inconsistency of IFPRs, because they calculate a multiplicative consisten IFPR by solving the optimal models constructed based on sufficient conditions for IFPRs to be mltiplicatively consistent. Finally, illustrative examples and comparative analysis are given to demonstrate the efficiency of the proposed method.

Published in	American Journal of Information Science and Technology (Volume 8, Issue 2)
DOI	10.11648/j.ajist.20240802.11
Page(s)	22-33
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), 2024. Published by Science Publishing Group

Keywords

Intuitionistic Fuzzy Preference Relation (IFPR), Multiplicative Consistency, Preference Information, Consistency Testing Matrix, Consistency Index

References

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APA Style

Oh, H., Ri, G., Kim, Y., Kim, C. (2024). A Method to Improve the Multiplicative Inconsistency Preserving the Preference Information of Every Element of an Intuitionistic Fuzzy Preference Relation. American Journal of Information Science and Technology, 8(2), 22-33. https://doi.org/10.11648/j.ajist.20240802.11

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ACS Style

Oh, H.; Ri, G.; Kim, Y.; Kim, C. A Method to Improve the Multiplicative Inconsistency Preserving the Preference Information of Every Element of an Intuitionistic Fuzzy Preference Relation. Am. J. Inf. Sci. Technol. 2024, 8(2), 22-33. doi: 10.11648/j.ajist.20240802.11

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AMA Style

Oh H, Ri G, Kim Y, Kim C. A Method to Improve the Multiplicative Inconsistency Preserving the Preference Information of Every Element of an Intuitionistic Fuzzy Preference Relation. Am J Inf Sci Technol. 2024;8(2):22-33. doi: 10.11648/j.ajist.20240802.11

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@article{10.11648/j.ajist.20240802.11,
  author = {Hyonil Oh and Gukchol Ri and Yungil Kim and Cholju Kim},
  title = {A Method to Improve the Multiplicative Inconsistency Preserving the Preference Information of Every Element of an Intuitionistic Fuzzy Preference Relation
},
  journal = {American Journal of Information Science and Technology},
  volume = {8},
  number = {2},
  pages = {22-33},
  doi = {10.11648/j.ajist.20240802.11},
  url = {https://doi.org/10.11648/j.ajist.20240802.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajist.20240802.11},
  abstract = {In general, almost intuitionistic fuzzy preference relations (IFPRs) provided by experts are multiplicutively inconsistent because of the complexity of a problem, lack of correct or sufficient knowledge about the problem domain, the ambiguity inherent in human thinking and so forth on. To solve this subject, we propose a method to improve the multiplicative inconsistency preserving the preference information of every element of an initial IFPR. For this, we formulate a formula that straightforwardly calculates the multiplicative consistent IFPR preserving the preference information of every element of the IFPR. Based on it, the necessary and sufficient results for the IFPR to be multiplicatively consistent are derived. By using the results, a consistency testing matrix and a consistency index that can select the most inconsistent elements in the IFPR are constructed and a method that revises them by a proper intuitionitic fuzzy numbers for improving inconsistency as well as preserving the initial preference information is proposed. Then, it is proved that the consistency index converges into zero. As a result, an acceptable consistent IFPR that preserves the preference information of every element and saves a lot of elements of the initial IFPR is constructed. In addition, this method needs a few calculations in comparison with previous methods to improve multiplicative inconsistency of IFPRs, because they calculate a multiplicative consisten IFPR by solving the optimal models constructed based on sufficient conditions for IFPRs to be mltiplicatively consistent. Finally, illustrative examples and comparative analysis are given to demonstrate the efficiency of the proposed method.
},
 year = {2024}
}

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TY  - JOUR
T1  - A Method to Improve the Multiplicative Inconsistency Preserving the Preference Information of Every Element of an Intuitionistic Fuzzy Preference Relation

AU  - Hyonil Oh
AU  - Gukchol Ri
AU  - Yungil Kim
AU  - Cholju Kim
Y1  - 2024/05/24
PY  - 2024
N1  - https://doi.org/10.11648/j.ajist.20240802.11
DO  - 10.11648/j.ajist.20240802.11
T2  - American Journal of Information Science and Technology
JF  - American Journal of Information Science and Technology
JO  - American Journal of Information Science and Technology
SP  - 22
EP  - 33
PB  - Science Publishing Group
SN  - 2640-0588
UR  - https://doi.org/10.11648/j.ajist.20240802.11
AB  - In general, almost intuitionistic fuzzy preference relations (IFPRs) provided by experts are multiplicutively inconsistent because of the complexity of a problem, lack of correct or sufficient knowledge about the problem domain, the ambiguity inherent in human thinking and so forth on. To solve this subject, we propose a method to improve the multiplicative inconsistency preserving the preference information of every element of an initial IFPR. For this, we formulate a formula that straightforwardly calculates the multiplicative consistent IFPR preserving the preference information of every element of the IFPR. Based on it, the necessary and sufficient results for the IFPR to be multiplicatively consistent are derived. By using the results, a consistency testing matrix and a consistency index that can select the most inconsistent elements in the IFPR are constructed and a method that revises them by a proper intuitionitic fuzzy numbers for improving inconsistency as well as preserving the initial preference information is proposed. Then, it is proved that the consistency index converges into zero. As a result, an acceptable consistent IFPR that preserves the preference information of every element and saves a lot of elements of the initial IFPR is constructed. In addition, this method needs a few calculations in comparison with previous methods to improve multiplicative inconsistency of IFPRs, because they calculate a multiplicative consisten IFPR by solving the optimal models constructed based on sufficient conditions for IFPRs to be mltiplicatively consistent. Finally, illustrative examples and comparative analysis are given to demonstrate the efficiency of the proposed method.

VL  - 8
IS  - 2
ER  -

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Author Information

Hyonil Oh

Institute of Mathematics, State Academy of Sciences, Pyongyang, DPR Korea

Contact Email

http://orcid.org/0000-0002-5624-6240
Gukchol Ri

Department of Basic Science, Institute of Engineering, Pyongsong, DPR Korea
Yungil Kim

Department of Application Mathematics, Kim Chaek University of Technology, Pyongyang, DPR Korea
Cholju Kim

Department of Information Engineering, University of Marine Transport, Rajin, DPR Korea

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APA Style

Oh, H., Ri, G., Kim, Y., Kim, C. (2024). A Method to Improve the Multiplicative Inconsistency Preserving the Preference Information of Every Element of an Intuitionistic Fuzzy Preference Relation. American Journal of Information Science and Technology, 8(2), 22-33. https://doi.org/10.11648/j.ajist.20240802.11

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ACS Style

Oh, H.; Ri, G.; Kim, Y.; Kim, C. A Method to Improve the Multiplicative Inconsistency Preserving the Preference Information of Every Element of an Intuitionistic Fuzzy Preference Relation. Am. J. Inf. Sci. Technol. 2024, 8(2), 22-33. doi: 10.11648/j.ajist.20240802.11

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AMA Style

Oh H, Ri G, Kim Y, Kim C. A Method to Improve the Multiplicative Inconsistency Preserving the Preference Information of Every Element of an Intuitionistic Fuzzy Preference Relation. Am J Inf Sci Technol. 2024;8(2):22-33. doi: 10.11648/j.ajist.20240802.11

Copy | Download

@article{10.11648/j.ajist.20240802.11,
  author = {Hyonil Oh and Gukchol Ri and Yungil Kim and Cholju Kim},
  title = {A Method to Improve the Multiplicative Inconsistency Preserving the Preference Information of Every Element of an Intuitionistic Fuzzy Preference Relation
},
  journal = {American Journal of Information Science and Technology},
  volume = {8},
  number = {2},
  pages = {22-33},
  doi = {10.11648/j.ajist.20240802.11},
  url = {https://doi.org/10.11648/j.ajist.20240802.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajist.20240802.11},
  abstract = {In general, almost intuitionistic fuzzy preference relations (IFPRs) provided by experts are multiplicutively inconsistent because of the complexity of a problem, lack of correct or sufficient knowledge about the problem domain, the ambiguity inherent in human thinking and so forth on. To solve this subject, we propose a method to improve the multiplicative inconsistency preserving the preference information of every element of an initial IFPR. For this, we formulate a formula that straightforwardly calculates the multiplicative consistent IFPR preserving the preference information of every element of the IFPR. Based on it, the necessary and sufficient results for the IFPR to be multiplicatively consistent are derived. By using the results, a consistency testing matrix and a consistency index that can select the most inconsistent elements in the IFPR are constructed and a method that revises them by a proper intuitionitic fuzzy numbers for improving inconsistency as well as preserving the initial preference information is proposed. Then, it is proved that the consistency index converges into zero. As a result, an acceptable consistent IFPR that preserves the preference information of every element and saves a lot of elements of the initial IFPR is constructed. In addition, this method needs a few calculations in comparison with previous methods to improve multiplicative inconsistency of IFPRs, because they calculate a multiplicative consisten IFPR by solving the optimal models constructed based on sufficient conditions for IFPRs to be mltiplicatively consistent. Finally, illustrative examples and comparative analysis are given to demonstrate the efficiency of the proposed method.
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - A Method to Improve the Multiplicative Inconsistency Preserving the Preference Information of Every Element of an Intuitionistic Fuzzy Preference Relation

AU  - Hyonil Oh
AU  - Gukchol Ri
AU  - Yungil Kim
AU  - Cholju Kim
Y1  - 2024/05/24
PY  - 2024
N1  - https://doi.org/10.11648/j.ajist.20240802.11
DO  - 10.11648/j.ajist.20240802.11
T2  - American Journal of Information Science and Technology
JF  - American Journal of Information Science and Technology
JO  - American Journal of Information Science and Technology
SP  - 22
EP  - 33
PB  - Science Publishing Group
SN  - 2640-0588
UR  - https://doi.org/10.11648/j.ajist.20240802.11
AB  - In general, almost intuitionistic fuzzy preference relations (IFPRs) provided by experts are multiplicutively inconsistent because of the complexity of a problem, lack of correct or sufficient knowledge about the problem domain, the ambiguity inherent in human thinking and so forth on. To solve this subject, we propose a method to improve the multiplicative inconsistency preserving the preference information of every element of an initial IFPR. For this, we formulate a formula that straightforwardly calculates the multiplicative consistent IFPR preserving the preference information of every element of the IFPR. Based on it, the necessary and sufficient results for the IFPR to be multiplicatively consistent are derived. By using the results, a consistency testing matrix and a consistency index that can select the most inconsistent elements in the IFPR are constructed and a method that revises them by a proper intuitionitic fuzzy numbers for improving inconsistency as well as preserving the initial preference information is proposed. Then, it is proved that the consistency index converges into zero. As a result, an acceptable consistent IFPR that preserves the preference information of every element and saves a lot of elements of the initial IFPR is constructed. In addition, this method needs a few calculations in comparison with previous methods to improve multiplicative inconsistency of IFPRs, because they calculate a multiplicative consisten IFPR by solving the optimal models constructed based on sufficient conditions for IFPRs to be mltiplicatively consistent. Finally, illustrative examples and comparative analysis are given to demonstrate the efficiency of the proposed method.

VL  - 8
IS  - 2
ER  -

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