G-Numbers: Importance-Necessity Concept in Uncertain Environment

Saeid Jafarzadeh Ghoushchi; Mohammad Khazaeili

doi:doi:10.11648/j.ijmfs.20190501.15

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G-Numbers: Importance-Necessity Concept in Uncertain Environment

Saeid Jafarzadeh Ghoushchi, Mohammad Khazaeili

Published in International Journal of Management and Fuzzy Systems (Volume 5, Issue 1)

Received: 20 March 2019 Accepted: 6 May 2019 Published: 30 May 2019

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Abstract

Decisions are mainly grounded on information; therefore, the information should have the least ambiguity and uncertainty to make beneficial and reliable decisions. Many concepts such as fuzzy sets theory, Z-Numbers, and D-Numbers, have been proposed. All the previous concepts have some desirable properties while they do not consider the concept of necessity. In this paper, a new concept, named as G-numbers is proposed to reduce the uncertainty of information based on importance and necessity concepts. In a G-numbers, G= (I, N), I is the Importance component and N is the Necessity component on the real-valued uncertain variables. In general, I and N are described as linguistic variables, Examples: an appointment (high, very high); investment in the stock market (high, medium). An ordered pair relates to computations with G-numbers. In this study, the concept of a G-number is introduced, and the arithmetic operations on G-numbers are presented. Finally, a numerical example is used to illustrate the efficiency of the proposed approach. The concept of G-numbers can be used for a wide range of practical issues in various areas, such as inter alia, social, economic, and risk assessment, and decision-making.

Published in	International Journal of Management and Fuzzy Systems (Volume 5, Issue 1)
DOI	10.11648/j.ijmfs.20190501.15
Page(s)	27-32
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

Importance, Necessity, Uncertain Information, Fuzzy Numbers, G-Numbers, Decision Making

References

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[4]	Seiti, H., A. Hafezalkotob, and L. Martínez, R-numbers, a new risk modeling associated with fuzzy numbers and its application to decision making. Information Sciences, 2019. 483: p. 206-231.
[5]	Memari, A., et al., Sustainable supplier selection: A multi-criteria intuitionistic fuzzy TOPSIS method. Journal of Manufacturing Systems, 2019. 50: p. 9-24.
[6]	Aboutorab, H., et al., ZBWM: The Z-number extension of Best Worst Method and its application for supplier development. Expert Systems with Applications, 2018. 107: p. 115-125.
[7]	Mohammadi, A. and S. A. Darestani, Green supplier selection problem using TOPSIS extended by D numbers in tractor manufacturing industry. International Journal of Services and Operations Management, 2019. 32 (3): p. 327-338.
[8]	Aqlan, F. and S. S. Lam, A fuzzy-based integrated framework for supply chain risk assessment. International Journal of Production Economics, 2015. 161: p. 54-63.
[9]	Abiyev, R. H., et al., Estimation of Food Security Risk Level Using Z-Number-Based Fuzzy System. Journal of Food Quality, 2018. 2018.
[10]	Bian, T., et al., Failure mode and effects analysis based on D numbers and TOPSIS. Quality and Reliability Engineering International, 2018. 34 (4): p. 501-515.
[11]	Capuano, N., et al., Fuzzy group decision making with incomplete information guided by social influence. IEEE Transactions on Fuzzy Systems, 2018. 26 (3): p. 1704-1718.
[12]	Deng, X. and Y. Deng, D-AHP method with different credibility of information. Soft Computing, 2019. 23 (2): p. 683-691.
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[18]	Chen, C.-T., Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy sets and systems, 2000. 114 (1): p. 1-9.

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Saeid Jafarzadeh Ghoushchi, Mohammad Khazaeili. (2019). G-Numbers: Importance-Necessity Concept in Uncertain Environment. International Journal of Management and Fuzzy Systems, 5(1), 27-32. https://doi.org/10.11648/j.ijmfs.20190501.15

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ACS Style

Saeid Jafarzadeh Ghoushchi; Mohammad Khazaeili. G-Numbers: Importance-Necessity Concept in Uncertain Environment. Int. J. Manag. Fuzzy Syst. 2019, 5(1), 27-32. doi: 10.11648/j.ijmfs.20190501.15

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AMA Style

Saeid Jafarzadeh Ghoushchi, Mohammad Khazaeili. G-Numbers: Importance-Necessity Concept in Uncertain Environment. Int J Manag Fuzzy Syst. 2019;5(1):27-32. doi: 10.11648/j.ijmfs.20190501.15

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@article{10.11648/j.ijmfs.20190501.15,
  author = {Saeid Jafarzadeh Ghoushchi and Mohammad Khazaeili},
  title = {G-Numbers: Importance-Necessity Concept in Uncertain Environment},
  journal = {International Journal of Management and Fuzzy Systems},
  volume = {5},
  number = {1},
  pages = {27-32},
  doi = {10.11648/j.ijmfs.20190501.15},
  url = {https://doi.org/10.11648/j.ijmfs.20190501.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmfs.20190501.15},
  abstract = {Decisions are mainly grounded on information; therefore, the information should have the least ambiguity and uncertainty to make beneficial and reliable decisions. Many concepts such as fuzzy sets theory, Z-Numbers, and D-Numbers, have been proposed. All the previous concepts have some desirable properties while they do not consider the concept of necessity. In this paper, a new concept, named as G-numbers is proposed to reduce the uncertainty of information based on importance and necessity concepts. In a G-numbers, G= (I, N), I is the Importance component and N is the Necessity component on the real-valued uncertain variables. In general, I and N are described as linguistic variables, Examples: an appointment (high, very high); investment in the stock market (high, medium). An ordered pair relates to computations with G-numbers. In this study, the concept of a G-number is introduced, and the arithmetic operations on G-numbers are presented. Finally, a numerical example is used to illustrate the efficiency of the proposed approach. The concept of G-numbers can be used for a wide range of practical issues in various areas, such as inter alia, social, economic, and risk assessment, and decision-making.},
 year = {2019}
}

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TY  - JOUR
T1  - G-Numbers: Importance-Necessity Concept in Uncertain Environment
AU  - Saeid Jafarzadeh Ghoushchi
AU  - Mohammad Khazaeili
Y1  - 2019/05/30
PY  - 2019
N1  - https://doi.org/10.11648/j.ijmfs.20190501.15
DO  - 10.11648/j.ijmfs.20190501.15
T2  - International Journal of Management and Fuzzy Systems
JF  - International Journal of Management and Fuzzy Systems
JO  - International Journal of Management and Fuzzy Systems
SP  - 27
EP  - 32
PB  - Science Publishing Group
SN  - 2575-4947
UR  - https://doi.org/10.11648/j.ijmfs.20190501.15
AB  - Decisions are mainly grounded on information; therefore, the information should have the least ambiguity and uncertainty to make beneficial and reliable decisions. Many concepts such as fuzzy sets theory, Z-Numbers, and D-Numbers, have been proposed. All the previous concepts have some desirable properties while they do not consider the concept of necessity. In this paper, a new concept, named as G-numbers is proposed to reduce the uncertainty of information based on importance and necessity concepts. In a G-numbers, G= (I, N), I is the Importance component and N is the Necessity component on the real-valued uncertain variables. In general, I and N are described as linguistic variables, Examples: an appointment (high, very high); investment in the stock market (high, medium). An ordered pair relates to computations with G-numbers. In this study, the concept of a G-number is introduced, and the arithmetic operations on G-numbers are presented. Finally, a numerical example is used to illustrate the efficiency of the proposed approach. The concept of G-numbers can be used for a wide range of practical issues in various areas, such as inter alia, social, economic, and risk assessment, and decision-making.
VL  - 5
IS  - 1
ER  -

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Author Information

Saeid Jafarzadeh Ghoushchi

Faculty of Industrial Engineering, Urmia University of Technology, Urmia, Iran
Mohammad Khazaeili

Faculty of Industrial Engineering, Urmia University of Technology, Urmia, Iran

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APA Style

Saeid Jafarzadeh Ghoushchi, Mohammad Khazaeili. (2019). G-Numbers: Importance-Necessity Concept in Uncertain Environment. International Journal of Management and Fuzzy Systems, 5(1), 27-32. https://doi.org/10.11648/j.ijmfs.20190501.15

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ACS Style

Saeid Jafarzadeh Ghoushchi; Mohammad Khazaeili. G-Numbers: Importance-Necessity Concept in Uncertain Environment. Int. J. Manag. Fuzzy Syst. 2019, 5(1), 27-32. doi: 10.11648/j.ijmfs.20190501.15

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AMA Style

Saeid Jafarzadeh Ghoushchi, Mohammad Khazaeili. G-Numbers: Importance-Necessity Concept in Uncertain Environment. Int J Manag Fuzzy Syst. 2019;5(1):27-32. doi: 10.11648/j.ijmfs.20190501.15

Copy | Download

@article{10.11648/j.ijmfs.20190501.15,
  author = {Saeid Jafarzadeh Ghoushchi and Mohammad Khazaeili},
  title = {G-Numbers: Importance-Necessity Concept in Uncertain Environment},
  journal = {International Journal of Management and Fuzzy Systems},
  volume = {5},
  number = {1},
  pages = {27-32},
  doi = {10.11648/j.ijmfs.20190501.15},
  url = {https://doi.org/10.11648/j.ijmfs.20190501.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmfs.20190501.15},
  abstract = {Decisions are mainly grounded on information; therefore, the information should have the least ambiguity and uncertainty to make beneficial and reliable decisions. Many concepts such as fuzzy sets theory, Z-Numbers, and D-Numbers, have been proposed. All the previous concepts have some desirable properties while they do not consider the concept of necessity. In this paper, a new concept, named as G-numbers is proposed to reduce the uncertainty of information based on importance and necessity concepts. In a G-numbers, G= (I, N), I is the Importance component and N is the Necessity component on the real-valued uncertain variables. In general, I and N are described as linguistic variables, Examples: an appointment (high, very high); investment in the stock market (high, medium). An ordered pair relates to computations with G-numbers. In this study, the concept of a G-number is introduced, and the arithmetic operations on G-numbers are presented. Finally, a numerical example is used to illustrate the efficiency of the proposed approach. The concept of G-numbers can be used for a wide range of practical issues in various areas, such as inter alia, social, economic, and risk assessment, and decision-making.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - G-Numbers: Importance-Necessity Concept in Uncertain Environment
AU  - Saeid Jafarzadeh Ghoushchi
AU  - Mohammad Khazaeili
Y1  - 2019/05/30
PY  - 2019
N1  - https://doi.org/10.11648/j.ijmfs.20190501.15
DO  - 10.11648/j.ijmfs.20190501.15
T2  - International Journal of Management and Fuzzy Systems
JF  - International Journal of Management and Fuzzy Systems
JO  - International Journal of Management and Fuzzy Systems
SP  - 27
EP  - 32
PB  - Science Publishing Group
SN  - 2575-4947
UR  - https://doi.org/10.11648/j.ijmfs.20190501.15
AB  - Decisions are mainly grounded on information; therefore, the information should have the least ambiguity and uncertainty to make beneficial and reliable decisions. Many concepts such as fuzzy sets theory, Z-Numbers, and D-Numbers, have been proposed. All the previous concepts have some desirable properties while they do not consider the concept of necessity. In this paper, a new concept, named as G-numbers is proposed to reduce the uncertainty of information based on importance and necessity concepts. In a G-numbers, G= (I, N), I is the Importance component and N is the Necessity component on the real-valued uncertain variables. In general, I and N are described as linguistic variables, Examples: an appointment (high, very high); investment in the stock market (high, medium). An ordered pair relates to computations with G-numbers. In this study, the concept of a G-number is introduced, and the arithmetic operations on G-numbers are presented. Finally, a numerical example is used to illustrate the efficiency of the proposed approach. The concept of G-numbers can be used for a wide range of practical issues in various areas, such as inter alia, social, economic, and risk assessment, and decision-making.
VL  - 5
IS  - 1
ER  -

Copy | Download