G-Numbers: Importance-Necessity Concept in Uncertain Environment

Saeid Jafarzadeh Ghoushchi; Mohammad Khazaeili

doi:doi:10.11648/j.ijmfs.20190501.15

| Peer-Reviewed

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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), 2019. Published by Science Publishing Group

Keywords

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

References

[1]	Zadeh, L. A., Fuzzy sets. Information and control, 1965. 8 (3): p. 338-353.
[2]	Zadeh, L. A., A note on Z-numbers. Information Sciences, 2011. 181 (14): p. 2923-2932.
[3]	Deng, Y., D numbers: theory and applications. Journal of Information & Computational Science, 2012. 9 (9): p. 2421-2428.
[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.
[13]	Baer, D., Dwight Eisenhower Nailed A Major Insight About Productivity. Business Insider, 2014.
[14]	Eisenhower, D., Address at the Second Assembly of the World Council of Churches, Evanston, Illinois. August, 1954. 19: p. 1954.
[15]	Zavadskas, E.K., Z. Turskis, and S. Kildienė, State of art surveys of overviews on MCDM/MADM methods. Technological and economic development of economy, 2014. 20 (1): p. 165-179.
[16]	Jafarzadeh Ghoushchi, S., Yousefi, S., & Khazaeili, M., An extended FMEA approach based on the Z-MOORA and fuzzy BWM for prioritization of failures. Applied Soft Computing, 2019. DOI: 10.1016/j.asoc.2019.105505.
[17]	Gupta, M. M., Introduction to fuzzy arithmetic: Theory and applications. 1985: New York, NY: Van Nostrand Reinhold Company.
[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.

Cite This Article

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

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

Download PDF

Sections

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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