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G-Numbers: Importance-Necessity Concept in Uncertain Environment

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), 2019. Published by Science Publishing Group

Keywords

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

References
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[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.
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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

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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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    T1  - G-Numbers: Importance-Necessity Concept in Uncertain Environment
    AU  - Saeid Jafarzadeh Ghoushchi
    AU  - Mohammad Khazaeili
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    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
  • Faculty of Industrial Engineering, Urmia University of Technology, Urmia, Iran

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

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