G-Numbers: Importance-Necessity Concept in Uncertain Environment
International Journal of Management and Fuzzy Systems
Volume 5, Issue 1, March 2019, Pages: 27-32
Received: Mar. 20, 2019; Accepted: May 6, 2019; Published: May 30, 2019
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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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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.
Importance, Necessity, Uncertain Information, Fuzzy Numbers, G-Numbers, Decision Making
To cite this article
Saeid Jafarzadeh Ghoushchi, Mohammad Khazaeili, G-Numbers: Importance-Necessity Concept in Uncertain Environment, International Journal of Management and Fuzzy Systems. Vol. 5, No. 1, 2019, pp. 27-32. doi: 10.11648/j.ijmfs.20190501.15
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This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Zadeh, L. A., Fuzzy sets. Information and control, 1965. 8 (3): p. 338-353.
Zadeh, L. A., A note on Z-numbers. Information Sciences, 2011. 181 (14): p. 2923-2932.
Deng, Y., D numbers: theory and applications. Journal of Information & Computational Science, 2012. 9 (9): p. 2421-2428.
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.
Memari, A., et al., Sustainable supplier selection: A multi-criteria intuitionistic fuzzy TOPSIS method. Journal of Manufacturing Systems, 2019. 50: p. 9-24.
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.
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.
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.
Abiyev, R. H., et al., Estimation of Food Security Risk Level Using Z-Number-Based Fuzzy System. Journal of Food Quality, 2018. 2018.
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.
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.
Deng, X. and Y. Deng, D-AHP method with different credibility of information. Soft Computing, 2019. 23 (2): p. 683-691.
Baer, D., Dwight Eisenhower Nailed A Major Insight About Productivity. Business Insider, 2014.
Eisenhower, D., Address at the Second Assembly of the World Council of Churches, Evanston, Illinois. August, 1954. 19: p. 1954.
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.
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.
Gupta, M. M., Introduction to fuzzy arithmetic: Theory and applications. 1985: New York, NY: Van Nostrand Reinhold Company.
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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