Chemical Technology, Control and Management


The Z-number concept is the attempt to model real-world uncertainty and relates to the issue of reliability of information, especially in the realms of economics and decision analysis. In this paper, we present an approach that can handle Z-numbers in the context of multi-criteria decision-making applying direct computations. In this paper we consider an Anаlytical Hierarchy Process based on Z-number valuations, taking into account the uncertаinty of the experts` opinion in estimаtion of the options. We considered a case of estimation of technical institutions with 7 criteria: campus infrastructure, faculty, students, academic ambience, teaching learning process, use of advance teaching aid, supplementary process and 3 alternatives: technical institutions.

First Page


Last Page





  1. C.Kahraman, S.C.Onar, B.Oztaysi, “Fuzzy Multicriteria Decision Making”, A Literature Review. Intern. Journal of Computational Intelligence Systems 8(4), pp. 637-666. 2015.
  2. J.Dodgson, M.Spackman, A.Pearman, L.Phillips, “MultiCriteria Analysis: A Manual”, 2nd ed, London, Department for Communities and Local Government, 2009, 168 p.
  3. A.Renato, Krohling, Artem dos Santos, André G. C. Pacheco: TODIM and TOPSIS with Znumbers. Frontiers of Information Technology & Electronic Engineering, 2016, 12 p.
  4. M.B.Ayhan, “A Fuzzy AHP Approach For Supplier Selection Problem”, A Case Study In A Gearmotor Company. Intern. Journal of Managing Value and Supply Chains 4(3), pp. 11-23, 2013.
  5. O.Kilincci, & S.A.Onal, “Fuzzy AHP approach for supplier selection in a washing machine company”, Expert Systems with Applications 38(8), pp. 9656-9664, 2011.
  6. A.Lotfi, Zadeh, “A note on a Znumber”, Information Sciences 181, pp. 2923-2932, 2011.
  7. Ronald R.Yager, “On Zvaluations using Zadeh`s Znumbers”, Intern. Journal of Intelligent Systems 27, pp. 259-278, 2012.
  8. Bingyi Kang, Daijun Wei, Ya Li, Yong Deng, “A method of converting Znumber to classical fuzzy number”, Journal of Information & Computational Science 9(3), pp.7 03-709, 2012.
  9. B.Kang, D.Wei, Y.Li, Y.Deng, “Decision Making Using Znumbers under Uncertain Environment”, Journal of Information & Computational Science 8(7), pp. 2807-2814, 2012.
  10. 10. A.Azadeh, M.Saberi, N.Z.Atashbar, E.Chang, P.Pazhoheshfar, ZAHP: “A Znumber extension of fuzzy analytical hierarchy process”. In: 7th IEEE International Conference on Digital Ecosystems and Technologies (DEST), pp. 141-147, 2013.

11. Shengsheng Zhang, “A model of based on Znumber and Fuzzy Analytic Hierarchy Process”, Journal of Mathematics and Informatics 7, pp. 63-71, 2017.

12. M.R.Feylizadeh, M.Bagherpour, “Manufacturing Performance Measurement Using Fuzzy MultiAttribute Utility Theory and ZNumber”, Trans. of FAMENA 42(1), pp.37-49, 2018.

13. R.A.Aliev, A.V.Alizadeh, O.H.Huseynov, “The arithmetic of discrete Znumbers”, Information Sciences, pp. 134-155, 2015.

14. R.AAliev, O.H.Huseynov, L.M.Zeinalova, “The arithmetic of continuous Znumbers” Information Sciences 373, pp. 41-60, 2016.

15. Prince Agarwal, Manjari Sahai, Vaibhav Mishra, Monark Bag, Vrijendra Singh.: “Supplier Selection in Dynamic Environment using Analytic Hierarchy Process”, Intern. Journal of Information Engineering and Electronic Business(IJIEEB) 4(6), pp. 20-26, 2014.

16. D.Chatterjee, and B.Mukherjee, “Study of fuzzy AHP model to search the criterion in the evaluation of the best technical institutions: a case study”, Intern. Journal of Engineering Science and Technology 2(7), pp. 2499-2510, 2010.

17. R.A.Aliev, O.H.Huseynov, R.R.Aliev, A.V.Alizadeh, “The arithmetic of Znumbers”, theory and applications. World Scientific Publishing Co., NJ, USA, 201

Included in

Engineering Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.