Analytical Hierarchy Process based on intuitionistic interval approximation of trapezoidal intuitionistic fuzzy numbers

Authors

  • Nik Muhammad Farhan Hakim Nik Badrul Alam College of Computing, Informatics and Mathematics, Universiti Teknologi MARA Pahang, 26400 Bandar Tun Abdul Razak Jengka, Pahang, Malaysia
  • Ku Muhammad Naim Ku Khalif Centre for Mathematical Sciences, Universiti Malaysia Pahang Al-Sultan Abdullah, Lebuh Persiaran Tun Khalil Yaakob, 26300 Kuantan, Pahang, Malaysia
  • Nor Izzati Jaini Centre for Mathematical Sciences, Universiti Malaysia Pahang Al-Sultan Abdullah, Lebuh Persiaran Tun Khalil Yaakob, 26300 Kuantan, Pahang, Malaysia

DOI:

https://doi.org/10.15282/daam.v5i2.11030

Keywords:

Trapezoidal intuitionistic fuzzy numbers, Analytical Hierarchy Process, Supplier selection, Interval-valued intuitionistic fuzzy numbers, Intuitionistic interval approximation

Abstract

The fuzzy Analytical Hierarchy Process (AHP) is a method in fuzzy decision-making, which helps decision makers make the best choice of alternatives when dealing with uncertainty. The objective of this paper is to propose a conversion method of trapezoidal intuitionistic fuzzy numbers (TrIFN) into interval-valued intuitionistic fuzzy numbers (IVIFN), followed by a new fuzzy AHP based on the proposed approximation. The linguistic judgments of decision makers are converted into TrIFN before being transformed into IVIFN using the nearest weighted intuitionistic interval approximation (NWIIA). The proposed model is implemented in supplier selection problems by taking into account five criteria comprising cost, quality, service, cycle time, and reputation. The results showed that the proposed model simplifies the fuzzy AHP using TrIFN without affecting the consistency of the solutions from the existing method, thus supporting the fact that TrIFN has a better capability of processing ill-defined quantities. This is because TrIFN entails a generalization of the triangular intuitionistic fuzzy number (TIFN), making it a better form of representation of linguistic variables for reducing the inexactness. 

References

[1] Aliev RA, Guirimov BG, Huseynov OH, Aliyev RR. A consistency-driven approach to construction of Z-number-valued pairwise comparison matrices. Iranian Journal of Fuzzy Systems. 2021;18(4):37–49.

[2] Partovi FY, Burton J, Banerjee A. Application of analytical hierarchy process in operations management. International Journal of Operations & Production Management. 1990;10(3):5–19.

[3] Saaty TL. The Analytic Hierarchy Process. New York, NY: McGraw-Hill; 1980.

[4] Kahraman C, Onar SC, Oztaysi B. Fuzzy multicriteria decision-making: A literature review. International Journal of Computational Intelligence Systems. 2015 May;8(4):637–66.

[5] Li W, Yu S, Pei H, Zhao C, Tian B. A hybrid approach based on fuzzy AHP and 2-tuple fuzzy linguistic method for evaluation in-flight service quality. Journal of Air Transport Management. 2017;60:49–64.

[6] Dožić S. Multi-criteria decision making methods: Application in the aviation industry. Journal of Air Transport Management. 2019;79:101683.

[7] Havle CA, Kılıç B. A hybrid approach based on the fuzzy AHP and HFACS framework for identifying and analyzing gross navigation errors during transatlantic flights. Journal of Air Transport Management. 2019;76:21–30.

[8] van Laarhoven PJM, Pedrycz W. A fuzzy extension of Saaty’s priority theory. Fuzzy Sets and Systems. 1983;11(1-3):229–41.

[9] Aliyev R, Temizkan H, Aliyev R. Fuzzy analytic hierarchy process-based multi-criteria decision making for universities ranking. Symmetry. 2020;12(8):1351.

[10] Deng Y. Chaos, Solitons & Fractals. Chaos Solitons & Fractals. 2016;91(C):549–53.

[11] Buckley JJ. Fuzzy hierarchical analysis. Fuzzy Sets and Systems. 1985;17(3):233–47.

[12] Chang DY. Applications of the extent analysis method on fuzzy AHP. European Journal of Operational Research. 1996;95(3):649–55.

[13] Liu Y, Eckert CM, Earl C. A review of fuzzy AHP methods for decision-making with subjective judgements. Expert Systems with Applications. 2020;161(1):113738.

[14] Atanassov KT. Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 1986;20(1):87–96.

[15] Xu Z, Liao H. Intuitionistic Fuzzy Analytic Hierarchy Process. IEEE Transactions on Fuzzy Systems. 2014;22(4):749–61.

[16] Zhang C, Li W, Yang H. A new drug risk assessment model of comprehensive hospitals. International Conference on Biomedical Engineering and Biotechnology. 2012;1165-8.

[17] Liao H, Xu Z. Consistency of the fused intuitionistic fuzzy preference relation in group intuitionistic fuzzy analytic hierarchy process. Applied Soft Computing. 2015;35:812–26.

[18] M. Deepika, Kannan ASK. Global supplier selection using intuitionistic fuzzy Analytic Hierarchy Process. International Conference on Electrical, Electronics, and Optimization Techniques 2016. 2016;2390–5.

[19] Sadiq R, Tesfamariam S. Environmental decision-making under uncertainty using intuitionistic fuzzy analytic hierarchy process (IF-AHP). Stochastic Environmental Research and Risk Assessment. 2007;23(1):75–91.

[20] Abdullah L, Najib L. Sustainable energy planning decision using the intuitionistic fuzzy analytic hierarchy process: choosing energy technology in Malaysia. International Journal of Sustainable Energy. 2016;35(4):360-77.

[21] Buyukozkan G, Feyzioglu O, Gocer F. Evaluation of hospital web services using intuitionistic fuzzy AHP and intuitionistic fuzzy VIKOR. International Conference on Industrial Engineering and Engineering Management IEEM. 2016;6451:607–11.

[22] Tavana M, Zareinejad M, Di Caprio D, Kaviani MA. An integrated intuitionistic fuzzy AHP and SWOT method for outsourcing reverse logistics. Applied Soft Computing. 2016;40:544–57.

[23] Büyüközkan G, Göçer F, Feyzioğlu O. Cloud computing technology selection based on interval-valued intuitionistic fuzzy MCDM methods. Soft Computing. 2018;22(15):5091–114.

[24] Wu J, Chiclana F. Non-dominance and attitudinal prioritisation methods for intuitionistic and interval-valued intuitionistic fuzzy preference relations. Expert Systems With Applications. 2012;39(18):13409–16.

[25] Atanassov K, Gargov G. Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems. 1989;31(3):343–9.

[26] Abdullah L, Najib L. A new preference scale mcdm method based on interval-valued intuitionistic fuzzy sets and the analytic hierarchy process. Soft Computing. 2014;20(2):511–23.

[27] Dogan O, Deveci M, Canıtez F, Kahraman C. A corridor selection for locating autonomous vehicles using an interval-valued intuitionistic fuzzy AHP and TOPSIS method. Soft Computing. 2020;24:8937-53.

[28] Büyüközkan G, Havle CA, Feyzioğlu O. A new digital service quality model and its strategic analysis in aviation industry using interval-valued intuitionistic fuzzy AHP. Journal of Air Transport Management. 2020;86:101817.

[29] Verma R, Chandra S. Interval-valued intuitionistic fuzzy-analytic hierarchy process for evaluating the impact of security attributes in fog based internet of things paradigm. Computer Communications. 2021;175:35–46.

[30] Kaur P. Selection of vendor based on intuitionistic fuzzy analytical hierarchy process. Advances in Operations Research. 2014;2014(1):1–10.

[31] Nirmala G, Uthra G. AHP based on triangular intuitionistic fuzzy number and its application to supplier selection problem. Materials Today: Proceedings. 2019;16:987–93.

[32] Tian D, Chen J, Wu X. A two stage risk assessment model based on interval-valued fuzzy numbers and risk attitudes. Engineering Applications of Artificial Intelligence. 2022;114:105086.

[33] Gong R, Ma L. A new score function and accuracy function of interval-valued intuitionistic fuzzy number and its application. Systems Engineering - Theory & Practice. 2019;39(2):463–75.

[34] Mahapatra GS, Mahapatra BS. Intuitionistic fuzzy fault tree analysis using intuitionistic fuzzy numbers. International Mathematical Forum. 2010;5(21):1015–24.

[35] Nagoor Gani A, Mohamed V. A method of ranking generalized trapezoidal intuitionistic fuzzy numbers. International Journal of Applied Engineering Research. 2015;10(10):25465–73.

[36] Chaira T. Fuzzy set and its extension: The intuitionistic fuzzy set. John Wiley & Sons, Inc.; 2019.

[37] Zhang Q, Sun D. Some notes on possibilistic variances of generalized trapezoidal intuitionistic fuzzy numbers. AIMS Mathematics. 2021;6(4):3720–40.

[38] Kumar M. Applying weakest t-norm based approximate intuitionistic fuzzy arithmetic operations on different types of intuitionistic fuzzy numbers to evaluate reliability of PCBA fault. Applied Soft Computing. 2014;23:387–406.

[39] Banerjee S, Roy T. Arithmetic operations on generalized trapezoidal fuzzy number and its applications. Turkish Journal of Fuzzy Systems. 2012;3(1):16–44.

[40] Cheraghi M, Eslami Baladeh A, Khakzad N. A fuzzy multi-attribute HAZOP technique (FMA-HAZOP): Application to gas wellhead facilities. Safety Science. 2019;114:12–22.

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Published

2024-09-30

Issue

Vol. 5 No. 2: September 2024

Section

Research Articles

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Copyright (c) 2025 The Author(s)

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

[1]
N. M. F. H. Nik Badrul Alam, K. M. N. Ku Khalif, and N. I. Jaini, “Analytical Hierarchy Process based on intuitionistic interval approximation of trapezoidal intuitionistic fuzzy numbers”, Data Anal. Appl. Math., vol. 5, no. 2, pp. 1–16, Sep. 2024, doi: 10.15282/daam.v5i2.11030.

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