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A Pythagorean cubic fuzzy methodology based on TOPSIS and TODIM methods and its application to software selection problem

  • Soft computing in decision making and in modeling in economics
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Abstract

Software selection process for many organizations is a challenging task to conduct their business activities and sustain competitiveness. This paper develops a new hybrid multi-criteria decision-making (MCDM) method to select the most efficient vendor-supplied software package which is used in all business activities for planning or designing, organizing, and supervising functions by operations management of a fuel oil company operated in Turkey. The proposed method is a hybridization of two well-known MCDM approaches, namely TODIM (an acronym in Portuguese for interactive and multi-criteria decision making) and TOPSIS (technique for order preference by similarity to an ideal solution) using Pythagorean cubic fuzzy sets to manage uncertainty, subjectivity and bias of decision makers. To prove the efficiency and applicability of the proposed method, a real-life application to select best software package for fuel oil company is conducted. Finally, sensitivity and comparison analyses are carried out to verify validity and stability of the results obtained by the proposed approach.

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References

  • Abbas SZ, Ali Khan MS, Abdullah S, Sun H, Hussain F (2019) Cubic Pythagorean fuzzy sets and their application to multi-attribute decision making with unknown weight information. J Intell Fuzzy Syst 37:1–16

    Google Scholar 

  • Aguilar-Cisneros JR, Rosas-Sumano JJ, Morales-Ignacio LA (2017). Selection of best software engineering practices: a multi-criteria decision making approach. Adv Soc Inf Appl, 47.

  • Arshadi Khamseh A, Mahmoodi M (2014). A new fuzzy TOPSIS-TODIM hybrid method for green supplier selection using fuzzy time function. Adv Fuzzy Syst

  • Atanassov K, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31(3):343–349

    MathSciNet  MATH  Google Scholar 

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    MATH  Google Scholar 

  • Atanassov KT (1995) Remark on the intuitionistic fuzzy sets – III. Fuzzy Sets Syst 75(3):401–402

    MathSciNet  MATH  Google Scholar 

  • Aydoğan EK, Özmen M (2020) Travel and tourism competitiveness of economies around the world using rough SWARA and TODIM Method. In: Strategic innovative marketing and tourism (pp. 765–774). Springer, Cham

  • Bakioglu G, Atahan AO (2021) AHP integrated TOPSIS and VIKOR methods with Pythagorean fuzzy sets to prioritize risks in self-driving vehicles. Appl Soft Comput 99:106948

    Google Scholar 

  • Beheshtinia MA, Omidi S (2017) A hybrid MCDM approach for performance evaluation in the banking industry. Kybernetes

  • Bera AK, Jana DK, Banerjee D, Nandy T (2019) Supplier selection using extended IT2 fuzzy TOPSIS and IT2 fuzzy MOORA considering subjective and objective factors. Soft Comput 24:1–17

    Google Scholar 

  • Bijoyeta R, Misra SK (2018) An Integrated fuzzy ANP and TOPSIS methodology for software selection under MCDM perspective. Int J Innov Res Comput Commun Eng 6(1):66–75

    Google Scholar 

  • Biswas A, Sarkar B (2019). Interval-valued Pythagorean fuzzy TODIM approach through point operator-based similarity measures for multicriteria group decision making. Kybernetes.

  • Çakır S (2016) Selecting appropriate ERP software using integrated fuzzy linguistic preference relations–fuzzy TOPSIS method. Int J Comput Intell Syst 9(3):433–449

    Google Scholar 

  • Chen TY (2015) The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making. Appl Soft Comput 26:57–73

    Google Scholar 

  • Eastham J, Tucker DJ, Varma S, Sutton SM (2014) PLM software selection model for project management using hierarchical decision modeling with criteria from PMBOK® knowledge areas. Eng Manag J 26(3):13–24. https://doi.org/10.1080/10429247.2014.11432016

    Article  Google Scholar 

  • Fahmi A, Yaqoob N, Chammam W (2021) Maclaurin symmetric mean aggregation operators based on cubic Pythagorean linguistic fuzzy number. J Ambient Intell Humaniz Comput 12(2):1925–1942

    Google Scholar 

  • Garg H (2017) A new improved score function of an interval-valued Pythagorean fuzzy set based TOPSIS method. Int J Uncertain Quantif 7(5):463–474

    Google Scholar 

  • Huang YH, Wei GW (2018) TODIM method for interval-valued Pythagorean fuzzy multiple attribute decision making. Int J Knowl-Based Intell Eng Syst 22(4):249–259

    Google Scholar 

  • Hussain A, Lee JR, Ali Khan MS, Shin DY (2021) Analysis of social networks by using pythagorean cubic fuzzy einstein weighted geometric aggregation operators. J Math

  • Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and applications. Springer, New York

    MATH  Google Scholar 

  • Ilbahar E, Kahraman C (2018) Retail store performance measurement using a novel interval-valued Pythagorean fuzzy WASPAS method. J Intell Fuzzy Syst 35(3):3835–3846

    Google Scholar 

  • Ilbahar E, Karaşan A, Cebi S, Kahraman C (2018) A novel approach to risk assessment for occupational health and safety using Pythagorean fuzzy AHP & fuzzy inference system. Saf Sci 103:124–136

    Google Scholar 

  • Ji P, Zhang HY, Wang JQ (2016) A projection-based TODIM method under multi-valued neutrosophic environments and its application in personnel selection. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2436-z

    Article  Google Scholar 

  • Karsak EE, Özogul CO (2009) An integrated decision making approach for ERP system selection. Expert Syst Appl 36(1):660–667

    Google Scholar 

  • Kazancoglu Y, Burmaoglu S (2013) ERP software selection with MCDM: application of TODIM method. Int J Bus Inf Syst 13(4):435–452

    Google Scholar 

  • Khan F, Abdullah S, Mahmood T, Shakeel M, Rahim M (2019a) Pythagorean cubic fuzzy aggregation information based on confidence levels and its application to multi-criteria decision making process. J Intell Fuzzy Syst 36(6):5669–5683

    Google Scholar 

  • Khan F, Khan MSA, Shahzad M, Abdullah S (2019b) Pythagorean cubic fuzzy aggregation operators and their application to multi-criteria decision making problems. J Intell Fuzzy Syst 36(1):595–607

    Google Scholar 

  • Khan MSA, Khan F, Lemley J, Abdullah S, Hussain F (2020) Extended topsis method based on Pythagorean cubic fuzzy multi-criteria decision making with incomplete weight information. J Intell Fuzzy Syst 38(2):2285–2296

    Google Scholar 

  • Kim G, Park CS, Yoon KP (1997) Identifying investment opportunities for advanced manufacturing systems with comparative-integrated performance measurement. Int J Prod Econ 50:23–33

    Google Scholar 

  • Krohling RA, Pacheco AG, dos Santos GA (2019) TODIM and TOPSIS with Z-numbers. Front Inf Technol Electron Eng 20(2):283–291

    Google Scholar 

  • Krohling RA, Pacheco AGC (2014) Interval-valued intuitionistic fuzzy TODIM”. Procedia Comput Sci 31:236–244

    Google Scholar 

  • Li M, Li Y, Peng Q, Wang J, Yu C (2021) Evaluating community question-answering websites using interval-valued intuitionistic fuzzy DANP and TODIM methods. Appl Soft Comput 99:106918

    Google Scholar 

  • Li Y, Shan Y, Liu P (2015) An extended TODIM method for group decision making with the interval intuitionistic fuzzy sets. Math Probl Eng 2015:1–9

    Google Scholar 

  • Liang D, Zhang Y, Xu Z, Jamaldeen A (2019) Pythagorean fuzzy VIKOR approaches based on TODIM for evaluating internet banking website quality of Ghanaian banking industry. Appl Soft Comput 78:583–594

    Google Scholar 

  • Lin YL, Ho LH, Yeh SL, Chen TY (2018) A Pythagorean fuzzy TOPSIS method based on novel correlation measures and its application to multiple criteria decision analysis of inpatient stroke rehabilitation. Int J Comput Intell Syst 12(1):410–425

    Google Scholar 

  • Liu D, Luo Y, Liu Z (2020) The linguistic picture fuzzy set and its application in multi-criteria decision-making: an illustration to the TOPSIS and TODIM methods based on entropy weight. Symmetry 12(7):1170

    Google Scholar 

  • Lo HW, Shiue W, Liou JJ, Tzeng GH (2020) A hybrid MCDM-based FMEA model for identification of critical failure modes in manufacturing. Soft Comput 24(20):15733–15745

    Google Scholar 

  • Lourenzutti R, Krohling RA (2013) A study of TODIM in a intuitionistic fuzzy and random environment. Expert Syst Appl 40(16):6459–6468

    Google Scholar 

  • Lourenzutti R, Krohling RA (2014) The Hellinger distance in multicriteria decision making: an illustration to the TOPSIS and TODIM methods. Expert Syst Appl 41(9):4414–4421

    Google Scholar 

  • Lourenzutti R, Krohling RA, Reformat MZ (2017) Choquet based TOPSIS and TODIM for dynamic and heterogeneous decision making with criteria interaction. Inf Sci 408:41–69

    MATH  Google Scholar 

  • Mulebeke JAW, Zheng L, L. (2006) Analytical network proc-ess for software selection in product development. J Eng Tech Manag 23(4):337–352

    Google Scholar 

  • Nguyen H (2017) Interval-valued intuitionistic fuzzy failure modes and effect analysis of the system failure risk estimation. J KONES 24:159–166

    Google Scholar 

  • Nirmala G, Uthra G (2016) Intuitionistic fuzzy analytic hierarchy process based on possibility degree. Int J Pure Appl Math 109(9):184–192

    Google Scholar 

  • Ozkaya G, Erdin C (2020) Evaluation of smart and sustainable cities through a hybrid MCDM approach based on ANP and TOPSIS technique. Heliyon 6(10):05052

    Google Scholar 

  • Peng X, Dai J (2017) Approaches to pythagorean fuzzy stochastic multi-criteria decision making based on prospect theory and regret theory with new distance measure and score function. Int J Intell Syst 32(11):1187–1214

    Google Scholar 

  • Peng XD, Yang Y (2016) Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators. Int J Intell Syst 31:444–487

    Google Scholar 

  • Rahman K, Abdullah S, Ali A, Amin F (2019) Interval-valued Pythagorean fuzzy Einstein hybrid weighted averaging aggregation operator and their application to group decision making. Complex Intell Syst 5(1):41–52

    Google Scholar 

  • Rao RV, Rajesh TS (2009) Software selection in manufacturing industries using a fuzzy multiple criteria decision making method. PROMETHEE Intell Inf Manag 1(03):159

    Google Scholar 

  • Razavi Hajiagha SH, Hashemi SS, Zavadskas EK (2013) A complex proportional assessment method for group decision making in an interval-valued intuitionistic fuzzy environment. Technol Econ Dev Econ 19(1):22–37

    Google Scholar 

  • Ren P, Xu Z, Gou X (2016) Pythagorean fuzzy TODIM approach to multi-criteria decision making. Appl Soft Comput 42:246–259

    Google Scholar 

  • Roy J, Das S, Kar S, Pamučar D (2019) An Extension of the CODAS approach using interval-valued intuitionistic fuzzy set for sustainable material selection in construction projects with incomplete weight information. Symmetry 11(3):393

    Google Scholar 

  • Sarkis J, Talluri S (2004) Evaluating and selecting e-com-merce software and communication systems for a supply chain. Eur J Oper Resh 159(2):318–329

    MATH  Google Scholar 

  • Talukdar P, Dutta P (2019) Distance measures for cubic Pythagorean fuzzy sets and its applications to multicriteria decision making. Granul Comput 6:1–18

    Google Scholar 

  • Tversky A, Kahneman D (1992) Advances in prospect theory: cumulative representation of uncertainty. J Risk Uncertain 5(4):297–323

    MATH  Google Scholar 

  • Victor M, Upadhyay N (2011) Selection of software testing technique: a multi criteria decision making approach. Springer, Berlin, pp 453–462

    Google Scholar 

  • Wang H, Qian G, Feng X (2011) An intuitionistic fuzzy AHP based on synthesis of eigenvectors and its application. Inf Technol J 10(10):1850–1866

    Google Scholar 

  • Wu J, Huang HB, Cao QW (2013) Research on AHP with interval-valued intuitionistic fuzzy sets and its application in multi-criteria decision making problems. Appl Math Model 37(24):9898–9906

    MathSciNet  MATH  Google Scholar 

  • Xu Z, Zhang X (2013) Hesitant fuzzy multi attribute decision making based on TOPSIS with incomplete weight information. Knowl Based Syst 52:53–64

    Google Scholar 

  • Xu W, Shang X, Wang J (2021) Multiple attribute group decision-making based on cubic linguistic Pythagorean fuzzy sets and power Hamy mean. Complex Intell Syst 7(3):1673–1693

    Google Scholar 

  • Yager RR, Abbasov AM (2013) Pythagorean membeship grades, complex numbers and decision making. Int J Intell Syst 28:436–452

    Google Scholar 

  • Yazgan HR, Boran S, Goztepe K (2009) An ERP software selection process with using artificial neural network based on analytic network process approach. Expert Syst Appl 36(5):9214–9222

    Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    MATH  Google Scholar 

  • Zanakis SH, Solomon A, Wishart N, Dublish S (1998) Multi-attribute decision making: a simulation comparison of selection methods. Eur J Oper Res 107:507–529

    MATH  Google Scholar 

  • Zhang S, Li X, Meng F (2016) An approach to multi-criteria decision-making under interval-valued intuitionistic fuzzy values and interval fuzzy measures. J Ind Product Eng 33(4):253–270

    Google Scholar 

  • Zhang X, Xu Z (2014) Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29(12):1061–1078

    MathSciNet  Google Scholar 

  • Zhou F, Chen TY (2019) A novel distance measure for pythagorean fuzzy sets and its applications to the technique for order preference by similarity to ideal solutions. Int J Comput Intell Syst 12(2):955–969

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Industrial Engineering Department, Yildiz Technical University, 34349, Yildiz, Istanbul, Turkey

    Sukran Seker

  2. Industrial Engineering Department, Istanbul Technical University, 34367, Macka, Istanbul, Turkey

    Cengiz Kahraman

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  1. Sukran Seker
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  2. Cengiz Kahraman
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Correspondence to Sukran Seker.

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Seker, S., Kahraman, C. A Pythagorean cubic fuzzy methodology based on TOPSIS and TODIM methods and its application to software selection problem. Soft Comput 26, 2437–2450 (2022). https://doi.org/10.1007/s00500-021-06469-8

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