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A VIKOR-based group decision-making approach to software reliability evaluation

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

Software reliability evaluation is important to attribute of software quality. A new group decision-making is provided to evaluate software reliability, where the model is based on an extended VIsekriterijumska optimizacija i KOmpromisno Resenje technique. The individual utility and individual regret in general VIKOR technique are extended to group utility and group regret. A specific regret matrix is provided in new VIKOR-based GDM method. A new ranking method is provided in a static environment. Another new ranking method is provided in a dynamic environment. To implement a user-based evaluation for software reliability, the picture fuzzy set is used for handling the questionnaire information. It is noted that the existing projection measure is not always reasonable in picture fuzzy setting. To solve this problem, a new normalization projection measure is provided in picture fuzzy setting. And a new GDM method is established for software reliability evaluation. The feasibility and practicability developed method in this work are illustrated by an experimental analysis.

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References

  • Abuta E, Tian J (2018) Reliability over consecutive releases of a semiconductor optical Endpoint Detection software system developed in a small company. J Syst Softw 137:355–365

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Bertsatos A, Christaki A, Chovalopoulou M-E (2019) Testing the reliability of 3D-ID software in sex and ancestry estimation with a modern Greek sample. Forensic Sci Int 297:132–137

    Article  Google Scholar 

  • Büyüközkan G, Göçer F, Karabulut Y (2019) A new group decision making approach with IF AHP and IF VIKOR for selecting hazardous waste carriers. Measurement 134:66–82

    Article  Google Scholar 

  • Büyüközkan G, Güler M (2020) Smart watch evaluation with integrated hesitant fuzzy linguistic SAW-ARAS technique. Measurement 153:107353

    Article  Google Scholar 

  • Çalı S, Balaman ŞY (2019) A novel outranking based multi criteria group decision making methodology integrating ELECTRE and VIKOR under intuitionistic fuzzy environment. Exp Syst Appl 119:36–50

    Article  Google Scholar 

  • Chen T-Y (2016) An interval-valued intuitionistic fuzzy permutation method with likelihood-based preference functions and its application to multiple criteria decision analysis. Appl Soft Comput 42:390–409

    Article  Google Scholar 

  • Chen T-Y (2018) Remoteness index-based Pythagorean fuzzy VIKOR methods with a generalized distance measure for multiple criteria decision analysis. Inform Fus 41:129–150

    Article  Google Scholar 

  • Cho J, Shin SM, Lee SJ, Jung W (2019) Exhaustive test cases for the software reliability of safety-critical digital systems in nuclear power plants. Nucl Eng Des 352:110151

    Article  Google Scholar 

  • Cuong BC (2014) Picture fuzzy sets. J Comput Sci Cybern 30(4):409–420

    Google Scholar 

  • Curiel-Esparza J, Reyes-Medina M, Martin-Utrillas M, Martinez-Garcia MP, Canto-Perello J (2019) Collaborative elicitation to select a sustainable biogas desulfurization technique for landfills. J Clean Prod 212:1334–1344

    Article  Google Scholar 

  • Dohi T, Zheng J, Okamura H, Trivedi KS (2018) Optimal periodic software rejuvenation policies based on interval reliability criteria. Reliab Eng Syst Saf 180:463–475

    Article  Google Scholar 

  • Greisberger A, Wolf B, Widhalm K, Kollmitzer D, Arbesser M, Putz P (2019) Intrarater and interrater reliability of angular measures using TEMPLO two-dimensional motion analysis software. J Manip Phys Ther 42:425–429

    Article  Google Scholar 

  • Guo J, Yang M, Zou B, Zhang Y, Yang J, Dai X (2018) Nuclear safety-critical Digital Instrumentation and Control system software: Reliability demonstration. Ann Nucl Energy 120:516–527

    Article  Google Scholar 

  • Gupta P, Mehlawat MK, Grover N (2016) Intuitionistic fuzzy multi-attribute group decision-making with an application to plant location selection based on a new extended VIKOR method. Inform Sci 370:184–203

    Article  Google Scholar 

  • Huo X, Li M (2019) On cost-effective software defect prediction: Classification or ranking? Neurocomputing 363:339–350

    Article  Google Scholar 

  • Islam MJ, Rahman A, Kabir S, Karim MR, Acharjee UK, Nasir MK, Band SS, Sookhak M, Wu S (2021) Blockchain-sdn based energy-aware and distributed secure architecture for IoTs in smart cities. IEEE Int Things J 9(5):3850–3864

    Article  Google Scholar 

  • Ju Y, Wang A (2013) Projection method for multiple criteria group decision making with incomplete weight information in linguistic setting. Appl Math Modell 37(20):9031–9040

    Article  MathSciNet  MATH  Google Scholar 

  • Kaliraj S, Bharathi A (2019) Path testing based reliability analysis framework of component based software system. Measurement 144:20–32

    Article  Google Scholar 

  • Kang HG, Lee SH, Lee SJ, Chu T-L, Varuttamaseni A, Yue M, Yang S, Eom HS, Cho J, Li M (2018) Development of a bayesian belief network model for software reliability quantification of digital protection systems in nuclear power plants. Ann Nucl Energy 120:62–73

    Article  Google Scholar 

  • Lanna A, Castro T, Alves V, Rodrigues G, Schobbens P-Y, Apel S (2018) Feature-family-based reliability analysis of software product lines. Inform Softw Technol 94:59–81

    Article  Google Scholar 

  • Levitin G, Xing L, Huang H-Z (2019) Optimization of partial software rejuvenation policy. Reliab Eng Syst Saf 188:289–296

    Article  Google Scholar 

  • Li Y, Wang J, Zhao D, Li G, Chen C (2018) A two-stage approach for combined heat and power economic emission dispatch: Combining multi-objective optimization with integrated decision making. Energy 162:237–254

    Article  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

    Article  Google Scholar 

  • Liao H, Zhang C, Luo L (2018) A multiple attribute group decision making method based on two novel intuitionistic multiplicative distance measures. Inform Sci 467:766–783

    Article  MathSciNet  MATH  Google Scholar 

  • Liu P, You X (2019) Bidirectional projection measure of linguistic neutrosophic numbers and their application to multi-criteria group decision making. Comput Ind Eng 128:447–457

    Article  Google Scholar 

  • Lyu MR (1996) Handbook of software reliability engineering. McGraw-Hill, New York

    Google Scholar 

  • Mahmoudi MR, Baleanu D, Qasem SN, Mosavi A, Shahab (2021) Fuzzy clustering to classify several time series models with fractional brownian motion errors. Alex Eng J 60(1):1137–1145

    Article  Google Scholar 

  • Moazzeni S, Khayyambashi MR, Movahhedinia N, Callegati F (2018) On reliability improvement of software-defined networks. Comput Netw 133:195–211

    Article  Google Scholar 

  • Mohammadzadeh A, Castillo O, Band SS, Mosavi A (2021) A novel fractional-order multiple-model type-3 fuzzy control for nonlinear systems with unmodeled dynamics. Int J Fuzzy Syst 23(6):1633–1651

    Article  Google Scholar 

  • Opricovic S (1998) Multicriteria optimization of civil engineering systems. Fac Civ Eng, Belgrad 2(1):5–21

    MathSciNet  Google Scholar 

  • Opricovic S, Tzeng G-H (2004) Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. Eur J Op Res 156(2):445–455

    Article  MATH  Google Scholar 

  • Opricovic S, Tzeng GH (2007) Extended VIKOR method in comparison with outranking methods. Eur J Op Res 178(2):514–529

    Article  MATH  Google Scholar 

  • Ploskas N, Papathanasiou J (2019) A decision support system for multiple criteria alternative ranking using TOPSIS and VIKOR in fuzzy and nonfuzzy environments. Fuzzy Sets Syst 377:1–30

    Article  MathSciNet  MATH  Google Scholar 

  • Rahman A, Chakraborty C, Anwar A, Karim M, Islam M, Kundu D, Rahman Z, Band SS, et al (2021) SDN–IoT empowered intelligent framework for industry 4.0 applications during COVID-19 pandemic. Cluster Computing, pages 1–18

  • Ren Z, Xu Z, Wang H (2017) Dual hesitant fuzzy VIKOR method for multi-criteria group decision making based on fuzzy measure and new comparison method. Inform Sci 388–389:1–16

    Article  MATH  Google Scholar 

  • Shan C, Mei S, Hu C, Liu L, Mao L (2019) Software structure characteristic measurement method based on weighted network. Comput Netw 152:178–185

    Article  Google Scholar 

  • Sinha S, Goyal NK, Mall R (2019) Early prediction of reliability and availability of combined hardware-software systems based on functional failures. J Syst Archit 92:23–38

    Article  Google Scholar 

  • Štirbanović Z, Stanujkić D, Miljanović I, Milanović D (2019) Application of MCDM methods for flotation machine selection. Miner Eng 137:140–146

    Article  Google Scholar 

  • Tang G, Chiclana F, Lin X, Liu P (2020) Interval type-2 fuzzy multi-attribute decision-making approaches for evaluating the service quality of Chinese commercial banks. Knowl-Based Syst 193:105438

    Article  Google Scholar 

  • Tsao C-Y, Chen T-Y (2016) A projection-based compromising method for multiple criteria decision analysis with interval-valued intuitionistic fuzzy information. Appl Soft Comput 45:207–223

    Article  Google Scholar 

  • Utkin LV, Coolen FP (2018) A robust weighted SVR-based software reliability growth model. Reliab Eng Syst Saf 176:93–101

    Article  Google Scholar 

  • Wan S-P, Li S-Q, Dong J-Y (2018) A three-phase method for Pythagorean fuzzy multi-attribute group decision making and application to haze management. Comput Ind Eng 123:348–363

    Article  Google Scholar 

  • Wang H, Pan X, Yan J, Yao J, He S (2020) A projection-based regret theory method for multi-attribute decision making under interval type-2 fuzzy sets environment. Inform Sci 512:108–122

    Article  MathSciNet  MATH  Google Scholar 

  • Wang J, Zhang C (2018) Software reliability prediction using a deep learning model based on the RNN encoder-decoder. Reliab Eng Syst Saf 170:73–82

    Article  Google Scholar 

  • Wang L, Wang H, Xu Z, Ren Z (2020) A bi-projection model based on linguistic terms with weakened hedges and its application in risk allocation. Appl Soft Comput 87:105996

    Article  Google Scholar 

  • Wei G (2017) Picture 2-tuple linguistic Bonferroni mean operators and their application to multiple attribute decision making. Int J Fuzzy Syst 19(4):997–1010

    Article  MathSciNet  Google Scholar 

  • Wei G, Alsaadi FE, Hayat T, Alsaedi A (2018) Projection models for multiple attribute decision making with picture fuzzy information. Int J Mach Learn Cyber 9(4):713–719

    Article  Google Scholar 

  • Wu H, Xu Z, Ren P, Liao H (2018) Hesitant fuzzy linguistic projection model to multi-criteria decision making for hospital decision support systems. Comput Ind Eng 115:449–458

    Article  Google Scholar 

  • Wu Q, Lin W, Zhou L, Chen Y, Chen H (2019) Enhancing multiple attribute group decision making flexibility based on information fusion technique and hesitant Pythagorean fuzzy sets. Comput Ind Eng 127:954–970

    Article  Google Scholar 

  • Wu Q, Zhou L, Chen Y, Chen H (2019) An integrated approach to green supplier selection based on the interval type-2 fuzzy best-worst and extended VIKOR methods. Inform Sci 502:394–417

    Article  Google Scholar 

  • Wu Z, Ahmad J, Xu J (2016) A group decision making framework based on fuzzy VIKOR approach for machine tool selection with linguistic information. Appl Soft Comput 42:314–324

    Article  Google Scholar 

  • Wu Z, Xu J, Jiang X, Zhong L (2019) Two MAGDM models based on hesitant fuzzy linguistic term sets with possibility distributions: VIKOR and TOPSIS. Inform Sci 473:101–120

    Article  MathSciNet  MATH  Google Scholar 

  • Xu G, Liu F (2013) An approach to group decision making based on interval multiplicative and fuzzy preference relations by using projection. Appl Math Modell 37(6):3929–3943

    Article  MathSciNet  MATH  Google Scholar 

  • Ye J (2017) Bidirectional projection method for multiple attribute group decision making with neutrosophic numbers. Neural Comput Appl 28(5):1021–1029

    Article  Google Scholar 

  • You X-Y, You J-X, Liu H-C, Zhen L (2015) Group multi-criteria supplier selection using an extended VIKOR method with interval 2-tuple linguistic information. Exp Syst with Appl 42(4):1906–1916

    Article  Google Scholar 

  • Yue C (2016) A geometric approach for ranking interval-valued intuitionistic fuzzy numbers with an application to group decision-making. Comput Ind Eng 102:233–245

  • Yue C (2017) Entropy-based weights on decision makers in group decision-making setting with hybrid preference representations. Appl Soft Comput 60:737–749

    Article  Google Scholar 

  • Yue C (2017) Two normalized projection models and application to group decision-making. J of Int Fuzzy Syst 32(6):4389–4402

    MATH  Google Scholar 

  • Yue C (2019) An interval-valued intuitionistic fuzzy projection-based approach and application to evaluating knowledge transfer effectiveness. Neural Comput Appl 31(11):7685–7706

    Article  Google Scholar 

  • Yue C (2019) A normalized projection-based group decision-making method with heterogeneous decision information and application to software development effort assessment. Appl Int 49(10):3587–3605

    Article  Google Scholar 

  • Yue C (2019) Projection-based approach to group decision-making with hybrid information representations and application to software quality evaluation. Comput Ind Eng 132:98–113

    Article  Google Scholar 

  • Yue C (2020) An intuitionistic fuzzy projection-based approach and application to software quality evaluation. Soft Comput 24:429–433

    Article  MATH  Google Scholar 

  • Yue C (2020) Picture fuzzy normalized projection and extended VIKOR approach to software reliability assessment. Applied Soft Computing, p 106056

  • Yue C, Yue Z (2019) Measuring the satisfaction and loyalty of Chinese smartphone users: A simple symbol-based decision-making method. Sci Iran 26(1):589–604

    Google Scholar 

  • Yue Z (2011) A method for group decision-making based on determining weights of decision makers using TOPSIS. Appl Math Modell 35(4):1926–1936

    Article  MathSciNet  MATH  Google Scholar 

  • Yue Z (2011) An extended TOPSIS for determining weights of decision makers with interval numbers. Knowl-Based Syst 24(1):146–153

    Article  Google Scholar 

  • Yue Z (2014) TOPSIS-based group decision-making methodology in intuitionistic fuzzy setting. Inform Sci 277:141–153

    Article  MathSciNet  MATH  Google Scholar 

  • Yue Z, Jia Y (2015) A group decision making model with hybrid intuitionistic fuzzy information. Comput Ind Eng 87:202–212

    Article  Google Scholar 

  • Yue Z, Jia Y (2017) A direct projection-based group decision-making methodology with crisp values and interval data. Soft Comput 21(9):2395–2405

    Article  MATH  Google Scholar 

  • Zadeh L (1965) Fuzzy sets Inform control 8(3):338–353

    Article  Google Scholar 

  • Zeng S, Chen S-M, Kuo L-W (2019) Multiattribute decision making based on novel score function of intuitionistic fuzzy values and modified VIKOR method. Inform Sci 488:76–92

    Article  Google Scholar 

  • Zhang X-Y, Wang J-Q, Hu J-H (2018) On novel operational laws and aggregation operators of picture 2-tuple linguistic information for MCDM problems. Int J Fuzzy Syst 20(3):958–969

    Article  MathSciNet  Google Scholar 

  • Zhao X, Band SS, Elnaffar S, Sookhak M, Mosavi A, Salwana E (2021) The implementation of border gateway protocol using software-defined networks: A systematic literature review. IEEE Access

  • Zhu M, Pham H (2017) Environmental factors analysis and comparison affecting software reliability in development of multi-release software. J Syst Softw 132:72–84

    Article  Google Scholar 

  • Zou B, Yang M, Yang J, Guo J, Su Y, Zhang C, Wang W (2018) Reliability analysis and allocation: Development of a hierarchical structure modeling platform in I &C system Software Life Cycle. Nucl Eng Des 328:345–352

    Article  Google Scholar 

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Acknowledgements

The author would like to thank the editors and the anonymous reviewers for their insightful and constructive comments and suggestions that have led to this improved version of the paper.

Funding

This work was supported partially by the Science and Technology Planning Project from Zhanjiang Science and Technology Bureau (No. 2020B01415) and Project of Teaching Innovation in 2022 from Guangdong Ocean University (No. PX-131223610).

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Correspondence to Chuan Yue.

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Yue, C. A VIKOR-based group decision-making approach to software reliability evaluation. Soft Comput 26, 9445–9464 (2022). https://doi.org/10.1007/s00500-022-07268-5

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