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A parametric scoring function and the associated method for interval neutrosophic multi-criteria decision-making

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Abstract

Multi-criteria decision-making (MCDM) is widely discussed in many management areas. Economic, social, cultural, and political affairs in a country, as well as institutions, organizations, and companies often face multi-criteria decision-making problems. Data and information on alternatives and criteria in the multi-criteria decision-making problem may sometimes be mixed with hesitancy, indeterminacy, and uncertainty. Such problems are among the neutrosophic multi-criteria decision-making problems. This paper has developed a method for solving interval neutrosophic multi-criteria decision-making problems. First, a parametric scoring function is developed for interval neutrosophic sets, and it has been shown that this function can be used to evaluate alternatives to an interval neutrosophic multi-criteria decision-making problem. Then, using this parametric scoring function, a TOPSIS based algorithm is proposed to solve interval neutrosophic multi-criteria decision-making problems. The method developed in this paper has relatively beneficial flexibility and can be used to provide suitable solutions for a neutrosophic multi-criteria decision-making problem with different perspectives such as a pessimistic, realistic and optimistic perspective. The proposed algorithm has various capabilities and enables it to be used to solve a wide range of neutrosophic multi-criteria decision-making problems.

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References

  • Abdel-Basset M, Mohamed M (2019) A novel and powerful framework based on neutrosophic sets to aid patients with cancer. Fut Gener Comput Syst 98:144–153

    Google Scholar 

  • Abdel-Basset M, Chang V, Mohamed M, Smarandache F (2019) A refined approach for forecasting based on neutrosophic time series. Symmetry 11(4):457

    Google Scholar 

  • Ali M, Smarandache F (2017) Complex neutrosophic set. Neural Comput Appl 28(7):1817–1834

    Google Scholar 

  • Ali M, Thanh ND, Van Minh N (2018) A neutrosophic recommender system for medical diagnosis based on algebraic neutrosophic measures. Appl Soft Comput 71:1054–1071

    Google Scholar 

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

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Awang A, Aizam NAH, Ab Ghani AT, Othman M, Abdullah L (2020) A normalized weighted bonferroni mean aggregation operator considering shapley fuzzy measure under interval-valued neutrosophic environment for decision-making. Int J Fuzzy Syst 22(1):321–336

    Google Scholar 

  • Bausys R, Kazakeviciute-Januskeviciene G, Cavallaro F, Usovaite A (2020) Algorithm selection for edge detection in satellite images by neutrosophic WASPAS method. Sustainability 12(2):548

    Google Scholar 

  • Broumi S, Smarandache F (2014) New distance and similarity measures of interval neutrosophic sets. Infinite Study, Conshohocken

    MATH  Google Scholar 

  • Broumi S, Smarandache F, Dhar M (2014) Rough neutrosophic sets. Infinite Study, Conshohocken

    MATH  Google Scholar 

  • Corrales DC, Ledezma A, Corrales JC (2020) A case-based reasoning system for recommendation of data cleaning algorithms in classification and regression tasks. Appl Soft Comput 90:106180

    Google Scholar 

  • Dey A, Broumi S, Bakali A, Talea M, Smarandache F (2019) A new algorithm for finding minimum spanning trees with undirected neutrosophic graphs. Granul Comput 4(1):63–69

    Google Scholar 

  • Garg H (2016) An improved score function for ranking neutrosophic sets and its application to decision-making process. Int J Uncertain Quantif 6(5):377–385

    Google Scholar 

  • Garg H (2018) Non-linear programming method for multi-criteria decision making problems under interval neutrosophic set environment. Appl Intell 48(8):2199–2213

    Google Scholar 

  • Garg H (2020) Multiple attribute decision making based on immediate probabilities aggregation operators for single-valued and interval neutrosophic sets. J Appl Math Comput 63:619–653

    MathSciNet  Google Scholar 

  • Guan H, Guan S, Zhao A (2017) Forecasting model based on neutrosophic logical relationship and Jaccard similarity. Symmetry 9(9):191

    Google Scholar 

  • Guan H, He J, Zhao A, Dai Z, Guan S (2018) A forecasting model based on multi-valued neutrosophic sets and two-factor. Third-order fuzzy fluctuation logical relationships. Symmetry 10(7):245

    Google Scholar 

  • Huang HL (2016) New distance measure of single-valued neutrosophic sets and its application. Int J Intell Syst 31(10):1021–1032

    Google Scholar 

  • Jha S, Kumar R, Priyadarshini I, Smarandache F, Long HV (2019) Neutrosophic image segmentation with dice coefficients. Measurement 134:762–772

    Google Scholar 

  • Ji P, Zhang HY (2016) A subsethood measure with the hausdorff distance for interval neutrosophic sets and its relations with similarity and entropy measures. In: 2016 Chinese control and decision conference (CCDC), IEEE, pp 4152–4157

  • Kakati P, Borkotokey S, Rahman S, Davvaz B (2020) Interval neutrosophic hesitant fuzzy Einstein Choquet integral operator for multicriteria decision making. Artif Intell Rev 53(3):2171–2206

    Google Scholar 

  • Liu P, You X (2017) Interval neutrosophic Muirhead mean operators and their application in multiple attribute group decision-making. Int J Uncertain Quantif 7(4):303–334

    Google Scholar 

  • Liu PD, Liu X, Xu L (2016) The TOPSIS method for multiple attribute group decision making with interval neutrosophic number based on cloud model. Rev Econ Manag 3:73–78

    Google Scholar 

  • Liu P, Khan Q, Mahmood T (2019) Application of interval neutrosophic power Hamy mean operators in MAGDM. Informatica 30(2):293–325

    Google Scholar 

  • Maji PK (2013) Neutrosophic soft set. Infinite Study, Conshohocken

    MATH  Google Scholar 

  • Nguyen GN, Ashour AS, Dey N (2019) A survey of the state-of-the-arts on neutrosophic sets in biomedical diagnoses. Int J Mach Learn Cybern 10(1):1–13

    Google Scholar 

  • Nie RX, Wang JQ, Zhang HY (2017) Solving solar-wind power station location problem using an extended weighted aggregated sum product assessment (WASPAS) technique with interval neutrosophic sets. Symmetry 9(7):106

    Google Scholar 

  • Palanisamy TSCA, Jayaraman M, Vellingiri K, Guo Y (2019) Optimization-based neutrosophic set for medical image processing. Neutrosophic set in medical image analysis. Academic Press, London, pp 189–206

    Google Scholar 

  • Pouresmaeil H, Shivanian E, Khorram E, Fathabadi HS (2017) An extended method using TOPSIS and VIKOR for multiple attribute decision making with multiple decision makers and single valued neutrosophic numbers. Adv Appl Stat 50:261–292

    MATH  Google Scholar 

  • Pozna C, Precup RE (2014) Applications of signatures to expert systems modelling. Acta Polytechn Hung 11(2):21–39

    Google Scholar 

  • Qin K, Wang L (2020) New similarity and entropy measures of single-valued neutrosophic sets with applications in multi-attribute decision making. Soft Comput 24:16165–16176

    Google Scholar 

  • Şahin R (2014) Multi-criteria neutrosophic decision making method based on score and accuracy functions under neutrosophic environment. arXiv preprint arXiv:1412.5202.

  • Şahin R (2017) Cross-entropy measure on interval neutrosophic sets and its applications in multicriteria decision making. Neural Comput Appl 28(5):1177–1187

    Google Scholar 

  • Şahin R, Karabacak M (2020) A novel similarity measure for single-valued neutrosophic sets and their applications in medical diagnosis, taxonomy, and clustering analysis. Optimization theory based on neutrosophic and plithogenic sets. Academic Press, London, pp 315–341

    Google Scholar 

  • Şahin R, Küçük A (2015) Subsethood measure for single valued neutrosophic sets. J Intell Fuzzy Syst 29(2):525–530

    MATH  Google Scholar 

  • Sengur A, Budak U, Akbulut Y, Karabatak M, Tanyildizi E (2019) A survey on neutrosophic medical image segmentation. Neutrosophic set in medical image analysis. Academic Press, London, pp 145–165

    Google Scholar 

  • Skoulikaris C, Papadopoulos C, Spiliotis M, Maris F (2020) Enhancement of socioeconomic criteria for the assessment of the vulnerability to flood events with the use of multicriteria analysis. Environmental sciences proceedings, vol 2, vol 1. Multidisciplinary Digital Publishing Institute, BaselBasel, p 52

    Google Scholar 

  • Smarandache F (1998) Neutrosophy: neutrosophic probability, set, and logic: Analytic synthesis and synthetic analysis. American Research Press: Rehoboth.

  • Smarandache F (1999) A unifying field in logics. Neutrosophy: neutrosophic probability, set and logic. American Research Press: Rehoboth.

  • Spiliotis M, Iglesias A, Garrote L (2021) A multicriteria fuzzy pattern recognition approach for assessing the vulnerability to drought: Mediterranean region. Evol Syst 12(1):109–122

    Google Scholar 

  • Thanh ND, Ali M (2017) A novel clustering algorithm in a neutrosophic recommender system for medical diagnosis. Cognit Comput 9(4):526–544

    Google Scholar 

  • Wang H, Smarandache F, Sunderraman R, Zhang YQ (2005) Interval neutrosophic sets and logic: theory and applications in computing: theory and applications in computing, vol 5. Infinite Study, Conshohocken

    MATH  Google Scholar 

  • Wang H, Smarandache F, Zhang Y, Sunderraman R (2010) Single valued neutrosophic sets. Infinite Study, Conshohocken

    MATH  Google Scholar 

  • Wu H, Yuan Y, Wei L, Pei L (2018) On entropy, similarity measure and cross-entropy of single-valued neutrosophic sets and their application in multi-attribute decision making. Soft Comput 22(22):7367–7376

    Google Scholar 

  • Ye J (2013) Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment. Int J Gen Syst 42(4):386–394

    MathSciNet  MATH  Google Scholar 

  • Ye J (2014) Some aggregation operators of interval neutrosophic linguistic numbers for multiple attribute decision making. J Intell Fuzzy Syst 27(5):2231–2241

    MathSciNet  MATH  Google Scholar 

  • Ye J (2014) Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making. J Intell Fuzzy Syst 26(1):165–172

    MATH  Google Scholar 

  • Ye J (2015a) Trapezoidal neutrosophic set and its application to multiple attribute decision-making. Neural Comput Appl 26(5):1157–1166

    Google Scholar 

  • Ye J (2015b) Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses. Artif Intell Med 63(3):171–179

    Google Scholar 

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

    MATH  Google Scholar 

  • Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8(3):199–249

    MathSciNet  MATH  Google Scholar 

  • Zall R, Kangavari MR (2019) On the construction of multi-relational classifier based on canonical correlation analysis. Inte J Artif Intell 17(2):23–43

    Google Scholar 

  • Zhang HY, Wang JQ, Chen XH (2014) Interval neutrosophic sets and their application in multicriteria decision making problems. Sci World J. https://doi.org/10.1155/2014/645953

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Islamic Azad University, Karaj Branch, Karaj, Iran

    Hassan Pouresmaeil

  2. Department of Mathematics, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

    Esmaile Khorram

  3. Department of Mathematics, Imam Khomeini International University, Qazvin, Iran

    Elyas Shivanian

Authors
  1. Hassan Pouresmaeil
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  2. Esmaile Khorram
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  3. Elyas Shivanian
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Correspondence to Esmaile Khorram.

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Pouresmaeil, H., Khorram, E. & Shivanian, E. A parametric scoring function and the associated method for interval neutrosophic multi-criteria decision-making. Evolving Systems 13, 347–359 (2022). https://doi.org/10.1007/s12530-021-09394-1

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