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Multiple attribute decision-making approach for Pythagorean neutrosophic normal interval-valued fuzzy aggregation operators

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Abstract

We present a communication which deals with some new methods to solve multiple attribute decision-making (MADM) problems based on Pythagorean neutrosophic normal interval-valued set (PNSNIVS). The Pythagorean neutrosophic interval-valued sets are based on further generalization of Pythagorean neutrosophic sets and interval-valued neutrosophic sets. Here we discuss about various aggregating operations that have been interpreted up to date. The focus of the article is to discuss a new notion of Pythagorean neutrosophic normal interval-valued weighted averaging (PNSNIVWA), Pythagorean neutrosophic normal interval-valued weighted geometric (PNSNIVWG), generalized Pythagorean neutrosophic normal interval-valued weighted averaging (GPNSNIVWA) and generalized Pythagorean neutrosophic normal interval-valued weighted geometric (GPNSNIVWG). Also, we obtain an algorithm that deals with the MADM problems based on these operators. We interact applicability of the Euclidean and hamming distance measures which are further extended in real life example. Finally, some important properties of these sets under various algebraic operations are to be elaborated in this communication.

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References

  • Akram M, Dudek WA, Ilyas F (2019a) Group decision making based on Pythagorean fuzzy TOPSIS method. Int J Intell Syst 34:1455–1475

    Article  Google Scholar 

  • Akram M, Dudek WA, Dar JM (2019b) Pythagorean Dombi fuzzy aggregation operators with application in multi-criteria decision-making. Int J Intell Syst 34:3000–3019

    Article  Google Scholar 

  • Akram M, Peng X, Al-Kenani AN, Sattar A (2020) Prioritized weighted aggregation operators under complex Pythagorean fuzzy information. J Intell Fuzzy Syst 39(3):4763–4783

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ejegwa PA (2020) Distance and similarity measures for Pythagorean fuzzy sets. Granul Comput 5:225–238

  • Hwang CL, Yoon K (1981) Multiple attributes decision-making methods and applications. Springer, Berlin

    Book  Google Scholar 

  • Jana C (2021) Multiple attribute group decision-making method based on extended bipolar fuzzy MABAC approach. Comput Appl Math 40:1–17

    Article  MathSciNet  Google Scholar 

  • Jana C, Pal M (2018) Application of bipolar intuitionistic fuzzy soft sets in decision-making problem. Int J Fuzzy Syst Appl 7(3):32–55

    Google Scholar 

  • Jana C, Pal M (2019) A robust single valued neutrosophic soft aggregation operators in multi criteria decision-making. Symmetry 11(110):1–19

    Google Scholar 

  • Jana C, Pal M (2021) Multi criteria decision-making process based on some single valued neutrosophic Dombi power aggregation operators. Soft Comput 25(7):5055–5072

    Google Scholar 

  • Jana C, Senapati T, Pal M (2019a) Pythagorean fuzzy Dombi aggregation operators and its applications in multiple attribute decision-making. Int J Intell Syst 34(9):2019–2038

    Article  Google Scholar 

  • Jana C, Pal M, Wang J (2019b) A robust aggregation operator for multi criteria decision-making method with bipolar fuzzy soft environment. Iran J Fuzzy Syst 16(6):1–16

    MathSciNet  MATH  Google Scholar 

  • Jana C, Pal M, Karaaslan F, Wang JQ (2020) Trapezoidal neutrosophic aggregation operators and their application to the multi-attribute decision-making process. Sci Iran 27(3):1655–1673

    Google Scholar 

  • Jana C, Muhiuddin G, Pal M (2021) Multi criteria decision-making approach based on SVTrN Dombi aggregation functions. Artif Intell Rev 54(4):3685–3723

    Article  Google Scholar 

  • Jansi R, Mohana K, Smarandache F (2019) Correlation measure for Pythagorean neutrosophic sets with \(T\) and \(F\) as dependent neutrosophic components. Neutrosophic Sets Syst 30:202–212

    Google Scholar 

  • Khan MSA (2019) The Pythagorean fuzzy Einstein Choquet integral operators and their application in group decision making. Comput Appl Math 38(128):1–35

    MathSciNet  Google Scholar 

  • Liu P, Shahzadi G, Akram M (2020) Specific types of q-rung picture fuzzy Yager aggregation operators for decision-making. Int J Comput Intell Syst 13(1):1072–1091

    Article  Google Scholar 

  • Peng XD, Dai J (2018) Approaches to single-valued neutrosophic MADM based on MABAC, TOPSIS and new similarity measure with score function. Neural Comput Appl 29(10):939–954

    Article  Google Scholar 

  • Peng X, Yang Y (2016) Fundamental properties of interval valued Pythagorean fuzzy aggregation operators. Int J Intell Syst 31(5):444–487

    Article  Google Scholar 

  • Rahman K, Abdullah S, Shakeel M, Khan MSA, Ullah M (2017) Interval valued Pythagorean fuzzy geometric aggregation operators and their application to group decision-making problem. Cogent Math 4:1–19

    Article  MathSciNet  Google Scholar 

  • Rahman K, Ali A, Abdullah S, Amin F (2018) Approaches to multi attribute group decision-making based on induced interval valued Pythagorean fuzzy Einstein aggregation operator. New Math Nat Comput 14(3):343–361

    Article  MathSciNet  Google Scholar 

  • Senapati T, Chen G (2021) Some novel interval-valued Pythagorean fuzzy aggregation operator based on Hamacher triangular norms and their application in MADM issues. Comput Appl Math 40(4):1–27

    Article  MathSciNet  Google Scholar 

  • Senapati T, Yager RR (2019) Some new operations over Fermatean fuzzy numbers and application of Fermatean fuzzy WPM in multiple criteria decision making. Informatica 30(2):391–412

    Article  Google Scholar 

  • Senapati T, Yager RR, Chen G (2021) Cubic intuitionistic WASPAS technique and its application in multi-criteria decision-making. J Ambient Intell Humaniz Comput 12(9):8823–8833

    Article  Google Scholar 

  • Shahzadi G, Akram M, Saeid AB (2017) An application of single-valued neutrosophic sets in medical diagnosis. Neutrosophic Sets Syst 18:80–88

    Google Scholar 

  • Singh PK (2019) Single-valued neutrosophic context analysis at distinct multi-granulation. Comput Appl Math 38(2):1–18

    Article  MathSciNet  Google Scholar 

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

  • Ullah K, Mahmood T, Ali Z, Jan N (2019) On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition. Complex Intell Syst 6:1–13

    Google Scholar 

  • Xu RN, Li CL (2001) Regression prediction for fuzzy time series. Appl Math J Chin Univ 16:451–461

    MathSciNet  Google Scholar 

  • Yager RR (2014) Pythagorean membership grades in multi criteria decision-making. IEEE Trans Fuzzy Syst 22:958–965

    Article  Google Scholar 

  • Yang Z, Chang J (2020) Interval-valued Pythagorean normal fuzzy information aggregation operators for multiple attribute decision making approach. IEEE Access 8:51295–51314

    Article  Google Scholar 

  • Yang MS, Ko CH (1996) On a class of fuzzy c-numbers clustering procedures for fuzzy data. Fuzzy Sets Syst 84:49–60

    Article  MathSciNet  Google Scholar 

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

    Article  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

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Annamalai University, Chennai, Tamil Nadu, 608002, India

    M. Palanikumar

  2. Bharath Institute of Higher Education and Research, Chennai, 600073, India

    K. Arulmozhi

  3. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India

    Chiranjibe Jana

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  1. M. Palanikumar
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  2. K. Arulmozhi
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  3. Chiranjibe Jana
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Palanikumar, M., Arulmozhi, K. & Jana, C. Multiple attribute decision-making approach for Pythagorean neutrosophic normal interval-valued fuzzy aggregation operators. Comp. Appl. Math. 41, 90 (2022). https://doi.org/10.1007/s40314-022-01791-9

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