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Erschienen in: Artificial Intelligence Review 6/2021

26.04.2021

Sine trigonometric operational laws and its based Pythagorean fuzzy aggregation operators for group decision-making process

verfasst von: Harish Garg

Erschienen in: Artificial Intelligence Review | Ausgabe 6/2021

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Abstract

The paper aims are to impersonate some robust sine-trigonometric operations laws to determine the group decision-making process under the Pythagorean fuzzy set (PFS) situation. The PFS has a notable feature to trade with the dubious information with a broader membership representation space than the intuitionistic fuzzy set. Based on it, the present paper is classified into three phases. The first phase is to introduce new operational laws for PFS. The main idea behind these proposed operations is to incorporate the qualities of the sine function, namely periodicity and symmetric about the origin towards the decisions of the objects. Secondly, based on these laws, numerous operators to aggregate the information are acquired along with their requisite properties and relations. Finally, an algorithm to interpret the multiattribute group decision making problem is outlined based on the stated operators and manifest it with an illustrative example. A detailed comparative interpretation is achieved with some of the existing methods to reveal their influences.

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Literatur
Zurück zum Zitat Akram M, Ilyas F, Garg H (2020) Multi-criteria group decision making based on ELECTRE I method in Pythagorean fuzzy information. Soft Comput 24(5):3425–3453CrossRef Akram M, Ilyas F, Garg H (2020) Multi-criteria group decision making based on ELECTRE I method in Pythagorean fuzzy information. Soft Comput 24(5):3425–3453CrossRef
Zurück zum Zitat Bustince H, Barrenechea E, Pagola M, Fernandez J, Xu Z, Bedregal B, Montero J, Hagras H, Herrera F, De Baets B (2016) A historical account of types of fuzzy sets and their relationships. IEEE Trans Fuzzy Syst 24(1):179–194CrossRef Bustince H, Barrenechea E, Pagola M, Fernandez J, Xu Z, Bedregal B, Montero J, Hagras H, Herrera F, De Baets B (2016) A historical account of types of fuzzy sets and their relationships. IEEE Trans Fuzzy Syst 24(1):179–194CrossRef
Zurück zum Zitat Chen T-Y (2019) Multiple criteria decision analysis under complex uncertainty: A pearson-like correlation-based Pythagorean fuzzy compromise approach. Int J Intell Syst 34(1):114–151CrossRef Chen T-Y (2019) Multiple criteria decision analysis under complex uncertainty: A pearson-like correlation-based Pythagorean fuzzy compromise approach. Int J Intell Syst 34(1):114–151CrossRef
Zurück zum Zitat Gao H (2018) Pythagorean fuzzy Hamacher prioritized aggregation operators in multiple attribute decision making. J Intell Fuzzy Syst 35(2):2229–2245CrossRef Gao H (2018) Pythagorean fuzzy Hamacher prioritized aggregation operators in multiple attribute decision making. J Intell Fuzzy Syst 35(2):2229–2245CrossRef
Zurück zum Zitat Gao H, Lu M, Wei G, Wei Y (2018) Some novel Pythagorean fuzzy interaction aggregation operators in multiple attribute decision making. Fundamenta Informaticae 159(4):385–428MathSciNetMATHCrossRef Gao H, Lu M, Wei G, Wei Y (2018) Some novel Pythagorean fuzzy interaction aggregation operators in multiple attribute decision making. Fundamenta Informaticae 159(4):385–428MathSciNetMATHCrossRef
Zurück zum Zitat Garg H (2016) A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. Int J Intell Syst 31(9):886–920CrossRef Garg H (2016) A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. Int J Intell Syst 31(9):886–920CrossRef
Zurück zum Zitat Garg H (2017) Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application. Eng Appl Artif Intell 60:164–174CrossRef Garg H (2017) Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application. Eng Appl Artif Intell 60:164–174CrossRef
Zurück zum Zitat Garg H (2017) Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process. Int J Intell Syst 32(6):597–630CrossRef Garg H (2017) Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process. Int J Intell Syst 32(6):597–630CrossRef
Zurück zum Zitat Garg H (2018) Generalized Pythagorean fuzzy geometric interactive aggregation operators using Einstein operations and their application to decision making. J Exp Theor Artif Intell 30(6):763–794CrossRef Garg H (2018) Generalized Pythagorean fuzzy geometric interactive aggregation operators using Einstein operations and their application to decision making. J Exp Theor Artif Intell 30(6):763–794CrossRef
Zurück zum Zitat Garg H (2018) New exponential operational laws and their aggregation operators for interval-valued Pythagorean fuzzy multicriteria decision - making. Int J Intell Syst 33(3):653–683CrossRef Garg H (2018) New exponential operational laws and their aggregation operators for interval-valued Pythagorean fuzzy multicriteria decision - making. Int J Intell Syst 33(3):653–683CrossRef
Zurück zum Zitat Garg H (2019) Novel neutrality operation-based Pythagorean fuzzy geometric aggregation operators for multiple attribute group decision analysis. Int J Intell Syst 34(10):2459–2489CrossRef Garg H (2019) Novel neutrality operation-based Pythagorean fuzzy geometric aggregation operators for multiple attribute group decision analysis. Int J Intell Syst 34(10):2459–2489CrossRef
Zurück zum Zitat Garg H (2019) New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications. Int J Intell Syst 34(1):82–106CrossRef Garg H (2019) New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications. Int J Intell Syst 34(1):82–106CrossRef
Zurück zum Zitat Garg H (2020) Neutrality operations-based Pythagorean fuzzy aggregation operators and its applications to multiple attribute group decision-making process. J Ambient Intell Humaniz Comput 11(7):3021–3041CrossRef Garg H (2020) Neutrality operations-based Pythagorean fuzzy aggregation operators and its applications to multiple attribute group decision-making process. J Ambient Intell Humaniz Comput 11(7):3021–3041CrossRef
Zurück zum Zitat Garg H (2020) Linguistic interval-valued Pythagorean fuzzy sets and their application to multiple attribute group decision-making process. Cogn Comput 12(6):1313–1337CrossRef Garg H (2020) Linguistic interval-valued Pythagorean fuzzy sets and their application to multiple attribute group decision-making process. Cogn Comput 12(6):1313–1337CrossRef
Zurück zum Zitat Garg H, Kumar K (2019) Linguistic interval-valued Atanassov intuitionistic fuzzy sets and their applications to group decision-making problems. IEEE Trans Fuzzy Syst 27(12):2302–2311CrossRef Garg H, Kumar K (2019) Linguistic interval-valued Atanassov intuitionistic fuzzy sets and their applications to group decision-making problems. IEEE Trans Fuzzy Syst 27(12):2302–2311CrossRef
Zurück zum Zitat Garg H, Kumar K (2020) A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory. Artif Intell Rev 53(1):595–624CrossRef Garg H, Kumar K (2020) A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory. Artif Intell Rev 53(1):595–624CrossRef
Zurück zum Zitat Gou XJ, Xu ZS (2017) Exponential operations for intuitionistic fuzzy numbers and interval numbers in multi-attribute decision making. Fuzzy Optim Decis Making 16(2):183–204MathSciNetMATHCrossRef Gou XJ, Xu ZS (2017) Exponential operations for intuitionistic fuzzy numbers and interval numbers in multi-attribute decision making. Fuzzy Optim Decis Making 16(2):183–204MathSciNetMATHCrossRef
Zurück zum Zitat Gou XJ, Xu ZS, Lei Q (2016) New operational laws and aggregation method of intuitionistic fuzzy information. J Intell Fuzzy Syst 30:129–141MATHCrossRef Gou XJ, Xu ZS, Lei Q (2016) New operational laws and aggregation method of intuitionistic fuzzy information. J Intell Fuzzy Syst 30:129–141MATHCrossRef
Zurück zum Zitat Herrera F, Herrera VE (1997) Aggregation operators for linguistic weighted information. IEEE Trans Syst Man Cybern- A: Syst Hum 27(5):646–656CrossRef Herrera F, Herrera VE (1997) Aggregation operators for linguistic weighted information. IEEE Trans Syst Man Cybern- A: Syst Hum 27(5):646–656CrossRef
Zurück zum Zitat Huang JY (2014) Intuitionistic fuzzy Hamacher aggregation operator and their application to multiple attribute decision making. J Intell and Fuzzy Syst 27:505–513MathSciNetMATHCrossRef Huang JY (2014) Intuitionistic fuzzy Hamacher aggregation operator and their application to multiple attribute decision making. J Intell and Fuzzy Syst 27:505–513MathSciNetMATHCrossRef
Zurück zum Zitat Hwang C-M, Yang M-S, Hung W-L (2018) New similarity measures of intuitionistic fuzzy sets based on the Jaccard index with its application to clustering. Int J Intell Syst 33(8):1672–1688CrossRef Hwang C-M, Yang M-S, Hung W-L (2018) New similarity measures of intuitionistic fuzzy sets based on the Jaccard index with its application to clustering. Int J Intell Syst 33(8):1672–1688CrossRef
Zurück zum Zitat Kumar K, Garg H (2018) TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment. Comput Appl Math 37(2):1319–1329MathSciNetMATHCrossRef Kumar K, Garg H (2018) TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment. Comput Appl Math 37(2):1319–1329MathSciNetMATHCrossRef
Zurück zum Zitat Li D, Zeng W, Yin Q (2017) Distance measures of Pythagorean fuzzy sets and their applications in multiattribute decision making. Control Decis 32(10):1817–1823MATH Li D, Zeng W, Yin Q (2017) Distance measures of Pythagorean fuzzy sets and their applications in multiattribute decision making. Control Decis 32(10):1817–1823MATH
Zurück zum Zitat Ma ZM, Xu ZS (2016) Symmetric Pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems. Int J Intell Syst 31(12):1198–1219CrossRef Ma ZM, Xu ZS (2016) Symmetric Pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems. Int J Intell Syst 31(12):1198–1219CrossRef
Zurück zum Zitat Nie R-X, Tian Z-P, Wang J-Q, Hu J-H (2019) Pythagorean fuzzy multiple criteria decision analysis based on shapley fuzzy measures and partitioned normalized weighted bonferroni mean operator. Int J Intell Syst 34(2):297–324CrossRef Nie R-X, Tian Z-P, Wang J-Q, Hu J-H (2019) Pythagorean fuzzy multiple criteria decision analysis based on shapley fuzzy measures and partitioned normalized weighted bonferroni mean operator. Int J Intell Syst 34(2):297–324CrossRef
Zurück zum Zitat Peng X, Garg H (2019) Multiparametric similarity measures on Pythagorean fuzzy sets with applications to pattern recognition. Appl Intell 49(12):4058–4096CrossRef Peng X, Garg H (2019) Multiparametric similarity measures on Pythagorean fuzzy sets with applications to pattern recognition. Appl Intell 49(12):4058–4096CrossRef
Zurück zum Zitat Qin J, Liu X (2014) An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators. J Intell Fuzzy Syst 27(5):2177–2190MathSciNetMATHCrossRef Qin J, Liu X (2014) An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators. J Intell Fuzzy Syst 27(5):2177–2190MathSciNetMATHCrossRef
Zurück zum Zitat Wei GW, Lu M (2018) Pythagorean fuzzy power aggregation operators in multiple attribute decision maig. Int J Intell Syst 33(1):169–186CrossRef Wei GW, Lu M (2018) Pythagorean fuzzy power aggregation operators in multiple attribute decision maig. Int J Intell Syst 33(1):169–186CrossRef
Zurück zum Zitat Wei G, Wei Y (2018) Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications. Int J Intell Syst 33(3):634–652CrossRef Wei G, Wei Y (2018) Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications. Int J Intell Syst 33(3):634–652CrossRef
Zurück zum Zitat Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187CrossRef Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187CrossRef
Zurück zum Zitat Xu Z, Yager RR (2011) Intuitionistic fuzzy bonferroni means. IEEE Trans Syst Man Cybern B Cybern 41(2):568–578CrossRef Xu Z, Yager RR (2011) Intuitionistic fuzzy bonferroni means. IEEE Trans Syst Man Cybern B Cybern 41(2):568–578CrossRef
Zurück zum Zitat Yager RR (2013) Pythagorean fuzzy subsets. In: Proceedings Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, pp 57–61 Yager RR (2013) Pythagorean fuzzy subsets. In: Proceedings Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, pp 57–61
Zurück zum Zitat Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965CrossRef Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965CrossRef
Zurück zum Zitat Yager RR, Abbasov AM (2013) Pythagorean membeship grades, complex numbers and decision making. Int J Intell Syst 28:436–452CrossRef Yager RR, Abbasov AM (2013) Pythagorean membeship grades, complex numbers and decision making. Int J Intell Syst 28:436–452CrossRef
Zurück zum Zitat Zeng S, Chen J, Li X (2016) A hybrid method for Pythagorean fuzzy multiple-criteria decision making. Int J Inf Technol Decis Making 15(2):403–422CrossRef Zeng S, Chen J, Li X (2016) A hybrid method for Pythagorean fuzzy multiple-criteria decision making. Int J Inf Technol Decis Making 15(2):403–422CrossRef
Zurück zum Zitat Zhang XL (2016) A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. Int J Intell Syst 31:593–611CrossRef Zhang XL (2016) A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. Int J Intell Syst 31:593–611CrossRef
Zurück zum Zitat Zhang XL, Xu ZS (2014) Extension of TOPSIS to multi-criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29(12):1061–1078CrossRef Zhang XL, Xu ZS (2014) Extension of TOPSIS to multi-criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29(12):1061–1078CrossRef
Metadaten
Titel
Sine trigonometric operational laws and its based Pythagorean fuzzy aggregation operators for group decision-making process
verfasst von
Harish Garg
Publikationsdatum
26.04.2021
Verlag
Springer Netherlands
Erschienen in
Artificial Intelligence Review / Ausgabe 6/2021
Print ISSN: 0269-2821
Elektronische ISSN: 1573-7462
DOI
https://doi.org/10.1007/s10462-021-10002-6

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