Skip to main content
main-content
Top

Hint

Swipe to navigate through the articles of this issue

24-05-2022 | Original Paper

Multiple attribute group decision-making based on generalized interval-valued Pythagorean fuzzy Einstein geometric aggregation operators

Author: Khaista Rahman

Published in: Granular Computing

Login to get access
share
SHARE

Abstract

The aim of the paper is to develop the notion of some generalized interval-valued Pythagorean fuzzy aggregation operators using Einstein operational laws. Interval-valued Pythagorean fuzzy information are the good way to express the fuzzy information for decision and Einstein operations are the best approximations, and the generalized aggregation operators are a generalization of most aggregation operators. Thus, the main contribution of our this paper is to introduce three generalized aggregation operators based on interval-valued Pythagorean fuzzy numbers such as, the generalized interval-valued Pythagorean fuzzy Einstein-weighted geometric (GIVPFEWG) operator, the generalized interval-valued Pythagorean fuzzy Einstein ordered weighted geometric (GIVPFEOWG) operator, and the generalized interval-valued Pythagorean fuzzy Einstein hybrid geometric (GIVPFEHG) operator. Some of their desirable properties namely monotonicity, boundedness and idempotency are developed. Moreover, these methods are used for the selection of an expert and professional manager for a medicine company; for this, the specialists and experts of the problems deliver their favorites to display the practicality, and value of the new presented and developing valuable work.
Literature
go back to reference Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96 CrossRef Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96 CrossRef
go back to reference Chen SM (1997) Interval-valued fuzzy hypergraph and fuzzy partition. IEEE Trans Syst Man Cybern Part b Cybern 27(4):725–733 CrossRef Chen SM (1997) Interval-valued fuzzy hypergraph and fuzzy partition. IEEE Trans Syst Man Cybern Part b Cybern 27(4):725–733 CrossRef
go back to reference Chen SM, Hsiao WH (2000) Bidirectional approximate reasoning for rule-based systems using interval-valued fuzzy sets. Fuzzy Sets Syst 113(2):185–203 MathSciNetCrossRef Chen SM, Hsiao WH (2000) Bidirectional approximate reasoning for rule-based systems using interval-valued fuzzy sets. Fuzzy Sets Syst 113(2):185–203 MathSciNetCrossRef
go back to reference Chen SM, Hsiao WH, Jong WT (1997) Bidirectional approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 91:339–353 MathSciNetCrossRef Chen SM, Hsiao WH, Jong WT (1997) Bidirectional approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 91:339–353 MathSciNetCrossRef
go back to reference Garg H (2016a) A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem. J Intell Fuzzy Syst 31(1):529–540 CrossRef Garg H (2016a) A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem. J Intell Fuzzy Syst 31(1):529–540 CrossRef
go back to reference Garg H (2016b) A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. Int J Intell Syst 31(9):886–920 CrossRef Garg H (2016b) A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. Int J Intell Syst 31(9):886–920 CrossRef
go back to reference Garg H (2016c) A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems. Appl Soft Comput 38:988–999 CrossRef Garg H (2016c) A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems. Appl Soft Comput 38:988–999 CrossRef
go back to reference Garg H (2016d) Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making. Comput Ind Eng 101:53–69 CrossRef Garg H (2016d) Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making. Comput Ind Eng 101:53–69 CrossRef
go back to reference Garg H (2017a) Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process. Int J Intell Syst 32(6):597–630 CrossRef Garg H (2017a) Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process. Int J Intell Syst 32(6):597–630 CrossRef
go back to reference Garg H (2017b) Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process. Comput Math Organ Theory 23(4):546–571 CrossRef Garg H (2017b) Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process. Comput Math Organ Theory 23(4):546–571 CrossRef
go back to reference Jamil M, Rahman K, Abdullah S, Khan MY (2020) The induced generalized interval-valued intuitionistic fuzzy Einstein hybrid geometric aggregation operator and their application to group decision-making. J Intell Fuzzy Syst 38(2):1737–1752 CrossRef Jamil M, Rahman K, Abdullah S, Khan MY (2020) The induced generalized interval-valued intuitionistic fuzzy Einstein hybrid geometric aggregation operator and their application to group decision-making. J Intell Fuzzy Syst 38(2):1737–1752 CrossRef
go back to reference Kumar K, Garg H (2016) H TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment. Comput Appl Math 37(2):1319–1329 MathSciNetCrossRef Kumar K, Garg H (2016) H TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment. Comput Appl Math 37(2):1319–1329 MathSciNetCrossRef
go back to reference Liu P, Liu J (2018a) Some q-rung orthopai fuzzy Bonferroni mean operators and their application to multi-attribute group decision making. Int J Intell Syst 33(2):315–347 CrossRef Liu P, Liu J (2018a) Some q-rung orthopai fuzzy Bonferroni mean operators and their application to multi-attribute group decision making. Int J Intell Syst 33(2):315–347 CrossRef
go back to reference Liu P, Wang P (2018b) Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. Int J Intell Syst 33(2):259–280 CrossRef Liu P, Wang P (2018b) Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. Int J Intell Syst 33(2):259–280 CrossRef
go back to reference Liu P, Wang P (2019a) Multiple-attribute decision making based on Archimedean Bonferroni operators of q-rung orthopair fuzzy numbers. IEEE Trans Fuzzy Syst 27(5):834–848 CrossRef Liu P, Wang P (2019a) Multiple-attribute decision making based on Archimedean Bonferroni operators of q-rung orthopair fuzzy numbers. IEEE Trans Fuzzy Syst 27(5):834–848 CrossRef
go back to reference Peng X, Yang Y (2015b) Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators. Int J Intell Syst 31(5):444–487 CrossRef Peng X, Yang Y (2015b) Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators. Int J Intell Syst 31(5):444–487 CrossRef
go back to reference Rahman K, Abdullah S (2019) Generalized interval-valued Pythagorean fuzzy aggregation operators and their application to group decision making. Granul Comput 4(1):15–25 CrossRef Rahman K, Abdullah S (2019) Generalized interval-valued Pythagorean fuzzy aggregation operators and their application to group decision making. Granul Comput 4(1):15–25 CrossRef
go back to reference Rahman K, Abdullah S, Husain F, Khan MSA (2016) Approaches to Pythagorean fuzzy geometric aggregation operators. Int J Comput Sci Inf Secur 14(9):174–200 Rahman K, Abdullah S, Husain F, Khan MSA (2016) Approaches to Pythagorean fuzzy geometric aggregation operators. Int J Comput Sci Inf Secur 14(9):174–200
go back to reference Rahman K, Khan MSA, Ullah M, Fahmi A (2017a) Multiple attribute group decision making for plant location selection with Pythagorean fuzzy weighted geometric aggregation operator. Nucleus 54(1):66–74 Rahman K, Khan MSA, Ullah M, Fahmi A (2017a) Multiple attribute group decision making for plant location selection with Pythagorean fuzzy weighted geometric aggregation operator. Nucleus 54(1):66–74
go back to reference Rahman K, Abdullah S, Hussain F, Khan MSA (2017b) Pythagorean fuzzy ordered weighted geometric aggregation operator and their application to multiple attribute group decision making. J Appl Environ Biol Sci 7(4):67–83 Rahman K, Abdullah S, Hussain F, Khan MSA (2017b) Pythagorean fuzzy ordered weighted geometric aggregation operator and their application to multiple attribute group decision making. J Appl Environ Biol Sci 7(4):67–83
go back to reference Rahman K, Abdullah S, Ahmed R, Ullah M (2017c) Pythagorean fuzzy Einstein weighted geometric aggregation operator and their application to multiple attribute group decision making. J Intell Fuzzy Syst 33(1):635–647 CrossRef Rahman K, Abdullah S, Ahmed R, Ullah M (2017c) Pythagorean fuzzy Einstein weighted geometric aggregation operator and their application to multiple attribute group decision making. J Intell Fuzzy Syst 33(1):635–647 CrossRef
go back to reference Rahman K, Ali A, Shakeel M, Khan MSA, Ullah M (2017d) Pythagorean fuzzy weighted averaging aggregation operator and its application to decision making theory. Nucleus 54(3):190–196 Rahman K, Ali A, Shakeel M, Khan MSA, Ullah M (2017d) Pythagorean fuzzy weighted averaging aggregation operator and its application to decision making theory. Nucleus 54(3):190–196
go back to reference Rahman K, Abdullah S, Shakeel M, Khan MSA, Ullah M (2017e) Interval-valued Pythagorean fuzzy geometric aggregation operators and their application to group decision making problem. Cogent Math 4:1338638 MathSciNetCrossRef Rahman K, Abdullah S, Shakeel M, Khan MSA, Ullah M (2017e) Interval-valued Pythagorean fuzzy geometric aggregation operators and their application to group decision making problem. Cogent Math 4:1338638 MathSciNetCrossRef
go back to reference Rahman K, Abdullah S, Jamil M, Khan MY (2018a) Some generalized intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute group decision making. Int J Fuzzy Syst 20(5):1567–1575 MathSciNetCrossRef Rahman K, Abdullah S, Jamil M, Khan MY (2018a) Some generalized intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute group decision making. Int J Fuzzy Syst 20(5):1567–1575 MathSciNetCrossRef
go back to reference Rahman K, Ali A, Khan MSA (2018b) Some interval-valued Pythagorean fuzzy weighted averaging aggregation operators and their application to multiple attribute decision making. Punjab Univ J Math 50(2):147–170 MathSciNet Rahman K, Ali A, Khan MSA (2018b) Some interval-valued Pythagorean fuzzy weighted averaging aggregation operators and their application to multiple attribute decision making. Punjab Univ J Math 50(2):147–170 MathSciNet
go back to reference Rahman K, Abdullah S, Khan MSA (2018c) Some interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operators and their application to group decision making. J Intell Syst 29(1):393–408 CrossRef Rahman K, Abdullah S, Khan MSA (2018c) Some interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operators and their application to group decision making. J Intell Syst 29(1):393–408 CrossRef
go back to reference Rahman K, Abdullah S, Ghani F (2019) Some new generalized interval-valued Pythagorean fuzzy aggregation operators using Einstein t-norm and t-conorm. J Intell Fuzzy Syst 37(3):3721–3742 CrossRef Rahman K, Abdullah S, Ghani F (2019) Some new generalized interval-valued Pythagorean fuzzy aggregation operators using Einstein t-norm and t-conorm. J Intell Fuzzy Syst 37(3):3721–3742 CrossRef
go back to reference Su Z, Xia GP, Chen MY (2011) Some induced intuitionistic fuzzy aggregation operators applied to multi-attribute group decision making. Int J Gen Syst 40(8):805–835 MathSciNetCrossRef Su Z, Xia GP, Chen MY (2011) Some induced intuitionistic fuzzy aggregation operators applied to multi-attribute group decision making. Int J Gen Syst 40(8):805–835 MathSciNetCrossRef
go back to reference Wang Z, Li KW, Wang W (2009) An approach to multi attribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights. Inf Sci 179:3026–3040 CrossRef Wang Z, Li KW, Wang W (2009) An approach to multi attribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights. Inf Sci 179:3026–3040 CrossRef
go back to reference Xu ZS, Jain C (2007) Approach to group decision making based on interval-valued intuitionistic Judgment matrices. Syst Eng Theory Pract 27(4):126–133 CrossRef Xu ZS, Jain C (2007) Approach to group decision making based on interval-valued intuitionistic Judgment matrices. Syst Eng Theory Pract 27(4):126–133 CrossRef
go back to reference Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965 CrossRef Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965 CrossRef
go back to reference Yager RR, Abbasov MA (2013a) Pythagorean membership grades, complex numbers and decision making. Int J Intell Syst 28(5):436–452 CrossRef Yager RR, Abbasov MA (2013a) Pythagorean membership grades, complex numbers and decision making. Int J Intell Syst 28(5):436–452 CrossRef
go back to reference Yager RR (2013b) Pythagorean fuzzy subsets. In: Proceeding joint IFSA world congress and NAFIPS annual meeting, Edmonton, pp 57–61 Yager RR (2013b) Pythagorean fuzzy subsets. In: Proceeding joint IFSA world congress and NAFIPS annual meeting, Edmonton, pp 57–61
go back to reference Zeng XL, Xu ZS (2014) Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29:1061–1078 CrossRef Zeng XL, Xu ZS (2014) Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29:1061–1078 CrossRef
go back to reference Zhang X (2016) Multicriteria Pythagorean fuzzy decision analysis: a hierarchical QUALIFLEX approach with the closeness index-based ranking. Inf Sci 330:104–124 CrossRef Zhang X (2016) Multicriteria Pythagorean fuzzy decision analysis: a hierarchical QUALIFLEX approach with the closeness index-based ranking. Inf Sci 330:104–124 CrossRef
Metadata
Title
Multiple attribute group decision-making based on generalized interval-valued Pythagorean fuzzy Einstein geometric aggregation operators
Author
Khaista Rahman
Publication date
24-05-2022
Publisher
Springer International Publishing
Published in
Granular Computing
Print ISSN: 2364-4966
Electronic ISSN: 2364-4974
DOI
https://doi.org/10.1007/s41066-022-00322-5

Premium Partner