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Published in: Granular Computing 2/2023

23-05-2022 | Original Paper

Interval neutrosophic matrix game-based approach to counter cybersecurity issue

Authors: Mijanur Rahaman Seikh, Shibaji Dutta

Published in: Granular Computing | Issue 2/2023

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Abstract

Everyone on this planet is now more reliant on information and communication technology. Cybersecurity does the protection from theft and damage of all categories of data that require to be retained top secret. Cybersecurity-related problems that are predicted on lingual data have become the center of attention for researchers in modern times. It is possible to design these uncertain problems by matrix game, where the respective attacker and defender are possibly interpreted as players. Interval-valued neutrosophic numbers (IVNNs) are used as an excellent tool to counter such uncertain circumstances in respect of fuzzy sets/intuitionistic fuzzy sets or ordinary intervals. IVNN addresses topics with a set of interval numbers in the real unit interval. In this paper, cybersecurity-related issues are explored using matrix game, where the respective payoffs are considered as IVNNs. A nonlinear programming approach is presented by constructing two interval-valued multi-objective problems for the players. Then, the subsequent problems are transferred into a pair of auxiliary nonlinear programming models. The weighted average approach is used to solve the reduced problems. A numerical example of the cybersecurity problem in the banking sector is illustrated to show the applicability of the proposed approach. A comparison analysis is performed with existing work to authenticate the feasibility of the proposed approach.

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Literature
go back to reference Atanassov KT (1999) Intuitionistic fuzzy sets: Theory and applications. Physica-Verlag, HeidelbergMATHCrossRef Atanassov KT (1999) Intuitionistic fuzzy sets: Theory and applications. Physica-Verlag, HeidelbergMATHCrossRef
go back to reference Attiah A, Chatterjee M, Zou CC (2018) A game theoretic approach to model cyber attack and defense strategies. IEEE Int Conf Commun 2018:1–7 Attiah A, Chatterjee M, Zou CC (2018) A game theoretic approach to model cyber attack and defense strategies. IEEE Int Conf Commun 2018:1–7
go back to reference Bector CR, Chandra S (2005) Fuzzy mathematical programming and fuzzy matrix games. Berlin: Springer 169 Bector CR, Chandra S (2005) Fuzzy mathematical programming and fuzzy matrix games. Berlin: Springer 169
go back to reference Bhaumik A, Roy SK (2021) Intuitionistic interval-valued hesitant fuzzy matrix games with a new aggregation operator for solving management problem. Granul Comput 6(2):359–375CrossRef Bhaumik A, Roy SK (2021) Intuitionistic interval-valued hesitant fuzzy matrix games with a new aggregation operator for solving management problem. Granul Comput 6(2):359–375CrossRef
go back to reference Bigdeli H, Hassanpour H, Tayyebi J (2019) Multiobjective security game with fuzzy payoffs. Iran J Fuzzy Syst 16(1):89–101MathSciNetMATH Bigdeli H, Hassanpour H, Tayyebi J (2019) Multiobjective security game with fuzzy payoffs. Iran J Fuzzy Syst 16(1):89–101MathSciNetMATH
go back to reference Brikaa MG, Zheng Z, Ammar ES (2021a) Mehar approach for solving matrix games with triangular dual hesitant fuzzy payoffs. Granul Comput 1-20 Brikaa MG, Zheng Z, Ammar ES (2021a) Mehar approach for solving matrix games with triangular dual hesitant fuzzy payoffs. Granul Comput 1-20
go back to reference Brikaa MG, Zheng Z, Ammar ES (2021b) Rough set approach to non-cooperative continuous differential games. Granul Comput 6:149–162CrossRef Brikaa MG, Zheng Z, Ammar ES (2021b) Rough set approach to non-cooperative continuous differential games. Granul Comput 6:149–162CrossRef
go back to reference Broumi S, Bakali A, Talea M, Smarandache F, Ulucay V, Sahin M, Dey A, Dhar M, Tan RP, Bahnasse A, Pramanik S (2018) Neutrosophic sets: an overview. New Trends Neutrosophic Theory Appl 2:403–434 Broumi S, Bakali A, Talea M, Smarandache F, Ulucay V, Sahin M, Dey A, Dhar M, Tan RP, Bahnasse A, Pramanik S (2018) Neutrosophic sets: an overview. New Trends Neutrosophic Theory Appl 2:403–434
go back to reference Chen SM (1997) Interval-valued fuzzy hypergraph and fuzzy partition. IEEE Trans Syst Man Cybern B Cybern 27(4):725–733CrossRef Chen SM (1997) Interval-valued fuzzy hypergraph and fuzzy partition. IEEE Trans Syst Man Cybern B Cybern 27(4):725–733CrossRef
go back to reference Chen SM, Hsiao WH, Jong WT (1997) Bidirectional approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 91(3):339–353MATHCrossRef Chen SM, Hsiao WH, Jong WT (1997) Bidirectional approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 91(3):339–353MATHCrossRef
go back to reference Chen SM, Hsiao WH, Jong WT (1997) Bidirectional approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 91(3):339–353MathSciNetMATHCrossRef Chen SM, Hsiao WH, Jong WT (1997) Bidirectional approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 91(3):339–353MathSciNetMATHCrossRef
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):185–203MathSciNetMATHCrossRef Chen SM, Hsiao WH (2000) Bidirectional approximate reasoning for rule-based systems using interval-valued fuzzy sets. Fuzzy Sets Syst 113(2):185–203MathSciNetMATHCrossRef
go back to reference Hyder B, Govindarasu M (2020) Optimization of cybersecurity investment strategies in the smart grid using game-theory. IEEE Power Energy Soc Innov Smart Grid Technol Conf 2020:1–5 Hyder B, Govindarasu M (2020) Optimization of cybersecurity investment strategies in the smart grid using game-theory. IEEE Power Energy Soc Innov Smart Grid Technol Conf 2020:1–5
go back to reference Ishibuchi H, Tanaka H (1990) Multiobjective programming in optimization of the interval objective function. Eur J Oper Res 48(2):219–225MATHCrossRef Ishibuchi H, Tanaka H (1990) Multiobjective programming in optimization of the interval objective function. Eur J Oper Res 48(2):219–225MATHCrossRef
go back to reference Jahan F, Sun W, Niyaz Q (2020) A non-cooperative game based model for the cybersecurity of autonomous systems. IEEE Secur Priv 2020:202–207 Jahan F, Sun W, Niyaz Q (2020) A non-cooperative game based model for the cybersecurity of autonomous systems. IEEE Secur Priv 2020:202–207
go back to reference Khan I, Mehra A (2020) A novel equilibrium solution concept for intuitionistic fuzzy bi-matrix games considering proportion mix of possibility and necessity expectations. Granul Comput 5:461–483CrossRef Khan I, Mehra A (2020) A novel equilibrium solution concept for intuitionistic fuzzy bi-matrix games considering proportion mix of possibility and necessity expectations. Granul Comput 5:461–483CrossRef
go back to reference Li DF, Nan JX (2014) An interval-valued programming approach to matrix games with payoffs of triangular intuitionistic fuzzy numbers. Iran J Fuzzy Syst 11(2):45–57MathSciNetMATH Li DF, Nan JX (2014) An interval-valued programming approach to matrix games with payoffs of triangular intuitionistic fuzzy numbers. Iran J Fuzzy Syst 11(2):45–57MathSciNetMATH
go back to reference Li DF, Liu JC (2014) A parameterized nonlinear programming approach to solve matrix games with payoffs of I-fuzzy numbers. IEEE Trans Fuzzy Syst 23(4):885–896CrossRef Li DF, Liu JC (2014) A parameterized nonlinear programming approach to solve matrix games with payoffs of I-fuzzy numbers. IEEE Trans Fuzzy Syst 23(4):885–896CrossRef
go back to reference Li DF (2010) Mathematical-programming approach to matrix games with payoffs represented by Atanassov’s interval-valued intuitionistic fuzzy sets. IEEE Trans Fuzzy Syst 18(6):1112–1128CrossRef Li DF (2010) Mathematical-programming approach to matrix games with payoffs represented by Atanassov’s interval-valued intuitionistic fuzzy sets. IEEE Trans Fuzzy Syst 18(6):1112–1128CrossRef
go back to reference Liu J, Chen Z, Chen Y, Li C (2021) Multiattribute group decision making based on interval-valued neutrosophic N-soft sets. Granul Comput 6(4):1009–1023CrossRef Liu J, Chen Z, Chen Y, Li C (2021) Multiattribute group decision making based on interval-valued neutrosophic N-soft sets. Granul Comput 6(4):1009–1023CrossRef
go back to reference Naqvi D, Aggarwal A, Sachdev G, Khan I (2021) Solving I-fuzzy two person zero-sum matrix games: Tanaka and Asai approach. Granul Comput 6(2):399–409CrossRef Naqvi D, Aggarwal A, Sachdev G, Khan I (2021) Solving I-fuzzy two person zero-sum matrix games: Tanaka and Asai approach. Granul Comput 6(2):399–409CrossRef
go back to reference Nikmehr N, Moghadam SM (2019) Game-theoretic cybersecurity analysis for false data injection attack on networked microgrids. IET Cyber-Phys Syst 4(4):365–373CrossRef Nikmehr N, Moghadam SM (2019) Game-theoretic cybersecurity analysis for false data injection attack on networked microgrids. IET Cyber-Phys Syst 4(4):365–373CrossRef
go back to reference Owen G (1982) Game theory. Academic Press, New York, p 2 Owen G (1982) Game theory. Academic Press, New York, p 2
go back to reference Seikh MR, Karmakar S, Xia M (2020) Solving matrix games with hesitant fuzzy pay-offs. Iran J Fuzzy Syst 17(4):25–40MathSciNetMATH Seikh MR, Karmakar S, Xia M (2020) Solving matrix games with hesitant fuzzy pay-offs. Iran J Fuzzy Syst 17(4):25–40MathSciNetMATH
go back to reference Seikh MR, Karmakar S, Nayak PK (2021) Matrix games with dense fuzzy payoffs. Int J Intell Syst 36(4):1770–1799CrossRef Seikh MR, Karmakar S, Nayak PK (2021) Matrix games with dense fuzzy payoffs. Int J Intell Syst 36(4):1770–1799CrossRef
go back to reference Seikh MR, Dutta S (2021) A nonlinear programming model to solve matrix games with pay-offs of single-valued neutrosophic numbers. Neutrosophic Sets Syst 47:366–383 Seikh MR, Dutta S (2021) A nonlinear programming model to solve matrix games with pay-offs of single-valued neutrosophic numbers. Neutrosophic Sets Syst 47:366–383
go back to reference Seikh MR, Karmakar S, Castillo O (2021) A novel defuzzification approach of type-2 fuzzy variable to solving matrix games: An application to plastic ban problem. Iran J Fuzzy Syst 18(5):155–172MathSciNetMATH Seikh MR, Karmakar S, Castillo O (2021) A novel defuzzification approach of type-2 fuzzy variable to solving matrix games: An application to plastic ban problem. Iran J Fuzzy Syst 18(5):155–172MathSciNetMATH
go back to reference Seikh MR, Dutta S, Li DF (2021a) Solution of matrix games with rough interval pay-offs and its application in the telecom market share problem. Int J Intell Syst 36(10):6066–6100CrossRef Seikh MR, Dutta S, Li DF (2021a) Solution of matrix games with rough interval pay-offs and its application in the telecom market share problem. Int J Intell Syst 36(10):6066–6100CrossRef
go back to reference Seikh MR, Dutta S (2021b) Solution of interval-valued matrix games using intuitionistic fuzzy optimisation technique: an effective approach. Int J Math Oper 20(3):297–322MathSciNetMATHCrossRef Seikh MR, Dutta S (2021b) Solution of interval-valued matrix games using intuitionistic fuzzy optimisation technique: an effective approach. Int J Math Oper 20(3):297–322MathSciNetMATHCrossRef
go back to reference Seikh MR, Karmakar S, Castillo O (2021c) A novel defuzzification approach of type-2 fuzzy variable to solving matrix games: An application to plastic ban problem. Iran J Fuzzy Syst 18(5):155–172MATH Seikh MR, Karmakar S, Castillo O (2021c) A novel defuzzification approach of type-2 fuzzy variable to solving matrix games: An application to plastic ban problem. Iran J Fuzzy Syst 18(5):155–172MATH
go back to reference Seikh MR, Dutta S, Li DF (2021d) Solution of matrix games with rough interval pay-offs and its application in the telecom market share problem. Int J Intell Syst 36(10):6066–6100CrossRef Seikh MR, Dutta S, Li DF (2021d) Solution of matrix games with rough interval pay-offs and its application in the telecom market share problem. Int J Intell Syst 36(10):6066–6100CrossRef
go back to reference Seikh MR, Dutta S (2022) Solution of matrix games with payoffs of single-valued trapezoidal neutrosophic numbers. Soft Comput 26:921–936CrossRef Seikh MR, Dutta S (2022) Solution of matrix games with payoffs of single-valued trapezoidal neutrosophic numbers. Soft Comput 26:921–936CrossRef
go back to reference Smarandache F (1998) A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic. Rehoboth: American Research Press Smarandache F (1998) A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic. Rehoboth: American Research Press
go back to reference Sodenkamp MA, Tavana M, Di Caprio D (2018) An aggregation method for solving group multi-criteria decision-making problems with single-valued neutrosophic sets. Appl Soft Comput 71:715–727CrossRef Sodenkamp MA, Tavana M, Di Caprio D (2018) An aggregation method for solving group multi-criteria decision-making problems with single-valued neutrosophic sets. Appl Soft Comput 71:715–727CrossRef
go back to reference Verma T, Kumar A (2017) Ambika methods for solving matrix games with Atanassov’s intuitionistic fuzzy payoffs. IEEE Trans Fuzzy Syst 26(1):270–283CrossRef Verma T, Kumar A (2017) Ambika methods for solving matrix games with Atanassov’s intuitionistic fuzzy payoffs. IEEE Trans Fuzzy Syst 26(1):270–283CrossRef
go back to reference Verma T, Kumar A (2020) Matrix games with fuzzy payoffs, In Fuzzy solution concepts for non-cooperative games. Stud Fuzziness Soft Comput 383:37–63CrossRef Verma T, Kumar A (2020) Matrix games with fuzzy payoffs, In Fuzzy solution concepts for non-cooperative games. Stud Fuzziness Soft Comput 383:37–63CrossRef
go back to reference Wang H, Smarandache F, Sunderraman R, Zhang YQ (2005) Interval neutrosophic sets and logic: Theory and applications in computing. Hexis, Phoenix, Ariz, USA, Infinite Study, p 5MATH Wang H, Smarandache F, Sunderraman R, Zhang YQ (2005) Interval neutrosophic sets and logic: Theory and applications in computing. Hexis, Phoenix, Ariz, USA, Infinite Study, p 5MATH
go back to reference Wang H, Smarandache F, Zhang YQ, Sunderraman R (2010) Single valued neutrosophic sets. Multispace Multistruct 4:410–413 Wang H, Smarandache F, Zhang YQ, Sunderraman R (2010) Single valued neutrosophic sets. Multispace Multistruct 4:410–413
go back to reference Xia M (2018) Interval-valued intuitionistic fuzzy matrix games based on Archimedean t-conorm and t-norm. Int J Gen Syst 47(3):278–293MathSciNetCrossRef Xia M (2018) Interval-valued intuitionistic fuzzy matrix games based on Archimedean t-conorm and t-norm. Int J Gen Syst 47(3):278–293MathSciNetCrossRef
go back to reference Xue W, Xu Z, Zeng XJ (2021) Solving matrix games based on Ambika method with hesitant fuzzy information and its application in the counter-terrorism issue. Appl Intell 51(3):1227–1243CrossRef Xue W, Xu Z, Zeng XJ (2021) Solving matrix games based on Ambika method with hesitant fuzzy information and its application in the counter-terrorism issue. Appl Intell 51(3):1227–1243CrossRef
go back to reference Yang J, Xu Z, Dai Y (2021) Simple noncooperative games with intuitionistic fuzzy information and application in ecological management. Appl Intell 51:6685–6697CrossRef Yang J, Xu Z, Dai Y (2021) Simple noncooperative games with intuitionistic fuzzy information and application in ecological management. Appl Intell 51:6685–6697CrossRef
go back to reference Zarreh A, Saygin C, Wan H, Lee Y, Bracho A (2018) Cybersecurity analysis of smart manufacturing system using game theory approach and quantal response equilibrium. Procedia Manuf 17:1001–1008CrossRef Zarreh A, Saygin C, Wan H, Lee Y, Bracho A (2018) Cybersecurity analysis of smart manufacturing system using game theory approach and quantal response equilibrium. Procedia Manuf 17:1001–1008CrossRef
go back to reference Zarreh A, Saygin C, Wan H, Lee Y, Bracho A (2018) A game theory based cybersecurity assessment model for advanced manufacturing systems. Procedia Manuf 26:1255–1264CrossRef Zarreh A, Saygin C, Wan H, Lee Y, Bracho A (2018) A game theory based cybersecurity assessment model for advanced manufacturing systems. Procedia Manuf 26:1255–1264CrossRef
go back to reference Ze-Shui X (2007) Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. J Control Decis 22(2):215–219 Ze-Shui X (2007) Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. J Control Decis 22(2):215–219
Metadata
Title
Interval neutrosophic matrix game-based approach to counter cybersecurity issue
Authors
Mijanur Rahaman Seikh
Shibaji Dutta
Publication date
23-05-2022
Publisher
Springer International Publishing
Published in
Granular Computing / Issue 2/2023
Print ISSN: 2364-4966
Electronic ISSN: 2364-4974
DOI
https://doi.org/10.1007/s41066-022-00327-0

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