Abstract
In this chapter, we present a novel strategy for solving linear programming (LP) problem under Pythagorean fuzzy (PF) and its application in Diet issue. LP is a part of optimization system which manages linear quantities, i.e., either constraints of linear equation type or inequalities type. In any case, when we consider the pragmatic circumstance, some of the data is unclear for the manager. At this point, LP will be unable to handle satisfactory results for decision-makers. Therefore, PF framework is one of the most proficient ways to deal with managing vulnerability and inadequate information. Maintaining this advantage, in this part we depict the PF arithmetic and scientific computation in PF condition. This proposed technique depends on score function and convert to its proportional crisp LP (CrLP) problem. To legitimize the proposed technique, some numerical tests are given to show the adequacy of the new model. Finally, some conclusion and future works are discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Bellman R, Zadeh LA (1970) Decision making in fuzzy environment. Manag Sci 17(B):141–164
Das S, Mandal T, Edalatpanah SA (2017) A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers. Appl Intell 46:509–517
Das S, Mandal T, Behera D (2019) A new approach for solving fully fuzzy linear programming problem. Int J Math Oper Res 15:296–309
Das S (2017) Modified method for solving fully fuzzy linear programming problem with triangular fuzzy numbers. Int J Res Indus Eng 6:293–311
Hashemi SM, Modarres M, Nasrabadi E, Nasrabadi MM (2006) Fully fuzzified linear programming, solution and duality. J Intell Fuzzy Syst 17:253–261
Hosseinzadeh Lotfi F, Allahviranloo T, Jondabeha MA, Alizadeh L (2009) Solving a fully fuzzy linear programming using lexicography method and fuzzy approximate solution. Appl Math Modell 33:3151–3156
Kumar A, Kaur J (2014) Fuzzy optimal solution of fully fuzzy linear programming problems using ranking function. J Intell Fuzzy Syst 26:337–344
Liu X (2001) Measuring the satisfaction of constraints in fuzzy linear programming. Fuzzy Sets Syst 122:263–275
Nasseri SH, Attari H, Ebrahimnejad A (2012) Revised simplex method and its application for solving fuzzy linear programming problems. Eur J Indus Eng 6:259–280
Tanaka H, Okuda T, Asai K (1974) On fuzzy mathematical programming. Journal of Cybernetics 3:37–46
Zimmermann HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1:45–55
Dehghan M, Hashemi B, Ghatee M (2006) Computational methods for solving fully fuzzy linear systems. Appl Math Comput 179:328–343
Das SK, Edalatpanah SA (2020) A new ranking function of triangular neutrosophic number and its application in integer programming. Int J Neutosophic Sci 4:82–92
Mahdavi-Amiri N, Nasseri SH (2006) Duality in fuzzy number linear programming by use of a certain linear ranking function. Appl Math Comp 180:206–216
Allahviranloo T, Shamsolkotabi KH, Kiani NA, Alizadeh L (2007) Fuzzy integer linear programming problems. Int J Contemp Math Sci 2:167–181
Ebrahimnejad A (2011) Some new results in linear programs with trapezoidal fuzzy numbers: finite convergence of the Ganesan and Veeramani’s method and a fuzzy revised simplex method. Appl Math Modell 35:4526–4540
Lai YJ, Hwang CL (1992) A new approach to some possibilistic linear programming problems. Fuzzy Sets Syst 49:121–133
Kumar A, Kaur J, Singh P (2011) A new method for solving fully fuzzy linear programming problems. Appl Math Model 35:817–823
Maleki HR, Mashinchi M (2004) Fuzzy number linear programming: a probabilistic approach (3). J Appl Math Comput 15:333–341
Lotfi FH, Allahviranloo T, Jondabeha MA, Alizadeh L (2009) Solving a fully fuzzy linear programming using lexicography method and fuzzy approximate solution. Appl Math Model 33:3151–3156
Allahviranloo T, Lotfi FH, Kiasary MKh, Kiani NA, Alizadeh L (2008) Solving fully fuzzy linear programming problem by the ranking function. Appl Math Sci 2:19–32
Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22:958–965
Yager RR (2013) Pythagorean fuzzy subsets. In: 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), vol 2, pp 57–61
Zhang X, Xu Z (2014) Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29:1061–1078
Zhang X (2016) A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. Int J Intell Syst 31:593–611
Ma Z, Xu Z (2016) Symmetric Pythagorean fuzzy weighted geometric averaging operators and their application in multicriteria decision-making problems. Int J Intell Syst 31:1198–1219
Bolturk E (2018) Pythagorean fuzzy CODAS and its application to supplier selection in a manufacturing firm. J Enterp Inf Manag 31:550–564
Qin J (2018) Generalized Pythagorean fuzzy maclaurin symmetric means and its application to multiple attribute sir group decision model. Int J Fuzzy Syst 20:943–957
Wan S-P, Li S-Q, Dong J-Y (2018) A three-phase method for Pythagorean fuzzy multi-attribute group decision making and application to haze management. Comput Ind Eng 123:348–363
Lin Y-L, Ho L-H, Yeh S-L, Chen T-Y (2018) A Pythagorean fuzzy topsis method based on novel correlation measures and its application to multiple criteria decision analysis of inpatient stroke rehabilitation. Int J Comput Intell Syst 12:410–425
Chen T-Y (2018) An outranking approach using a risk attitudinal assignment model involving Pythagorean fuzzy information and its application to financial decision making. Appl Soft Comput 71:460–487
Ilbahar E, Karaşan A, Cebi S, Kahraman C (2018) A novel approach to risk assessment for occupational health and safety using Pythagorean fuzzy AHP & fuzzy inference system. Saf Sci 103:124–136
Karasan A, Ilbahar E, Kahraman C (2018) A novel Pythagorean fuzzy AHP and its application to landfill site selection problem. Soft Comput. https://doi.org/10.1007/s00500-018-3649-0
Zeng S, Wang N, Zhang C, Su W (2018) A novel method based on induced aggregation operator for classroom teaching quality evaluation with probabilistic and pythagorean fuzzy information. Eurasia J Math Sci Technol Educ 14:3205–3212
Ejegwa PA (2019) Improved composite relation for Pythagorean fuzzy sets and its application tomedical diagnosis.Granul Comput. https://doi.org/10.1007/s41066-019-00156-8
Sudha AS, Vimalavirginmary S, Sathya S (2017) A novel approach for solving fuzzy linear programming problem using pentagonal fuzzy numbers. Int J Adv Res Educ Technol 4:42–45
Garg H (2017) A new improved score function of an interval-valued pythagorean fuzzy set based topsis method. Int J Uncertainty Quant 7:463–474
Garg H (2018) A linear programming method based on an improved score function for interval-valued pythagorean fuzzy numbers and its application to decision-making. Int J Uncertainty Fuzziness Knowl Based Syst 26:67–80
Garg H (2016) A novel correlation coefficients between pythagorean fuzzy sets and its applications to decision-making processes. Int J Intell Syst 31:1234–1252
Kumar R, Edalatpanah SA, Jha S, Singh R (2019) A Pythagorean fuzzy approach to the transportation problem. Comp Intell Syst 5:255–263
Ejegwa PA (2019) Pythagorean fuzzy set and its application in career placements based on academic performance using max-min-max composition. Comp Intell Syst 5:165–175
Sakawa M, Nishizaki I, Uemura Y (2001) Fuzzy programming and profit and cost allocation for a production and transportation problem. Eur J Oper Res 131:1–15
Garg H (2016) A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem J. Intell Fuzzy Syst 31:529–540
Wu S-J, Wei G-W (2017) Pythagorean fuzzy hamacher aggregation operators and their application to multiple attribute decision making. Int J Knowl Based Intell Eng Syst 21:189–201
Das S, Mandal T, Edalatpanah SA (2016) A new approach for solving fully fuzzy linear fractional programming problems using the multi-objective linear programming. RAIRO-Oper Res 51:285–297
Das S, Mandal T, Edalatpanah SA (2016) A new procedure for solving fuzzy linear fractional programming problem: numerical point of view. J Comput Sci 25:367–375
Das S, Mandal T, Edalatpanah SA. A new method for solving linear fractional programming problem with absolute value functions. Int J Oper Res 36:455–466
Garg H (2017) A novel improved accuracy function for interval valued Pythagorean fuzzy sets and its applications in decision making process. Int J Intell Syst 31:1247–1260
Ren PJ, Xu ZS, Gou XJ (2016) Pythagorean fuzzy TODIM approach to multi-criteria decision making. Appl Soft Comput 42:246–259
Geng Y, Liu P, Teng F, Liu Z (2017) Pythagorean fuzzy uncertain linguistic TODIM method and their application to multiple criteria group decision making. J Intell Fuzzy Syst 33:3383–3395
Li Z, Wei G, Lu M (2018) Pythagorean fuzzy hamy mean operators in multiple attribute group decision making and their application to supplier selection. Symmetry 10:505–538
Das S, Dash JK (2020) Modified solution for neutrosophic linear programming problems with mixed constraints. Int J Res Indus Eng 9:13–24
Edalatpanah SA (2019) A nonlinear approach for neutrosophic linear programming. J Appl Res Indus Eng 6:367–373
Najafi SH, Edalatpanah SA (2013) A note on “A new method for solving fully fuzzy linear programming problems.” Appl Math Model 37:7865–7867
Najafi SH, Edalatpanah SA, Dutta H (2016) A nonlinear model for fully fuzzy linear programming with fully unrestricted variables and parameters. Alexandria Eng J 55:2589–2595
Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96
Liu F, Yuan XH (2007) Fuzzy number intuitionistic fuzzy set. Fuzzy Syst Math 21:88–91
Abdullah L, Goh P (2019) Decision making method based on Pythagorean fuzzy sets and its application to solid waste management. Comp Intell Syst 5:185–198
Akram M, Habib A, Alcantud JCR (2020) An optimization study based on Dijkstra algorithm for a network with picture trapezoidal fuzzy number. Neural Comput Appl. https://doi.org/10.1007/s00521-020-05034-y
Akram M, Sattar A (2020) Competition graphs under complex Pythagorean fuzzy information. J Appl Math Comput 63:543–583
Akram M, Iiyas F, Garg H (2020) Multi-criteria group decision making based on ELECTRE I method in Pythagorean fuzzy information. Soft Comput 24:3425–3453
Akram M, Dar JM, Shahzadi S (2019) Decision making approach under Pythagorean Dombi fuzzy graphs for selection of leading textile industry. Math Comput Appl 24:102–135
Akram M, Dudek WA, Dar JM (2019) Pythagorean Dombi fuzzy aggregation operators with application in multi-criteria decision-making. Int J Intell Syst 34:3000–3019
Garg H (2020) Novel neutrality operations based Pythagorean fuzzy geometric aggregation operators for multiple attribute group decision analysis. Int J Intell Syst 34:2459–2489
Wang L, Garg H (2020) Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weights. Soft Comput. Springer. https://doi.org/10.1007/s00500-020-05193-z
Garg H (2020) Linguistic interval-valued Pythagorean fuzzy sets and their application to multiple attribute group decision-making process. Cogn Comput. Springer. https://doi.org/10.1007/s12559-020-09750-4
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Das, S.K., Edalatpanah, S.A. (2021). Application of Linear Programming in Diet Problem Under Pythagorean Fuzzy Environment. In: Garg, H. (eds) Pythagorean Fuzzy Sets. Springer, Singapore. https://doi.org/10.1007/978-981-16-1989-2_13
Download citation
DOI: https://doi.org/10.1007/978-981-16-1989-2_13
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-1988-5
Online ISBN: 978-981-16-1989-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)