nach oben

Granular Computing

Erschienen in:

06.08.2022 | Original Paper

A solution algorithm for finding the best and the worst fuzzy compromise solutions of fuzzy rough linear programming problem with triangular fuzzy rough number coefficients

verfasst von: Gizem Temelcan

Erschienen in: Granular Computing | Ausgabe 3/2023

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

An algorithm for the solution of the fuzzy rough linear programming (FRLP) problems with triangular fuzzy rough number parameters is proposed to overcome the uncertainty in decision-making problems. While the costs of the objective function and the coefficients of constraints are triangular fuzzy rough numbers, the variables are in the triangular fuzzy form. Fuzzy optimal solutions are found by solving two distinct fully fuzzy linear programming (FFLP) problems, obtained from the lower and upper approximations of the FRLP problem. These solutions are utilized to evaluate different fuzzy objective function values, and these values are compared according to their supports to specify the worst and the best fuzzy rough compromise solutions. The decision-maker (DM) can make a final decision within the bounds of these supports according to the direction of the optimization. Also, the algorithm yields approximate fuzzy rough compromise solutions in the infeasibility case of the FFLP problems. To demonstrate the efficiency of the algorithm, some numerical examples are illustrated.

Vorheriger Artikel Multi-attribute decision-making based on the advanced possibility degree measure of intuitionistic fuzzy numbers

Nächster Artikel Winsorized dendritic neuron model artificial neural network and a robust training algorithm with Tukey’s biweight loss function based on particle swarm optimization

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Abdelwahed Khalifa H (2018) Study on multi-objective nonlinear programming in optimization of the rough interval constraints. Int J Ind Eng Product Res 29(4):407–413. https://doi.org/10.22068/ijiepr.29.4.407CrossRef

Ahlatcioglu Ozkok B, Albayrak I, Gonce Kocken H et al (2016) An approach for finding fuzzy optimal and approximate fuzzy optimal solution of fully fuzzy linear programming problems with mixed constraints. J Intell Fuzzy Syst 31(1):623–632. https://doi.org/10.3233/IFS-162176CrossRefMATH

Akilbasha A, Natarajan G, Pandian P (2017) Solving transportation problems with mixed constraints in rough environment. Int J Pure Appl Math 113(9):130–138

Akram M, Ullah I, Allahviranloo T (2022) A new method for the solution of fully fuzzy linear programming models. Comput Appl Math 41(1):1–25. https://doi.org/10.1007/s40314-021-01756-4MathSciNetCrossRefMATH

Allahviranloo T, Lotfi F, Kiasary MK et al (2008) Solving fully fuzzy linear programming problem by the ranking function. Appl Math Sci 2(1):19–32MathSciNetMATH

Ammar E, Brikaa M (2019) On solution of constraint matrix games under rough interval approach. Granular Comput 4:601–614. https://doi.org/10.1007/s41066-018-0123-4CrossRef

Ammar S, Eljerbi T (2019) On solving fuzzy rough multiobjective integer linear fractional programming problem. J Intell Fuzzy Syst 37(5):6499–6511. https://doi.org/10.3233/JIFS-182552CrossRef

Ammar S, Emsimir A (2021) A mathematical model for solving fuzzy integer linear programming problems with fully rough intervals. Granular Comput 6:567–578. https://doi.org/10.1007/s41066-020-00216-4CrossRef

Ammar S, Muamer M (2016) On solving fuzzy rough linear fractional programming problem. Int Res J Eng Technol 3(4):2099–2120

Arciszewski T, Ziarko W (1999) Adaptive expert system for preliminary design of wind bracings in steel skeleton structures. In: Second Century of the Skyscraper. Springer, New York, p 847–855

Brikaa M, Zheng Z, Ammar S (2019) Fuzzy multi-objective programming approach for constrained matrix games with payoffs of fuzzy rough numbers. Symmetry 11(5):26. https://doi.org/10.3390/sym11050702

Brikaa M, Zheng Z, Ammar E (2021) Rough set approach to non-cooperative continuous differential games. Granular Comput 6:149–162. https://doi.org/10.1007/s41066-019-00179-1CrossRef

Buckley J, Feuring T (2000) Evolutionary algorithm solution to fuzzy problems: fuzzy linear programming. Fuzzy Sets Syst 109(1):35–53. https://doi.org/10.1016/S0165-0114(98)00022-0MathSciNetCrossRefMATH

Cadenas J, Verdegay J (1997) Using fuzzy numbers in linear programming. IEEE Trans Syst Man Cybern Part B (Cybern) 27(6):1016–1022

Das A, Bera U, Maiti M (2016) A profit maximizing solid transportation model under a rough interval approach. IEEE Trans Fuzzy Syst 25(3):485–498CrossRef

Dong J, Wan S (2018) A new trapezoidal fuzzy linear programming method considering the acceptance degree of fuzzy constraints violated. Knowl-Based Syst 148:100–114. https://doi.org/10.1016/j.knosys.2018.02.030CrossRef

Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst 17(2–3):191–209CrossRefMATH

El-Feky S, Abou-El-Enien T (2019) Hybrid algorithm for rough multi-level multi-objective decision making problems. Ingenierie des Systemes d’Information 24(1):1–17. https://doi.org/10.18280/isi.240101CrossRef

Emam O, Fathy E, Abohany A (2016) An interactive model for fully rough three level large scale integer linear programming problem. Int J Comput Appl 155(12):1–11

Ezzati R, Khorram E, Enayati R (2015) A new algorithm to solve fully fuzzy linear programming problems using the molp problem. Appl Math Model 39(12):3183–3193. https://doi.org/10.1016/j.apm.2013.03.014MathSciNetCrossRefMATH

Fang S, Hu C, Wang H et al (1999) Linear programming with fuzzy coefficients in constraints. Comput Math Appl 37(10):63–76. https://doi.org/10.1016/S0898-1221(99)00126-1MathSciNetCrossRefMATH

Fibak J, Pawlak Z, Słowiński K et al (1986) Rough sets based decision algorithm for treatment of duodenal ulcer by hsv. Biol Sci 34:227–249

Ganesan K, Veeramani P (2006) Fuzzy linear programs with trapezoidal fuzzy numbers. Ann Oper Res 143(1):305–315. https://doi.org/10.1007/s10479-006-7390-1CrossRefMATH

Garai T, Chakraborty D, Roy T (2019) A fuzzy rough multi-objective multi-item inventory model with both stock-dependent demand and holding cost rate. Granular Comput 4(1):71–88. https://doi.org/10.1007/s41066-018-0085-6CrossRef

Hamzehee A, Yaghoobi M, Mashinchi M (2014) Linear programming with rough interval coefficients. J Intell Fuzzy Syst 26(3):1179–1189. https://doi.org/10.3233/IFS-130804MathSciNetCrossRefMATH

Hamzehee A, Yaghoobi M, Mashinchi M (2016) A class of multiple objective mathematical programming problems in a rough environment. Sci Iran 23(1):301–315

Jiménez M, Arenas M, Bilbao A et al (2007) Linear programming with fuzzy parameters: an interactive method resolution. Eur J Oper Res 177(3):1599–1609. https://doi.org/10.1016/j.ejor.2005.10.002MathSciNetCrossRefMATH

Khan I, Ahmad T, Maan N (2013) A simplified novel technique for solving fully fuzzy linear programming problems. J Optim Theory Appl 159:536–546. https://doi.org/10.1007/s10957-012-0215-2MathSciNetCrossRefMATH

Kumar A, Kaur J (2013) General form of linear programming problems with fuzzy parameters. J Appl Res Technol 11(5):629–635. https://doi.org/10.1016/S1665-6423(13)71570-0CrossRef

Kumar A, Kaur J, Singh P (2011) A new method for solving fully fuzzy linear programming problems. Appl Math Model 35(2):817–823. https://doi.org/10.1016/j.apm.2010.07.037MathSciNetCrossRefMATH

Liu B, Liu B (2009) Theory and practice of uncertain programming, vol 239. Springer, New York

Liu X (2001) Measuring the satisfaction of constraints in fuzzy linear programming. Fuzzy Sets Syst 122(2):263–275. https://doi.org/10.1016/S0165-0114(00)00114-7MathSciNetCrossRefMATH

Maleki H, Tata M, Mashinchi M (2000) Linear programming with fuzzy variables. Fuzzy Sets Syst 109(1):21–33. https://doi.org/10.1016/S0165-0114(98)00066-9MathSciNetCrossRefMATH

Mitatha S, Dejhan K, Cheevasuvit F et al (2003) Some experimental results of using rough sets for printed thai characters recognition. Int J Comput Cognit 1(4):109–121

Munakata T (1997) Rough control: a perspective. In: Rough Sets and Data Mining. p 77–88

Omran M, Emam O, Mahmoud A (2016) On solving three level fractional programming problem with rough coefficient in constraints. J Adv Math Comput Sci 12(6):1–13

Osman M, Lashein E, Youness E et al (2011) Mathematical programming in rough environment. Optimisation 60(5):603–611. https://doi.org/10.1080/02331930903536393MathSciNetCrossRefMATH

Osman M, El-Sherbiny M, Khalifa H et al (2016) A fuzzy technique for solving rough interval multiobjective transportation problem. Int J Comput Appl 147(10):49–57

Pamučar D, Ćirović G, Božanić D (2019) Application of interval valued fuzzy-rough numbers in multi-criteria decision making: the ivfrn-mairca model. Yugoslav J Oper Res 29(2):221–247MathSciNetCrossRefMATH

Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):341–356CrossRefMATH

Pawlak Z, Słowiński K, Słowiński R (1986) Rough classification of patients after highly selective vagotomy for duodenal ulcer. Int J Man Mach Stud 24(5):413–433CrossRef

Roy S, Midya S, Yu V (2018) Multi-objective fixed-charge transportation problem with random rough variables. Int J Uncertain Fuzzy Knowl-Based Syst 26(06):971–996. https://doi.org/10.1142/S0218488518500435MathSciNetCrossRefMATH

Saad O, Fathy E (2019) On the solution of linear programming problems with rough interval coefficients in a fuzzy environment. Ann Fuzzy Math Inform 18(2):161–171. https://doi.org/10.30948/afmi.2019.18.2.161MathSciNetCrossRefMATH

Saad O, Emam O, Sleem M (2014) On the solution of a rough interval bi-level multi-objective quadratic programming problem. Int J Eng Innovat Res 3(6):803–809

Singh P, Huang Y (2020) A four-way decision-making approach using interval-valued fuzzy sets, rough set and granular computing: a new approach in data classification and decision-making. Granular Comput 5:397–409. https://doi.org/10.1007/s41066-019-00165-7CrossRef

Wan S, Dong J (2014) Possibility linear programming with trapezoidal fuzzy numbers. Appl Math Model 38(5):1660–1672. https://doi.org/10.1016/j.apm.2013.09.006MathSciNetCrossRefMATH

Wei JM (2003) Rough set based approach to selection of node. Int J Comput Cognit 1(2):25–40MathSciNet

Youness E (2006) Characterizing solutions of rough programming problems. Eur J Oper Res 168(3):1019–1029. https://doi.org/10.1016/j.ejor.2004.05.019MathSciNetCrossRefMATH

Zadeh L (1965) Fuzzy sets. Inf Control 8(5):338–353CrossRefMATH

Zhu G, Hu J, Ren H (2020) A fuzzy rough number-based ahp-topsis for design concept evaluation under uncertain environments. Appl Soft Comput 91:106–228. https://doi.org/10.1016/j.asoc.2020.106228CrossRef

Zimmermann H (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1(1):45–55MathSciNetCrossRefMATH

Titel: A solution algorithm for finding the best and the worst fuzzy compromise solutions of fuzzy rough linear programming problem with triangular fuzzy rough number coefficients
verfasst von: Gizem Temelcan
Publikationsdatum: 06.08.2022
Verlag: Springer International Publishing
Erschienen in: Granular Computing / Ausgabe 3/2023
Print ISSN: 2364-4966
Elektronische ISSN: 2364-4974
DOI: https://doi.org/10.1007/s41066-022-00341-2

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 3/2023

Extended CODAS method for multi-attribute group decision-making based on 2-tuple linguistic Fermatean fuzzy Hamacher aggregation operators

Solving Pythagorean fuzzy fractional differential equations using Laplace transform

Variable precision multi-granulation covering rough intuitionistic fuzzy sets

Winsorized dendritic neuron model artificial neural network and a robust training algorithm with Tukey’s biweight loss function based on particle swarm optimization

Finite-difference method for fuzzy singular integro-differential equation deriving from fuzzy non-linear differential equation

Developing a novel stock index trend predictor model by integrating multiple criteria decision-making with an optimized online sequential extreme learning machine