Skip to main content
Top
Published in: Granular Computing 3/2021

17-02-2020 | Original Paper

A hybrid decision-making framework using rough mF bipolar soft environment

Authors: Muhammad Akram, Ghous Ali, Muhammad Shabir

Published in: Granular Computing | Issue 3/2021

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this article, we present the notions of two novel hybrid multi-attribute decision-making models, namely m-polar fuzzy bipolar soft set (mFBSS, for short) model and rough mFBSS model. These mathematical models allow us to handle multipolar information under fuzziness with bipolar soft sets. We use these proposed models to handle complicated problems in which the degree of membership of an object in a given set uses m fuzzy values, to rank all the objects, and to find a suitable option. We illustrate our proposed concepts with examples. Furthermore, we investigate some useful properties, including complement, restricted union and intersection, extended union and intersection, AND and OR. We discuss two practical applications of mFBSSs and rough mFBSSs, that is, selecting a suitable employee for promotion and place for house construction, respectively. We develop efficient algorithms to solve multi-attribute decision-making problems. We also discuss a comparison analysis of the proposed approaches with some existing models.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

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!

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!

Literature
go back to reference Akram M, Ali G, Alcantud JCR (2019a) Hybrid multi-attribute decision-making model based on \((m, N)\)-soft rough sets. J Intell Fuzzy Syst 36(6):6325–6342 Akram M, Ali G, Alcantud JCR (2019a) Hybrid multi-attribute decision-making model based on \((m, N)\)-soft rough sets. J Intell Fuzzy Syst 36(6):6325–6342
go back to reference Akram M, Ali G, Alshehri NO (2017) A new multi-attribute decision-making method based on \(m\)-polar fuzzy soft rough sets. Symmetry 9(11):271MATH Akram M, Ali G, Alshehri NO (2017) A new multi-attribute decision-making method based on \(m\)-polar fuzzy soft rough sets. Symmetry 9(11):271MATH
go back to reference Akram M, Ali G, Waseem N, Davvaz B (2018) Decision-making methods based on hybrid \(m\)F models. J Intell Fuzzy Syst 35(3):3387–3403 Akram M, Ali G, Waseem N, Davvaz B (2018) Decision-making methods based on hybrid \(m\)F models. J Intell Fuzzy Syst 35(3):3387–3403
go back to reference Akram M, Ali G (2020) Hybrid models for decision making based on rough Pythagorean fuzzy bipolar soft information. Granul Comput 5(1):1–15MathSciNet Akram M, Ali G (2020) Hybrid models for decision making based on rough Pythagorean fuzzy bipolar soft information. Granul Comput 5(1):1–15MathSciNet
go back to reference Akram M, Ali G, Alcantud JCR (2019b) New decision-making hybrid model: intuitionistic fuzzy N-soft rough sets. Soft Comput 23(20):9853–9868MATH Akram M, Ali G, Alcantud JCR (2019b) New decision-making hybrid model: intuitionistic fuzzy N-soft rough sets. Soft Comput 23(20):9853–9868MATH
go back to reference Ali G (2019) Decision-making methods based on \(m\)-polar fuzzy \(N\)-soft rough sets. University of the Punjab, HEC (PhD Thesis) Ali G (2019) Decision-making methods based on \(m\)-polar fuzzy \(N\)-soft rough sets. University of the Punjab, HEC (PhD Thesis)
go back to reference Ali G, Akram M, Koam ANA, Alcantud JCR (2019) Parameter reductions of bipolar fuzzy soft sets with their decision-making algorithms. Symmetry 11(8):949 Ali G, Akram M, Koam ANA, Alcantud JCR (2019) Parameter reductions of bipolar fuzzy soft sets with their decision-making algorithms. Symmetry 11(8):949
go back to reference Ali MI, Shabir M (2010) Comments on De Morgan’s law in fuzzy soft sets. J Fuzzy Math 18(3):679–686MathSciNetMATH Ali MI, Shabir M (2010) Comments on De Morgan’s law in fuzzy soft sets. J Fuzzy Math 18(3):679–686MathSciNetMATH
go back to reference Ali MI, Feng F, Liu XY, Min WK, Shabir M (2009) On some new operations in soft set theory. Comput Math Appl 57(9):1547–1553MathSciNetMATH Ali MI, Feng F, Liu XY, Min WK, Shabir M (2009) On some new operations in soft set theory. Comput Math Appl 57(9):1547–1553MathSciNetMATH
go back to reference Bai SM, Chen SM (2008a) Automatically constructing grade membership functions of fuzzy rules for students’ evaluation. Expert Syst Appl 35(3):1408–1414 Bai SM, Chen SM (2008a) Automatically constructing grade membership functions of fuzzy rules for students’ evaluation. Expert Syst Appl 35(3):1408–1414
go back to reference Bai SM, Chen SM (2008b) Automatically constructing concept maps based on fuzzy rules for adapting learning systems. Expert Syst Appl 35(1–2):41–49 Bai SM, Chen SM (2008b) Automatically constructing concept maps based on fuzzy rules for adapting learning systems. Expert Syst Appl 35(1–2):41–49
go back to reference Chen SM, Cheng SH, Lan TC (2016) A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Inf Sci 343:15–40MathSciNetMATH Chen SM, Cheng SH, Lan TC (2016) A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Inf Sci 343:15–40MathSciNetMATH
go back to reference Chen SM, Manalu GMT, Pan JS, Liu HC (2013) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and particle swarm optimization techniques. IEEE Trans Cybern 43(3):1102–1117 Chen SM, Manalu GMT, Pan JS, Liu HC (2013) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and particle swarm optimization techniques. IEEE Trans Cybern 43(3):1102–1117
go back to reference Chen SM, Chu HP, Sheu TW (2012) TAIEX forecasting using fuzzy time series and automatically generated weights of multiple factors. IEEE Trans Syst Man Cybern Part A Syst Hum 42(6):1485–1495 Chen SM, Chu HP, Sheu TW (2012) TAIEX forecasting using fuzzy time series and automatically generated weights of multiple factors. IEEE Trans Syst Man Cybern Part A Syst Hum 42(6):1485–1495
go back to reference Chen SM, Chen SW (2014) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and the probabilities of trends of fuzzy logical relationships. IEEE Trans Cybern 45(3):391–403 Chen SM, Chen SW (2014) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and the probabilities of trends of fuzzy logical relationships. IEEE Trans Cybern 45(3):391–403
go back to reference Chen J, Li S, Ma S, Wang X (2014) \(m\)-polar fuzzy sets: an extension of bipolar fuzzy sets. Sci World J 2014:1–8 (Article ID 416530) Chen J, Li S, Ma S, Wang X (2014) \(m\)-polar fuzzy sets: an extension of bipolar fuzzy sets. Sci World J 2014:1–8 (Article ID 416530)
go back to reference Chen SM, Han WH (2019) Multiattribute decision making based on nonlinear programming methodology, particle swarm optimization techniques and interval-valued intuitionistic fuzzy values. Inf Sci 471:252–268MathSciNetMATH Chen SM, Han WH (2019) Multiattribute decision making based on nonlinear programming methodology, particle swarm optimization techniques and interval-valued intuitionistic fuzzy values. Inf Sci 471:252–268MathSciNetMATH
go back to reference Chen SM, Fan KY (2019) Multiattribute decision making based on probability density functions and the variances and standard deviations of largest ranges of evaluating interval-valued intuitionistic fuzzy values. Inf Sci 490:329–343 Chen SM, Fan KY (2019) Multiattribute decision making based on probability density functions and the variances and standard deviations of largest ranges of evaluating interval-valued intuitionistic fuzzy values. Inf Sci 490:329–343
go back to reference Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst 17(2–3):191–209MATH Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst 17(2–3):191–209MATH
go back to reference Feng F, Li C, Davvaz B, Ali MI (2010a) Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput 14(9):899–911MATH Feng F, Li C, Davvaz B, Ali MI (2010a) Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput 14(9):899–911MATH
go back to reference Feng F (2011) Soft rough sets applied to multicriteria group decision making. Ann Fuzzy Math Inf 2(1):69–80MathSciNetMATH Feng F (2011) Soft rough sets applied to multicriteria group decision making. Ann Fuzzy Math Inf 2(1):69–80MathSciNetMATH
go back to reference Feng F, Jun YB, Liu X, Li L (2010b) An adjustable approach to fuzzy soft set based decision-making. J Comput Appl Math 234(1):10–20MathSciNetMATH Feng F, Jun YB, Liu X, Li L (2010b) An adjustable approach to fuzzy soft set based decision-making. J Comput Appl Math 234(1):10–20MathSciNetMATH
go back to reference Karaaslan F, Karatas S (2015) A new approach to bipolar soft sets and its applications. Discrete Math Algorithm Appl 7(04):1550054MathSciNetMATH Karaaslan F, Karatas S (2015) A new approach to bipolar soft sets and its applications. Discrete Math Algorithm Appl 7(04):1550054MathSciNetMATH
go back to reference Karaaslan F, Çaǧman N (2018) Bipolar soft rough sets and their applications in decision making. Afrika Matematika 29(5–6):823–839MathSciNetMATH Karaaslan F, Çaǧman N (2018) Bipolar soft rough sets and their applications in decision making. Afrika Matematika 29(5–6):823–839MathSciNetMATH
go back to reference Liu X, Wang L (2020) An extension approach of TOPSIS method with OWAD operator for multiple criteria decision-making. Granul Comput 5(1):135–148 Liu X, Wang L (2020) An extension approach of TOPSIS method with OWAD operator for multiple criteria decision-making. Granul Comput 5(1):135–148
go back to reference Liu P, Chen SM, Wang Y (2020) Multiattribute group decision making based on intuitionistic fuzzy partitioned Maclaurin symmetric mean operators. Inf Sci 512:830–854MathSciNetMATH Liu P, Chen SM, Wang Y (2020) Multiattribute group decision making based on intuitionistic fuzzy partitioned Maclaurin symmetric mean operators. Inf Sci 512:830–854MathSciNetMATH
go back to reference Liu P, Wang P (2018) Some \(q\)-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. Int J Intell Syst 33(2):259–280 Liu P, Wang P (2018) Some \(q\)-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. Int J Intell Syst 33(2):259–280
go back to reference Ma X, Liu Q, Zhan J (2017) A survey of decision making methods based on certain hybrid soft set models. Artif Intell Rev 47:507–530 Ma X, Liu Q, Zhan J (2017) A survey of decision making methods based on certain hybrid soft set models. Artif Intell Rev 47:507–530
go back to reference Maji PK, Roy AR, Biswas R (2002) An application of soft sets in a decision-making problem. Comput Math Appl 44(8):1077–1083MathSciNetMATH Maji PK, Roy AR, Biswas R (2002) An application of soft sets in a decision-making problem. Comput Math Appl 44(8):1077–1083MathSciNetMATH
go back to reference Malik N, Shabir M (2019) Rough fuzzy bipolar soft sets and application in decision-making problems. Soft Comput 23(5):1603–1614MATH Malik N, Shabir M (2019) Rough fuzzy bipolar soft sets and application in decision-making problems. Soft Comput 23(5):1603–1614MATH
go back to reference Mandal P, Ranadive AS (2019) Hesitant bipolar-valued fuzzy sets and bipolar-valued hesitant fuzzy sets and their applications in multi-attribute group decision making. Granul Comput 4(3):559–583 Mandal P, Ranadive AS (2019) Hesitant bipolar-valued fuzzy sets and bipolar-valued hesitant fuzzy sets and their applications in multi-attribute group decision making. Granul Comput 4(3):559–583
go back to reference Mishra AR, Chandel A, Motwani D (2020) Extended MABAC method based on divergence measures for multi-criteria assessment of programming language with interval-valued intuitionistic fuzzy sets. Granul Comput 5(1):97–117 Mishra AR, Chandel A, Motwani D (2020) Extended MABAC method based on divergence measures for multi-criteria assessment of programming language with interval-valued intuitionistic fuzzy sets. Granul Comput 5(1):97–117
go back to reference Naz M, Shabir M (2014) On fuzzy bipolar soft sets, their algebraic structures and applications. J Intell Fuzzy Syst 26(4):1645–1656MathSciNetMATH Naz M, Shabir M (2014) On fuzzy bipolar soft sets, their algebraic structures and applications. J Intell Fuzzy Syst 26(4):1645–1656MathSciNetMATH
go back to reference Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):145–172MATH Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):145–172MATH
go back to reference Roy AR, Maji PK (2007) A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 203(2):412–418MATH Roy AR, Maji PK (2007) A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 203(2):412–418MATH
go back to reference Zhang X, Dai J, Yu Y (2015) On the union and intersection operations of rough sets based on various approximation spaces. Inf Sci 292:214–229MathSciNetMATH Zhang X, Dai J, Yu Y (2015) On the union and intersection operations of rough sets based on various approximation spaces. Inf Sci 292:214–229MathSciNetMATH
go back to reference Zhang WR (1998) Bipolar fuzzy sets. In: Proc of FUZZ-IEEE, pp 835-840 Zhang WR (1998) Bipolar fuzzy sets. In: Proc of FUZZ-IEEE, pp 835-840
go back to reference Zhang WR (1994) Bipolar fuzzy sets and relations. a computational framework for cognitive modeling and multiagent decision analysis. In: Proc. of IEEE Conf., pp 305-309 Zhang WR (1994) Bipolar fuzzy sets and relations. a computational framework for cognitive modeling and multiagent decision analysis. In: Proc. of IEEE Conf., pp 305-309
go back to reference Zou Y, Xiao Z (2008) Data analysis approaches of soft sets under incomplete information. Knowl Based Syst 21(8):941–945 Zou Y, Xiao Z (2008) Data analysis approaches of soft sets under incomplete information. Knowl Based Syst 21(8):941–945
Metadata
Title
A hybrid decision-making framework using rough mF bipolar soft environment
Authors
Muhammad Akram
Ghous Ali
Muhammad Shabir
Publication date
17-02-2020
Publisher
Springer International Publishing
Published in
Granular Computing / Issue 3/2021
Print ISSN: 2364-4966
Electronic ISSN: 2364-4974
DOI
https://doi.org/10.1007/s41066-020-00214-6

Other articles of this Issue 3/2021

Granular Computing 3/2021 Go to the issue

Premium Partner