Skip to main content
SpringerLink
Log in

Human attitude analysis based on fuzzy soft differential equations with Bonferroni mean

  • Published:
Computational and Applied Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we model a system of fuzzy soft differential equations to analyze the behavior over the time of an individual depending on their companion’s actions under any particular situation against some decision. The Bonferroni mean (BM) is a very useful tool for group decision-making problems when arguments are interrelated to each other as Bonferroni mean can capture the interrelationship of the individual arguments. Using this ability of BM, we define Bonferroni fuzzy soft matrix (BFSM) and weighted Bonferroni fuzzy soft matrix (WBFSM) for data representation. WBFSM is a decision matrix and provide the optimum fuzzy soft constant (OFSC) which is the key element of fuzzy soft differential equation. By utilizing the OFSC, we develop a system of fuzzy soft differential equations to study a dynamical process with nonlinear uncertain and vague data. Second, we present a novel efficient technique for analyzing the future attitude of people due to their present decisions. To illustrate the practicality and feasibility of proposed technique an illustrative example is also discussed with the help of phase portrait and line graphs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Basu TM, Mahapatra NK, Mondal SK (2012) Different types of matrices in fuzzy soft set theory and their application in decision making problems. Eng Sci Technol Int J 2:2250–2268

    Google Scholar 

  • Beg I, Rashid T (2014) An improved clustering algorithm using fuzzy relation for the performance evaluation of humanistic systems. Int J Intell Syst 29:1181–1199

    Article  Google Scholar 

  • Beliakov G, James S, Mordelova J, Rockschlossova R, Yager R (2012) Generalized Bonferroni mean operators in multi-criteria aggregation. Fuzzy Set Syst 161:2227–2242

    Article  MathSciNet  MATH  Google Scholar 

  • Bonferroni C (1950) Sulle medie multiple di potenze. Bolletino Matematica Italiana 5:267–270

    MathSciNet  MATH  Google Scholar 

  • Borah NK, Neog TJ (2012) Gradation of NGO’s role in rural development, a fuzzy soft set theoretic approach. Int J Comput Org Tren 2:99–101

    Google Scholar 

  • Celik Y, Yamak S (2013) Fuzzy soft set theory applied to medical diagnosis using fuzzy arithmetic operations. J Inequal Appl 2:182–190

    MathSciNet  MATH  Google Scholar 

  • Chaudhuri AK, De K, Chatterjee D (2009) Solution of the decision making problems using fuzzy soft relations. Int J Inf Tech 15:78–107

    Google Scholar 

  • Das PK, Borgohain R (2012) An application of fuzzy soft set in multicriteria decision making problem. Int J Comput Apll 38:33–37

    Google Scholar 

  • Dushmanta KS (2012) An application of fuzzy soft relation in decision making problems. Int J Math Trends Technol 3:50–53

    Google Scholar 

  • Dyckhoff H, Pedrycz W (1984) Generalized means as model of compensative connectives. Fuzzy Set Syst 14:143–154

    Article  MathSciNet  MATH  Google Scholar 

  • Jabeur K, Martel JM (2004) A distance-based collective preorder integrating the relative importance of the group’s members. Group Decis Negot 13:327–349

    Article  Google Scholar 

  • Maji PK, Biswas R, Roy AR (2001) Soft set theory. J Fuzzy Math 9:589–602

    MathSciNet  MATH  Google Scholar 

  • Maji PK, Biswas R, Roy AR (2007) A fuzzy soft set theoratic apporach to decision making problems. J Comput Appl Math 20:412–418

    Google Scholar 

  • Molodtsov D (1999) Soft set theory-first results. Comput Math Appl 37:19–31

    Article  MathSciNet  MATH  Google Scholar 

  • Naim C (2010) Fuzzy parameterized fuzzy soft set theory and its applications. Turkish J Fuzzy Syst 1:21–35

    Google Scholar 

  • Neog TJ, Sut DK (2011) Application of fuzzy soft sets in decision making problem using fuzzy soft matrices. Int J Math Arch 2:2253–2258

    Google Scholar 

  • Rashid T, Beg I, Husnine SM (2014) Robot selection by using generalized interval-valued fuzzy numbers with TOPSIS. Appl Soft Comput 21:462–468

    Article  Google Scholar 

  • Sprott JC (2004) Dynamical models of love. Nonlinear Dyn Psychol Life Sci 8:303–313

    Google Scholar 

  • Sunaga T (1958) Theory of interval algebra and its application to numerical analysis. Res Assoc Appl Geom 2:29–46

    MATH  Google Scholar 

  • Strogatz SH (1994) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. Perseus Books, Reading MA

    MATH  Google Scholar 

  • Tang X, Fu C, Xu D, Yang S (2017) Analysis of fuzzy Hamacher aggregation functions for uncertain multiple attribute decision making. Inf Sci. doi:10.1016/j.ins.2016.12.045

  • Turksen IB, Zhong Z (1988) An approximate analogical reasoning approach based on similarity measure. IEEE T Syst Man Cyb 6:1049–1056

    Article  Google Scholar 

  • Wang TJ, Lu ZD, Li F (2002) Bi-directional approximate reasoning based on weighted similarity measures of sets. J Comput Eng Sci 24:96–100

    Google Scholar 

  • Wang WQ, Xin XL (2005) Distance measure between intuitionistic fuzzy sets. Pattern Recongn Lett 26:2063–2069

    Article  Google Scholar 

  • Yager RR (1988) On ordered weighted averaging operators in multicriteria decision-making. IEEE T Syst Man Cyb 18:183–190

    Article  MATH  Google Scholar 

  • Yager RR (2009) On generalized Bonferroni mean operators for multi-criteria aggregation. Int J Approx Reason 50:1279–1286

    Article  MathSciNet  MATH  Google Scholar 

  • Yager RR, Xu ZS (2011) Intuitionistic fuzzy Bonferroni means. IEEE T Syst Man Cy B 41:568–578

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–358

    Article  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the editors and the anonymous reviewers, whose insightful comments and constructive suggestions helped us to significantly improve the quality of this paper.

Author information

Authors and Affiliations

  1. Centre for Mathematics and Statistical Sciences, Lahore School of Economics, Lahore, 53200, Pakistan

    Ismat Beg

  2. Department of Mathematics, University of Management and Technology, Lahore, 54770, Pakistan

    Tabasam Rashid & Raja Noshad Jamil

Authors
  1. Ismat Beg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tabasam Rashid
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Raja Noshad Jamil
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ismat Beg.

Additional information

Communicated by Rosana Sueli da Motta Jafelice.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Beg, I., Rashid, T. & Jamil, R.N. Human attitude analysis based on fuzzy soft differential equations with Bonferroni mean. Comp. Appl. Math. 37, 2632–2647 (2018). https://doi.org/10.1007/s40314-017-0469-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40314-017-0469-2

Keywords

Mathematics Subject Classification

Search

Navigation