Skip to main content

Several Applications Based on the Definite Integral Models for (Generalized) Intuitionistic (Multiplicative) Fuzzy Information

  • Chapter
  • First Online:
Generalized Intuitionistic Multiplicative Fuzzy Calculus Theory and Applications

Part of the book series: Uncertainty and Operations Research ((UOR))

Abstract

As we know, information fusion is an important part in decision making. Since the data information collected may not be independent but associated, as well as their weight vector would also depend on the support level from the others, in this circumstance, other prepotent ways to aggregate correlative data must be found.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.

    Article  Google Scholar 

  • Atanassov, K., Vassilev, P., & Tsvetkov, R. (2013). Intuitionistic fuzzy sets, measures and integrals. “Prof. M. Drinov” Academic Publishing House, Sofia.

    Google Scholar 

  • Ban, A., & Fechete, I. (2007). Componentwise decomposition of some lattice-valued fuzzy integrals. Information Science, 177(6), 1430–1440.

    Article  Google Scholar 

  • Bustince, H., Fernández, J., Kolesárová, A., & Mesiar, R. (2013a). Generation of linear orders for intervals by means of aggregation functions. Fuzzy Sets and Systems, 220, 69–77.

    Article  Google Scholar 

  • Bustince, H., Galar, M., Bedregal, B., Kolesárová, A., & Mesiar, R. (2013b). A new approach to interval-valued Choquet integrals and the problem of ordering in interval-valued fuzzy sets applications. IEEE Transactions on Fuzzy Systems, 21(6), 1150–1162.

    Article  Google Scholar 

  • Chen, S. M., & Tan, J. M. (1994). Handling multicriteria fuzzy decision-making problems based on vague set-theory. Fuzzy Sets and Systems, 67(2), 163–172.

    Article  Google Scholar 

  • Choquet, G. (1953). Theory of capacities. Annales de l’Institut Fourier (Crenoble), 5(4), 131–295.

    Google Scholar 

  • Cornelis, C., Deschrijver, G., & Kerre, E. E. (2004). Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: Construction, classification, application. International Journal of Approximate Reasoning, 35(1), 55–95.

    Article  Google Scholar 

  • Cui, L., Li, Y. M., & Zhang, X. H. (2009). Intuitionistic fuzzy linguistic quantifiers based on intuitionistic fuzzy-valued fuzzy measures and integrals. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 17(3), 427–448.

    Article  Google Scholar 

  • Grabisch, M. (1995). Fuzzy integral in multicriteria decision making. Fuzzy Sets and Systems, 69(3), 279–298.

    Article  Google Scholar 

  • Ha, M.H., & Yang, L.sZ. (2009). Intuitionistic fuzzy Riemann integral. 21st Chinese Control and Decision Conference (1–6, pp. 3783–3787).

    Google Scholar 

  • Hong, D. H., & Choi, C. H. (2000). Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems, 114(1), 103–113.

    Article  Google Scholar 

  • Lan, Y. X., Dong, X. L., Deng, X. Y., Pan, Y. X., & He, Y. H. (2014). Research on risk management of public crisis event’s network public opinion based on HHM. Journal of Intelligence, 33(10), 33–39.

    Google Scholar 

  • Lan, Y. X., Wang, F., Zhang, Q. B., Liu, B. Y., & Zhang, P. (2016). Research on the governance model of network public opinion and countermeasures in emergency under the big data background. Library & Information, 3, 28–37.

    Google Scholar 

  • Lei, Q., & Xu, Z. S. (2015a). Derivative and differential operations of intuitionistic fuzzy numbers. International Journal of Intelligent Systems, 30(4), 468–498.

    Article  Google Scholar 

  • Lei, Q., & Xu, Z. S. (2015b). Fundamental properties of intuitionistic fuzzy calculus. Knowledge-Based Systems, 76, 1–16.

    Article  Google Scholar 

  • Lei, Q., Xu, Z. S., Bustince, H., & Burusco, A. (2015). Definite integrals of Atanassov’s intuitionistic fuzzy information. IEEE Transactions on Fuzzy Systems, 23(5), 1519–1533.

    Article  Google Scholar 

  • Liang, G. H., & Ju, Y. M. (2018). The analysis of public opinion risk assessment of sudden events based on public relation life cycle. Information Science, 36(10), 48–53.

    Google Scholar 

  • Li, L. H., & Han, S. N. (2019). Spreading mechanism of network public opinion and prevention of terrorist incidents: An empirical analysis of typical cases in Britain. Journal of Intelligence, 38(11), 102–111.

    Google Scholar 

  • Liu, J., & Li, L. (2014). Analysis of micro-blogger features and sentiment tendency under the violence and terrorism topic. Journal of Intelligence, 33(12), 109–113.

    Google Scholar 

  • Ngwenyama, O. K., & Bryson, N. (1999). Eliciting and mapping qualitative preferences to numeric ranking in group decision making. European Journal of Operational Research, 116(3), 487–497.

    Article  Google Scholar 

  • Qu, Z. K., Zhang, Q. B., Lan, Y. X., Jiao, Y., & Yuan, Y. (2016). Risk early warning research of network public opinion of violence and terrorist incidents. Journal of Intelligence, 35(6), 40–46.

    Google Scholar 

  • Tan, C. Q., & Chen, X. H. (2010). Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making. Expert Systems with Applications, 37(1), 149–157.

    Article  Google Scholar 

  • Torra, V. (2003). Information fusion in data mining. Berlin: Springer.

    Book  Google Scholar 

  • Wang, T. T., Wang, G. Y., & Chen, Y. (2012). A model of online public opinion pre-warning based on fuzzy comprehensive evaluation. Journal of Intelligence, 31(6), 47–51.

    Google Scholar 

  • Wang, Z., & Klir, G. (1992). Fuzzy measure theory. New York: Plenum Press.

    Book  Google Scholar 

  • Xia, M. M., Xu, Z. S., & Liao, H. C. (2013). Preference relations based on intuitionistic multiplicative information. IEEE Transactions on Fuzzy Systems, 21(1), 113–133.

    Article  Google Scholar 

  • Xu, Z. S. (2007). Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems, 15(6), 1179–1187.

    Article  Google Scholar 

  • Xu, Z. S. (2010). Choquet integrals of weighted intuitionistic fuzzy information. Information Sciences, 180(5), 726–736.

    Article  Google Scholar 

  • Xu, Z.S., & Cai, X.Q. (2012). Intuitionistic fuzzy information aggregation: Theory and applications. Beijing: Science Press and Berlin, Heidelberg: Springer-Verlag.

    Google Scholar 

  • Xu, Z. S., & Yager, R. R. (2006). Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems, 35(4), 417–433.

    Article  Google Scholar 

  • Yager, R. R. (2004). Choquet aggregation using order inducing variables. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12(1), 69–88.

    Article  Google Scholar 

  • Yager, R. R. (2009). On generalized Bonferroni mean operators for multi-criteria aggregation. International Journal of Approximate Reasoning, 50(8), 1279–1286.

    Article  Google Scholar 

  • Yu, D. J. (2015). Group decision making under interval-valued multiplicative intuitionistic fuzzy environment based on Archimedean t-conorm and t-norm. International Journal of Intelligent Systems, 30(5), 590–616.

    Article  Google Scholar 

  • Yu, S., & Xu, Z. S. (2016a). Definite integrals of multiplicative intuitionistic fuzzy information in decision making. Knowledge-Based Systems, 100, 59–73.

    Article  Google Scholar 

  • Yu, S., & Xu, Z. S. (2016b). An approach based on definite integrals to multi-criteria decision making with correlative intuitionistic fuzzy information. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 24(6), 807–829.

    Article  Google Scholar 

  • Yu, S., & Xu, Z.S. (2019). The interaction effect by the external agents of the network public opinion in violence and terrorist incidents. Technical Report.

    Google Scholar 

  • Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.

    Article  Google Scholar 

  • Zhang, Y. T., & Xie, W. (2012). Building of the five forces model for university emergency network public opinion based on entropy theory. Journal of Intelligence, 31(11), 19–22.

    Google Scholar 

  • Zhang, Y. W., Qi, J. Y., Fang, B. X., & Li, Y. X. (2012). Online public opinion risk warning based on Bayesian network modeling. Library and Information Service, 52(2), 76–81.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zeshui Xu .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Yu, S., Xu, Z. (2020). Several Applications Based on the Definite Integral Models for (Generalized) Intuitionistic (Multiplicative) Fuzzy Information. In: Generalized Intuitionistic Multiplicative Fuzzy Calculus Theory and Applications. Uncertainty and Operations Research. Springer, Singapore. https://doi.org/10.1007/978-981-15-5612-8_5

Download citation

Publish with us

Policies and ethics