Research Article
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Year 2020, Volume: 69 Issue: 1, 232 - 251, 30.06.2020
https://doi.org/10.31801/cfsuasmas.540529

Abstract

References

  • Zadeh, L.A., Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. Systems Man and Cybernetics, 3(1) (1973), 28-44.
  • Zadeh, L.A., Theory of approximate reasoning. in I.E. Hayes, D. Michie and L.I. Mikulich, Eds. Machine intelligence (Ellis Horwood Ltd. Chichester, U.K.) (1970), 149-194.
  • Kutlu, F., Atan, Ö. and Bilgin, T., Distance Measure, Similarity Measure, Entropy and Inclusion Measure on Temporal Intuitionistic Fuzzy Sets, Proceedings of IFSCOM 2016, (2016) 130-148.
  • Atanassov, K.T., On Intuitionistic Fuzzy Sets Theory. Springer, Berlin, 2012.
  • Atanassov, K. and Gargov, G., Elements of intuitionistic fuzzy logic, Part I, Fuzzy sets and systems,95(1) (1998), 39-52.
  • Atanassov, K.T., On intuitionistic fuzzy negations, In Computational Intelligence, Theory and Applications, Springer, Berlin, Heidelberg, (2006), 159-167.
  • Atanassov, K.T., On the intuitionistic fuzzy implications and negations, In Intelligent Techniques and Tools for Novel System Architectures, Springer, Berlin, Heidelberg, (2008), 381-394.
  • Yılmaz, S. and Çuvalcıoğlu, G., On level operators for temporal intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 20(2) (2014), 6-15.
  • Çuvalcıoglu, G., Expand the modal operator diagram with Z_{α,β,γ}, In Proc. Jangjeon Math. Soc, 13(3) (2010), 403-412.
  • Zadeh, L.A., Fuzzy Sets, Information and Control, 8(1965), 338-353.
  • Bede, B., Mathematics of Fuzzy Sets and Fuzzy Logic, Springer-Verlag Berlin Heidelberg, 2013.
  • Bustince, H., Barrenechea, E. and Mohedano, V., Intuitionistic fuzzy implication operators an expression and main properties, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12(03) (2004), 387-406.
  • Lin, L. and Xia, ZQ., Intuitionistic fuzzy implication operators: Expressions and properties, Journal of Applied Mathematics and Computing, 22(3) (2006), 325-338.
  • Rangasamy, P. and Geetha, SP., A note on properties of temporal intuitionistic fuzzy sets, Notes on IFS, 15(1) (2009), 42-48.
  • Dubois, D. and Prade, H., Fuzzy sets in approximate reasoning, Part 1: Inference with possibility distributions, Fuzzy Sets and Systems, 40(1991), 143-202.
  • Atanassov, K.T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986), 87-96.
  • Atanassov, K.T., Temporal intuitionistic fuzzy sets, Comptes Rendus de l'Academie Bulgare, 7(1991), 5-7.
  • Atanassov, K.T., On Intuitionistic Fuzzy Sets Theory, Springer, Berlin, 2012.
  • Lv, Y. and Guo, S., Relationships among fuzzy entropy, similarity measure and distance measure of intuitionistic fuzzy sets, Fuzzy Information and Engineering, 78(2010), 539-548.
  • Chen, L. and Tu, C., Time-validating-based Atanassov's intuitionistic fuzzy decision-making, IEEE Transcations on Fuzzy Systems, 23(4) (2015), 743-756.
  • Du, W.S. and Hu, B.Q., Aggregation distance measure and its induced similarity measure between intuitionistic fuzzy sets, Pattern Recog. Lett., 60(2015), 65-71.
  • Parvathi, R. and Geetha, S.P., A note on properties of temporal intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 15(1) (2009), 42-48.
  • Yılmaz, S. and Çuvalcıoğlu, G., On level operators for temporal intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 20(2) (2014), 6-15.
  • Deschrijver, G., Cornelis, C. and Kerre, E., On the representation of intuitionistic fuzzy t-norms and t-conorms, IEEE transactions on fuzzy systems, 12(1) (2004), 45-61.
  • Bustince, H., Kacprzyk, J. and Mohedano, V., Intuitionistic fuzzy generators Application to intuitionistic fuzzy complementation, Fuzzy Sets and Systems, 114(2000), 485-504.
  • Fodor, J.C. and Roubens, M., Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer, Dordrecht, 1994.
  • Baczynski, M., On some properties of intuitionistic fuzzy implications, in: M. Wagenknecht, R. Hampel (Eds.), Proc. Third Internat. Conf. on Fuzzy Logic and Technology, (2003), 168-171.

Introduction to temporal intuitionistic fuzzy approximate reasoning

Year 2020, Volume: 69 Issue: 1, 232 - 251, 30.06.2020
https://doi.org/10.31801/cfsuasmas.540529

Abstract

In this study; temporal intuitionistic fuzzy negation, temporal intuitionistic
fuzzy triangular norm and temporal intuitionistic fuzzy triangular
conorm have been researched. The aim of this study is to dene negator, tnorm
and t-conorms, which is the generalization of negation, conjunctions and
disconjunctions in the temporal intuitionistic fuzzy sets and to examine the
De Morgan relations between these concepts. The thing to note here is that
conjunctions generalized with t􀀀norm and t􀀀conorm is changed depending
on time. We will carry concept of implication and coimplication to temporal
intuitionistic fuzzy sets. With the new implication denitions, a causal structure
will be established which will match the variable structure of the systems
depending on the position and time variables. It is evident that successful
results will be achieved in this type of system, which is being dealt with by
this new structure.

References

  • Zadeh, L.A., Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. Systems Man and Cybernetics, 3(1) (1973), 28-44.
  • Zadeh, L.A., Theory of approximate reasoning. in I.E. Hayes, D. Michie and L.I. Mikulich, Eds. Machine intelligence (Ellis Horwood Ltd. Chichester, U.K.) (1970), 149-194.
  • Kutlu, F., Atan, Ö. and Bilgin, T., Distance Measure, Similarity Measure, Entropy and Inclusion Measure on Temporal Intuitionistic Fuzzy Sets, Proceedings of IFSCOM 2016, (2016) 130-148.
  • Atanassov, K.T., On Intuitionistic Fuzzy Sets Theory. Springer, Berlin, 2012.
  • Atanassov, K. and Gargov, G., Elements of intuitionistic fuzzy logic, Part I, Fuzzy sets and systems,95(1) (1998), 39-52.
  • Atanassov, K.T., On intuitionistic fuzzy negations, In Computational Intelligence, Theory and Applications, Springer, Berlin, Heidelberg, (2006), 159-167.
  • Atanassov, K.T., On the intuitionistic fuzzy implications and negations, In Intelligent Techniques and Tools for Novel System Architectures, Springer, Berlin, Heidelberg, (2008), 381-394.
  • Yılmaz, S. and Çuvalcıoğlu, G., On level operators for temporal intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 20(2) (2014), 6-15.
  • Çuvalcıoglu, G., Expand the modal operator diagram with Z_{α,β,γ}, In Proc. Jangjeon Math. Soc, 13(3) (2010), 403-412.
  • Zadeh, L.A., Fuzzy Sets, Information and Control, 8(1965), 338-353.
  • Bede, B., Mathematics of Fuzzy Sets and Fuzzy Logic, Springer-Verlag Berlin Heidelberg, 2013.
  • Bustince, H., Barrenechea, E. and Mohedano, V., Intuitionistic fuzzy implication operators an expression and main properties, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12(03) (2004), 387-406.
  • Lin, L. and Xia, ZQ., Intuitionistic fuzzy implication operators: Expressions and properties, Journal of Applied Mathematics and Computing, 22(3) (2006), 325-338.
  • Rangasamy, P. and Geetha, SP., A note on properties of temporal intuitionistic fuzzy sets, Notes on IFS, 15(1) (2009), 42-48.
  • Dubois, D. and Prade, H., Fuzzy sets in approximate reasoning, Part 1: Inference with possibility distributions, Fuzzy Sets and Systems, 40(1991), 143-202.
  • Atanassov, K.T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986), 87-96.
  • Atanassov, K.T., Temporal intuitionistic fuzzy sets, Comptes Rendus de l'Academie Bulgare, 7(1991), 5-7.
  • Atanassov, K.T., On Intuitionistic Fuzzy Sets Theory, Springer, Berlin, 2012.
  • Lv, Y. and Guo, S., Relationships among fuzzy entropy, similarity measure and distance measure of intuitionistic fuzzy sets, Fuzzy Information and Engineering, 78(2010), 539-548.
  • Chen, L. and Tu, C., Time-validating-based Atanassov's intuitionistic fuzzy decision-making, IEEE Transcations on Fuzzy Systems, 23(4) (2015), 743-756.
  • Du, W.S. and Hu, B.Q., Aggregation distance measure and its induced similarity measure between intuitionistic fuzzy sets, Pattern Recog. Lett., 60(2015), 65-71.
  • Parvathi, R. and Geetha, S.P., A note on properties of temporal intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 15(1) (2009), 42-48.
  • Yılmaz, S. and Çuvalcıoğlu, G., On level operators for temporal intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 20(2) (2014), 6-15.
  • Deschrijver, G., Cornelis, C. and Kerre, E., On the representation of intuitionistic fuzzy t-norms and t-conorms, IEEE transactions on fuzzy systems, 12(1) (2004), 45-61.
  • Bustince, H., Kacprzyk, J. and Mohedano, V., Intuitionistic fuzzy generators Application to intuitionistic fuzzy complementation, Fuzzy Sets and Systems, 114(2000), 485-504.
  • Fodor, J.C. and Roubens, M., Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer, Dordrecht, 1994.
  • Baczynski, M., On some properties of intuitionistic fuzzy implications, in: M. Wagenknecht, R. Hampel (Eds.), Proc. Third Internat. Conf. on Fuzzy Logic and Technology, (2003), 168-171.
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Fatih Kutlu 0000-0002-1731-9558

Feride Tuğrul 0000-0001-7690-8080

Mehmet Çitil 0000-0003-3899-3434

Publication Date June 30, 2020
Submission Date March 16, 2019
Acceptance Date September 19, 2019
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

APA Kutlu, F., Tuğrul, F., & Çitil, M. (2020). Introduction to temporal intuitionistic fuzzy approximate reasoning. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 232-251. https://doi.org/10.31801/cfsuasmas.540529
AMA Kutlu F, Tuğrul F, Çitil M. Introduction to temporal intuitionistic fuzzy approximate reasoning. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):232-251. doi:10.31801/cfsuasmas.540529
Chicago Kutlu, Fatih, Feride Tuğrul, and Mehmet Çitil. “Introduction to Temporal Intuitionistic Fuzzy Approximate Reasoning”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 232-51. https://doi.org/10.31801/cfsuasmas.540529.
EndNote Kutlu F, Tuğrul F, Çitil M (June 1, 2020) Introduction to temporal intuitionistic fuzzy approximate reasoning. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 232–251.
IEEE F. Kutlu, F. Tuğrul, and M. Çitil, “Introduction to temporal intuitionistic fuzzy approximate reasoning”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 232–251, 2020, doi: 10.31801/cfsuasmas.540529.
ISNAD Kutlu, Fatih et al. “Introduction to Temporal Intuitionistic Fuzzy Approximate Reasoning”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 232-251. https://doi.org/10.31801/cfsuasmas.540529.
JAMA Kutlu F, Tuğrul F, Çitil M. Introduction to temporal intuitionistic fuzzy approximate reasoning. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:232–251.
MLA Kutlu, Fatih et al. “Introduction to Temporal Intuitionistic Fuzzy Approximate Reasoning”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 232-51, doi:10.31801/cfsuasmas.540529.
Vancouver Kutlu F, Tuğrul F, Çitil M. Introduction to temporal intuitionistic fuzzy approximate reasoning. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):232-51.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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