Abstract
In this paper, we examine the concept of center of gravity and its relationship to the concept of possibilistic mean. We propose new transformations between the center of gravity and the possibilistic mean for triangular and trapezoidal fuzzy numbers.
Similar content being viewed by others
References
Alexandrini P (340) Mathematicae Collectiones
Carlsson C, Fuller R (2001) On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets Syst 122(2):315–326
Collan M, Fullér R, Mezei J (2009) A fuzzy pay-off method for real option valuation. J Appl Math Decis Sci. https://doi.org/10.1155/2009/238196
Delgado M, Moral S (1987) On the concept of possibility-probability consistency. Fuzzy Sets Syst 21(3):311–318. https://doi.org/10.1016/0165-0114(87)90132-1
Dubois D, Prade H (1988) Possibility theory: an approach to computerized processing of uncertainty. Plenum Press, New York, p 139. https://doi.org/10.1007/978-1-4614-1800-9139
Dubois D, Prade H (1993) Fuzzy sets and probability: misunderstandings, bridges and gaps. In: Proceedings of the second IEEE international conference on fuzzy systems, San Francisco, pp 1059–1068. https://doi.org/10.1109/FUZZY.1993.327367
Dubois D, Prade H (2015) The legacy of 50 years of fuzzy sets: a discussion. Fuzzy Sets Syst 281:21–31. https://doi.org/10.1016/j.fss.2015.09.004
Dubois D, Prade H (2016) Practical methods for constructing possibility distributions. Int J Intell Syst 31(3):215–239. https://doi.org/10.1002/int
Dubois D, Foulloy L, Mauris G, Prade H (2004) Probability-possibility transformations, triangular fuzzy sets, and probabilistic inequalities. Relib Comput 10(4):273–297. https://doi.org/10.1023/B:REOM.0000032115.22510.b5
Klir GJ, Harmanec D (1994) On modal logic interpretation of possibility theory. Int J Uncertain Fuzziness Knowl Based Syst 2(2):237–245
Klir GJ, Parviz B (1992) Probability-possibility transformations: a comparison. Int J Gen Syst 21(3):291–310. https://doi.org/10.1080/03081079208945083
Klir GJ, Yuan B (1995) Fuzzy sets and fuzzy logic: theory and aplications. Prentice Hall, Upper Saddle River
Link S, Prade H (2016) Possibilistic functional dependencies and their relationship to possibility theory. IEEE Trans Fuzzy Syst 24(3):757–763. https://doi.org/10.1109/TFUZZ.2015.2466074
Pota M, Esposito M, De Pietro G (2014) Fuzzy partitioning for clinical DSSs using statistical information transformed into possibility-based knowledge. Knowl Based Syst 67(1):1–15. https://doi.org/10.1016/j.knosys.2014.06.021
Ruspini EH (1991) On the semantics of fuzzy logic. Int J Approx Reason 5(1):45–88. https://doi.org/10.1002/int.20034
Schafer G (1987) Belief functions and possibility measures. In: Bezdek JC (ed) Analysis of fuzzy information, vol 1, mathematic edn. CRC Press, Boca Raton, pp 51–84
Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1(1):3–28
Zadeh LA (2014) A note on similarity-based definitions of possibility and probability. Inf Sci 267:334–336. https://doi.org/10.1016/j.ins.2014.01.046
Acknowledgements
The research presented in this paper was partially supported by the Grant IGA_FF_2017_011 of the internal grant agency of Palacký University Olomouc.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
All the authors declare that they have no conflict of interest.
Human and animal rights
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Communicated by A. Di Nola.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Luukka , P., Stoklasa, J. & Collan, M. Transformations between the center of gravity and the possibilistic mean for triangular and trapezoidal fuzzy numbers. Soft Comput 23, 3229–3235 (2019). https://doi.org/10.1007/s00500-018-3204-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-018-3204-z