Abstract
The first step of the development of the idea of intuitionistic fuzziness (see [1]), was related to introducing an intuitionistic fuzzy interpretation of the classical (standard) modal operators “necessity” and “possibility” (see, e.g., [2,3,4,5]). In the period 1988–1993, we defined eight new operators, extending the first two ones. In the end of last and in the beginning of this century, a lot of new operators were introduced. Here, we discuss the most interesting ones of them and study their basic properties.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Atanassov K. Intuitionistic fuzzy sets, VII ITKR’s Session; 1983 (Deposed in Central Sci. - Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulg.), Reprinted: Int J Bioautomation. 2016;2(S1):S1–S6.
Blackburn P, van Bentham J, Wolter F. Modal logic. Amsterdam: North Holland; 2006.
Feys R. Modal logics. Paris: Gauthier-Villars; 1965.
Fitting M, Mendelsohn R. First order modal logic. Dordrecht: Kluwer; 1998.
Mints G. A short introduction to modal logic. Chicago: University of Chicago Press; 1992.
Atanassov K. Elements of intuitionistic fuzzy logics. Part II: Intuitionistic fuzzy modal logics. Adv Stud Contemp Math. 2002;5(1):1–13.
Atanassov K. Intuitionistic fuzzy sets. Heidelberg: Springer; 1999.
Atanassov K. A new topological operator over intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets. 2015;21(3):90–2.
Atanassov K. On intuitionistic fuzzy sets theory. Berlin: Springer; 2012.
Atanassov K. A short remark on intuitionistic fuzzy operators \(X_{a, b, c, d, e, f}\) and \(x_{a, b, c, d, e, f}\). Notes on Intuitionistic Fuzzy Sets. 2013;19(1):54–6.
Atanassov K. A property of the intuitionistic fuzzy modal logic operator \(X_{a, b, c, d, e, f}\). Notes on Intuitionistic Fuzzy Sets. 2015;21(1):1–5.
Atanassov K. Some operators on intuitionistic fuzzy sets. In: Kacprzyk J, Atanassov K, editors. Proceedings of the First International Conference on Intuitionistic Fuzzy Sets. Sofia, Oct 18-19, 1997; Notes on Intuitionistic Fuzzy Sets. 1997;3(4):28–33. http://ifigenia.org/wiki/issue:nifs/3/4/28-33.
Atanassov K. On one type of intuitionistic fuzzy modal operators. Notes on Intuitionistic Fuzzy Sets. 2005;11(5):24–28. http://ifigenia.org/wiki/issue:nifs/11/5/24-28.
Atanassov K. The most general form of one type of intuitionistic fuzzy modal operators. Notes on Intuitionistic Fuzzy Sets. 2006;12(2):36–38. http://ifigenia.org/wiki/issue:nifs/12/2/36-38.
Atanassov K. Some properties of the operators from one type of intuitionistic fuzzy modal operators. Adv Stud Contemp Math. 2007;15(1):13–20.
Atanassov K. The most general form of one type of intuitionistic fuzzy modal operators. Part 2. Notes on Intuitionistic Fuzzy Sets. 2008;14(1):27–32. http://ifigenia.org/wiki/issue:nifs/14/1/27-32.
Dencheva K. Extension of intuitionistic fuzzy modal operators and . Proceedings of the Second Int. IEEE Symposium: Intelligent Systems, Varna, June 22–24, vol. 3; 2004. p. 21–22.
Çuvalcioǧlu G. Some properties of \(E_{\alpha ,\beta }\) operator. Adv Stud Contemp Math. 2007;14(2):305–310.
Atanassov K, Çuvalcioǧlu G, Atanassova V. A new modal operator over intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets. 2014;20(5):1–8.
Atanassov, K. On Pseudo-fixed Points of the Intuitionistic Fuzzy Quantifiers and Operators, Proceedings of the 8th European Symposium on Computational Intelligence and Mathematics, Sofia, Bulgaria, 5–8 October 2016:66–76.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Atanassov, K.T. (2017). Intuitionistic Fuzzy Modal Logics. In: Intuitionistic Fuzzy Logics. Studies in Fuzziness and Soft Computing, vol 351. Springer, Cham. https://doi.org/10.1007/978-3-319-48953-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-48953-7_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48952-0
Online ISBN: 978-3-319-48953-7
eBook Packages: EngineeringEngineering (R0)