Abstract
The Haar measure on invariant state for fuzzy sets is constructed in a locally compact space. Moreover, the invariant state is studied on MV-algebra generated by a family of intuitionistic fuzzy sets, important as well as from the theoretical point of view as from the applications.
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Atanassov K (1999) Intuitionistic fuzzy sets. Physica, Heidelberg, pp 1–137
Ciungu L, Riečan B (2009) General form of probabilities on IF-sets, fuzzy logic and applications. In: Proceedings of the WILF Palermo, pp 101–107
Ciungu L, Riečan B (2010) Representation theorem for probabilities on IFS-events. Inf Sci 180:793–798
Čunderlíková K (2008) The individual ergodic theorem on IF events. Soft computing a fusion of foundations, methodologies and applications, generalized nets and related topics, vol I, 3360. EXIT, Warsaw
De SK, Biswas R, Roy AR (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets Syst 117(2):209–213
\(\check{\text{D}}\)urica M (2010) Hudetz entropy on IF events. Developments in fuzzy sets, intuitionistic fuzzy sets, generalized nets, and related topics, vol I. IBS PAN SRI PAS, Warsaw, pp 73–86
Halmos PR (1950) Measure theory. Van Nostrand, New York
Jurečková M, Riečan B (2005) On invariant observables and the individual ergodic theorem. Int J Theor Phys 4:1587–1597
Lašová L (2010) The individual ergodic theorem on IF events. Developments in fuzzy sets, intuitionistic fuzzy sets, generalized nets, and related topics, vol I. IBS PAN SRI PAS, Warsaw, pp 131–140
Markechová D, Riečan B, Rényi entropy and Rényi divergence in the intuitionistic fuzzy case. Entropy (to appear)
Markechová D, Stehlíková D, Tirpáková A (2016) The uniqueness of a left Haar measure in topological IP-loops. Mathematica Slovaca 66(5):1–8
Michalíková A Riečan B (2017) On the Lebesgue IF measure, notes on intuitionistic fuzzy sets. ISSN: 1310–4926, pp 8–12
Riečan B (2006) On a problem of Radko Mesiar: general form of IF-probabilities. Fuzzy Sets Syst 152:1485–1490
Riečan B (2009) Poincaré recurrence theorem in MV-algebras. In: Prov. IFSA/EUSFLAT congress Lisabon, pp 1880–1881
Riečan B (2012) In: Koleshko V (ed) Analysis of fuzzy logic models, intelligent systems. INTECH, London, pp 217–244
Riečan B (2013) Variations on a Poincaré theorem. Fuzzy Sets Syst 232:39–45
Schwarz Š (1957) On the existence of invariant measures on certain type of bicompact semigroups (in Russian). Czech Math J 7:165–182
Stehlíková B, Markechová D, Tirpáková A (2011) On the existence of a Haar measure in topological IP-loops. Kybernetika 47(5):740–754
Szmidt E, Kacprzyk J (2001) Intuitionistic fuzzy sets in some medical applications. Notes IFS 7(4):58–64
Zadeh L (1965) Fuzzy sets. Inf Control 8:338–358
Zadeh L (1968) Probability measures of fuzzy events. J Math Anal Appl 23:421–427
Acknowledgements
This work was supported by the Slovak Research and Development Agency under the contract No. APVV-0219-12.
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Michalíková, A., Riečan, B. On invariant IF-state. Soft Comput 22, 5043–5049 (2018). https://doi.org/10.1007/s00500-018-3278-7
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DOI: https://doi.org/10.1007/s00500-018-3278-7