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Institute for Mathematical Methods in Medicine and Data Based Modeling
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Publications


[J1] Pseudoeffect algebras,
J. Electr. Eng. 51 (2000), 96 - 98.

 

[J2], opens an external URL in a new window (with A. Dvurečenskij) Pseudoeffect algebras. I. Basic properties,
Int. J. Theor. Phys. 40 (2001), 685 - 701.

 

[J3], opens an external URL in a new window (with A. Dvurečenskij) Pseudoeffect algebras. II. Group representations,
Int. J. Theor. Phys. 40 (2001), 703 - 726.

 

[J4] Generalized pseudoeffect algebras and related quantum structures,
J. Electr. Eng. 52 (2001), 71 - 73.

 

[J5], opens an external URL in a new window (with A. Dvurečenskij) Congruences and states on pseudoeffect algebras,
Found. Phys. Letters 14 (2001), 425 - 446.

 

[J6], opens an external URL in a new window (with A. Dvurečenskij) Algebras in the positive cone of po-groups,
Order 19 (2002), 127 - 146.

 

[J7] Nearly commutative pseudoeffect algebras,
J. Electr. Eng. 53 (2002), 94 - 96.

 

[J8], opens an external URL in a new window (with A. Dvurečenskij) Infinitary lattice and Riesz properties for pseudoeffect algebras and po-groups,
J. Aust. Math. Soc. 75 (2003), 295 - 311.

 

[J9], opens an external URL in a new window Existence of states on PE-algebras,
Int. J. Theor. Phys. 42 (2003), 673 - 695.

 

[J10], opens an external URL in a new window (with A. Dvurečenskij) Archimedeaness and the MacNeille completion of pseudoeffect algebras and po-groups,
Algebra Univers. 50 (2003), 207 - 230.

 

[J11], opens an external URL in a new window (with A. Dvurečenskij) On pseudoeffect algebras which can be covered by pseudo-MV algebras,
Demonstr. Math. 36 (2003), 261 - 282.

 

[J12] Weak effect algebras,
J. Electr. Eng. 54 (2003), 61 - 64.

 

[J13], opens an external URL in a new window (with A. Dvurečenskij) Non-commutative algebras and quantum structures,
Int. J. Theor. Phys. 43 (2004), 1599-1612.

 

[J14], opens an external URL in a new window BL-algebras and quantum structures,
Math. Slovaca 54 (2004), 127 - 141 (pdf, opens an external URL in a new window).

 

[J15], opens an external URL in a new window BL-algebras and effect algebras,
Soft Comput. 9 (2005), 557 - 564 (pdf, opens an external URL in a new window).

 

[J16], opens an external URL in a new window Partial algebras for Łukasiewicz logics and its extensions,
Arch. Math. Logics 44 (2005), 913 - 933 (pdf, opens an external URL in a new window).

 

[J17], opens an external URL in a new window t-norms induced by metrics on Boolean algebras,
Soft Comput. 10 (2006), 995 - 1000 (pdf, opens an external URL in a new window).

 

[J18], opens an external URL in a new window Spline interpolation between hyperspaces of convex of fuzzy sets,
Fuzzy Sets Syst. 157 (2006), 2472 - 2481 (pdf, opens an external URL in a new window).

 

[J19], opens an external URL in a new window (with M. Štĕpnička) Completing fuzzy if-then rule bases by means of smoothing splines,
Int. J. Uncertain. Fuzziness Knowl. Based Syst. 14 (2006), 235 - 244 (pdf, opens an external URL in a new window).

 

[J20], opens an external URL in a new window (with M. Navara) Defuzzification using Steiner points,
Fuzzy Sets Syst. 157 (2006), 1455 - 1462 (pdf, opens an external URL in a new window).

 

[J21], opens an external URL in a new window Weak effect algebras,
Algebra Univers. 58 (2008), 129 - 143 (pdf, opens an external URL in a new window).

 

[J22], opens an external URL in a new window Fuzzy logic as a logic of the expressive strength of information,
Soft Comput. 12 (2008), 479 - 485 (pdf, opens an external URL in a new window).

 

[J23], opens an external URL in a new window Boolean algebras with an automorphism group: a framework for Łukasiewicz logic,
J. Mult.-Val. Log. Soft Comput. 14 (2008), 51 - 67 (pdf, opens an external URL in a new window).

 

[J24], opens an external URL in a new window Residuated lattices arising from equivalence relations on Boolean and Brouwerian algebras,
Math. Log. Q. 54 (2008), 350 - 367 (pdf, opens an external URL in a new window).

 

[J25], opens an external URL in a new window A way to interpret Łukasiewicz Logic and Basic Logic,
Studia Logica 90 (2008), 407 - 423 (pdf, opens an external URL in a new window).

 

[J26], opens an external URL in a new window Analytic calculi for logics of ordinal multiples of standard t-norms,
J. Log. Comput. 18 (2008), 35 - 57 (pdf, opens an external URL in a new window).

 

[J27], opens an external URL in a new window Regular left-continuous t-norms,
Semigroup Forum 77 (2008), 339 - 379 (pdf, opens an external URL in a new window).

 

[J28], opens an external URL in a new window MTL-algebras arising from partially ordered groups,
Fuzzy Sets and Systems 161 (2010),  433 - 443 (pdf, opens an external URL in a new window).

 

[J29], opens an external URL in a new window Pseudo-BCK algebras as partial algebas,
Information Sciences 180 (2010), 5101 - 5114 (, opens an external URL in a new windowpdf, opens an external URL in a new window).

 

[J30], opens an external URL in a new window (with A. Ciabattoni) On the (fuzzy) logical content of CADIAG-2,
Fuzzy Sets and Systems, 161 (2010), 1941 - 1958 (pdf, opens an external URL in a new window).

 

[J31], opens an external URL in a new window (with H. Mandl and K.-P. Adlassnig) Fuzzy Arden Syntax: a fuzzy programming language for medicine,
Artificial Intelligence in Medicine 49 (2010), 1 - 10 (pdf, opens an external URL in a new window).

 

[J32], opens an external URL in a new window Partial quantum logics revisited,
International Journal of General Systems 40 (2011), 23 - 38 (, opens an external URL in a new windowpdf, opens an external URL in a new window).

 

[J33], opens an external URL in a new window Plausible reasoning and graded information: a unified approach,
Fuzzy Sets Syst. 197 (2012), 71 - 94 (pdf, opens an external URL in a new window).

 

[J34], opens an external URL in a new window (with F. Esteva, R. Rodríguez, and Ll. Godo) Logics for approximate and strong entailment,
Fuzzy Sets Syst. 197 (2012), 59 - 70 (pdf, opens an external URL in a new window).

 

[J35], opens an external URL in a new window Vagueness: where degree-based approaches are useful, and where we can do without,
Soft Computing 16 (2012), 1833 - 1844 (pdf, opens an external URL in a new window).

 

[J36], opens an external URL in a new window (with A. Ciabattoni, D. Picado Muiño, M. El-Zekey) Formal approaches to rule-based systems in medicine: the case of CADIAG-2,
Int. J. Approx. Reasoning 54 (2013), 132 - 148 (pdf, opens an external URL in a new window).

 

[J37, opens an external URL in a new window] The construction of left-continuous t-norms: a geometric approach in two dimensions,
Fuzzy Sets Syst. 252 (2014), 1 - 24 (pdf, opens an external URL in a new window).

 

[J38], opens an external URL in a new window Logic of approximate entailment in quasimetric spaces,
Int. J. Approx. Reasoning 64 (2015), 39 - 53 (pdf, opens an external URL in a new window).

 

[J39], opens an external URL in a new window Totally ordered monoids based on triangular norms,
Commun. Algebra 43 (2015), 2643 - 2679 (pdf, opens an external URL in a new window).

 

[J40] , opens an external URL in a new windowThe approximation of left-continuous t-norms,
Fuzzy Sets Syst. 292 (2016), 411 - 423 (pdf, opens an external URL in a new window).

 

[J41], opens an external URL in a new window On positive commutative tomonoids,
Algebra Univers. 75 (2016), 381 - 404 (pdf, opens an external URL in a new window).

 

[J42], opens an external URL in a new window (with A. Zamansky) Reasoning with graded information: the case of diagnostic scales in healthcare,
Fuzzy Sets Syst. 298 (2016), 411 - 423 (pdf, opens an external URL in a new window).

 

[J43], opens an external URL in a new window Real coextensions as a tool for constructing triangular norms,
Information Sciences 348 (2016), 357 - 376 (pdf, opens an external URL in a new window).

 

[J44], opens an external URL in a new window (with F. Esteva and Ll. Godo) Logic for approximate entailment in ordered universes of discourse,
Int. J. Approx. Reasoning 71 (2016), 50 - 63 (pdf, opens an external URL in a new window).

 

[J45], opens an external URL in a new window (with M. Petrík) Rees coextensions of finite, negative tomonoids,
J. Log. Comput. 27 (2017), 337 - 356 (pdf, opens an external URL in a new window).

 

[J46], opens an external URL in a new window A representation of finite, positive, commutative tomonoids,
J. of Mult.-Valued Logic & Soft Computing 29 (2017), 83 - 104 (pdf, opens an external URL in a new window).

 

[J47], opens an external URL in a new window Logic of approximate entailment in quasimetric and in metric spaces,
Soft Comput. 21 (2017), 4953 - 4961 (pdf, opens an external URL in a new window).

 

[J48], opens an external URL in a new window (with J. Janda) The coextension of pomonoids and its application to triangular norms,
Quaest. Math. 42 (2019), 319 - 345 (pdf, opens an external URL in a new window).

 

[J49], opens an external URL in a new window (with D. Kruml, J. Paseka) On the coextension of cut-continuous pomonoids,
Order 36 (2019), 271 - 290 (pdf, opens an external URL in a new window).

 

[J50], opens an external URL in a new window (with M. Petrík) Rees coextensions of finite tomonoids and free pomonoids,
Semigroup Forum 99 (2019), 345 - 367 (pdf, opens an external URL in a new window).

 

[J51], opens an external URL in a new window Orthogonality spaces of finite rank and the complex Hilbert spaces,
Int. J. Geom. Methods Mod. Phys. 16 (2019), 1950080 (pdf, opens an external URL in a new window).

 

[J52], opens an external URL in a new window Orthogonality spaces arising from infinite-dimensional complex Hilbert spaces,
Int. J. Theor. Phys. 60 (2021), 727 - 738 (pdf, opens an external URL in a new window).

 

[J53], opens an external URL in a new window Gradual transitivity in orthogonality spaces of finite rank,
Aequationes Math. 95 (2021), 483 - 503 (pdf, opens an external URL in a new window).

 

[J54], opens an external URL in a new window (with M. Pankov) A geometric approach to Wigner-type theorems,
Bull. London Math. Soc. 53 (2021), 1653 - 1662 (pdf, opens an external URL in a new window).

 

[J55], opens an external URL in a new window (with J. Paseka) Categories of orthogonality spaces,
J. Pure Appl. Algebra 226 (2022), 106859 (pdf, opens an external URL in a new window).

 

[J56], opens an external URL in a new window (with J. Paseka) Normal orthogonality spaces,
J. Math. Anal. Appl. 507 (2022), 125730 (pdf, opens an external URL in a new window).

 

[J57], opens an external URL in a new window Transitivity and homogeneity of orthosets and inner-product spaces over subfields of ℝ,
Geom. Dedicata 216 (2022), 216:36 (pdf, opens an external URL in a new window).
 

[J58] (with B. Lindenhovius) A characerisation of orthomodular spaces by Sasaki maps,
Int. J. Theor. Phys., to appear (arxiv, opens an external URL in a new window).
 

[J59] (with J. Paseka) Linear orthosets and orthogeometries,
Int. J. Theor. Phys., to appear (pdf, opens an external URL in a new window).
 

[J60] (with K. Emir and J. Paseka) Finitary prelinear and linear orthosets, submitted (pdf, opens an external URL in a new window).

 

[B1] (with A. Dvurečenskij) Generalized pseudoeffect algebras,
in: A. Di Nola, G. Gerla (eds.), "Lectures on Soft Computing and Fuzzy Logic",
Springer-Verlag, Berlin, Heidelberg 2001; 89 - 111.

 

[B2] Vagueness - a mathematician's perspective,
in: P. Cintula, C. Fermüller, Ll. Godo, P. Hájek (eds.), "Understanding vagueness", College Publication 2011; 65 - 91 (pdf, opens an external URL in a new window).

 

[B3] (with D. Picado Muiño, A. Ciabattoni) Towards an interpretation of the medical expert system CADIAG2; in: R. Seising, M. Tabacchi (eds.), "Fuzziness and Medicine: Philosophical Reflections and Application Systems in Health Care", Springer-Verlag, Berlin, Heidelberg 2013; 327 - 342 (pdf, opens an external URL in a new window).

 

[B4] Algebraic semantics: the structure of residuated chains; in: P. Cintula, C. Fermüller, C. Noguera (Eds.), "Handbook of Mathematical
Fuzzy Logic", vol. 3, College Publications, London 2015; 929 - 967 (pdf, opens an external URL in a new window).

 

[B5] (with M. Petrík) The semantic of fuzzy logics: two approaches to finite tomonoids, in: R. Mesiar, S. Saminger-Platz (Hg.), "On logical, algebraic, and probabilistic aspects of fuzzy set theory", Springer-Verlag, Berlin 2016, 83 - 108 (pdf, opens an external URL in a new window).

 

[P1] Smooth extensions of fuzzy if-then rule bases,
in: B. Reusch (ed.), "Computational intelligence. Theory and applications",
Proceedings 8th Fuzzy Days (Dortmund 2004), Springer-Verlag, Berlin 2005; 53 - 59 (pdf, opens an external URL in a new window).

 

[P2] (with M. Navara) The Steiner centroid of fuzzy sets,
in: Proceedings IFSA 2005, 28. - 31. 7. 2005 in Peking; 1256 - 1258 (pdf, opens an external URL in a new window).

 

[P3] Towards a Proof Theory of Basic Logic,
in: O. Castillo et al., Theoretical Advances and Applications of Fuzzy Logic and Soft Computing,
Proceedings IFSA (Cancún 2007), Springer-Verlag, Berlin 2007; 850 - 860 (pdf, opens an external URL in a new window).

 

[P4] Left-continuous t-norms as functional algebras,
in: M. Štěpnička, V. Novák, and U. Bodenhofer,
New Dimensions in Fuzzy Logic and Related Technologies,
Proceedings of the 6th EUSFLAT conference (Ostrava 2007); 37 - 43 (pdf, opens an external URL in a new window).

 

[P5] (with M. Navara and J. Liang) Different representations of fuzzy vectors,
in: Claudio Sossai Gaetano Chemello (eds.), Symbolic and Quantitative Approaches to Reasoning with Uncertainty,
Proceedings of the 10th ECSQARU (Verona 2009); 700 - 711 (pdf, opens an external URL in a new window).

 

[P6] (with K.-P. Adlassnig) The medical expert system Cadiag-2, and the limits of reformulation by means of formal logics,
in: G. Schreier et al. (eds.), eHealth 2009 - Health Informatics meets eHealth - von der Wissenschaft zur Anwendung und zurück,
Tagungsband der eHealth 2009 & eHealth Benchmarking 2009 (Vienna 2009); 123 - 128 (doc, opens an external URL in a new window).

 

[P7] (with K.-P. Adlassnig) T-norm-based fuzzy logics and logics for reasoning under vagueness,
in: J. P. Carvalho, D. Dubois, U. Kaymak and J. M. C. Sousa,
Proceedings of the Joint EUSFLAT and IFSA conference (Lisbon 2009); 1085 - 1090 (pdf, opens an external URL in a new window).

 

[P8] (with A. Ciabattoni and K.-P. Adlassnig) A formal logical framework for Cadiag-2,
in: K.-P. Adlassnig, B. Blobel, J. Mantas, and I. Mašić, Medical Informatics in a Healthy and United Europe,
Proceedings of the 30th MIE conference (Sarajevo 2009); 648 - 652 (pdf, opens an external URL in a new window).

 

[P9] (with F. Esteva, Ll. Godo, R. O. Rodríguez) On the logics of similarity-based approximate and strong entailment,
Actas del XV Congreso Español Sobre Tecnologías y Logica Fuzzy (Proceedings of the 15th  Spanish Congress on Fuzzy Logic and Technology) (Huelva 2010); 187 - 192 (pdf, opens an external URL in a new window).

 

[P10] (with H. Mandl, K.-P. Adlassnig) Processing Gradual Information with Fuzzy Arden Syntax,
13th World Congress on Medical and Health Informatics (MEDINFO) (Cape Town 2010) (pdf, opens an external URL in a new window).

 

[P11], opens an external URL in a new window A logic of the similarity with prototypes and its relationship to fuzzy logic,
Proceedings of the EUSFLAT-LFA conference (Aix-les-Bains 2011); 196 - 202 (pdf, opens an external URL in a new window).

 

[P12] A logic for approximate reasoning with a comparative connective,
Proceedings of the Workshop WL4AI at the 20th ECAI conference (Montpellier 2012); 77 - 81 (pdf, opens an external URL in a new window).

 

[P13], opens an external URL in a new window Tomonoid extensions: the key for the construction of t-norms,
Proceedings of the EUSFLAT conference (Milano 2013); 48 - 55 (pdf, opens an external URL in a new window).

 

[P14] (with M. Petrík) Algorithm to generate the Archimedean, finite, negative tomonoids,
Proceedings of the SCIS & ISIS conference (Fukuoka 2014) (pdf, opens an external URL in a new window).

 

[P15], opens an external URL in a new window Logic of prototypes and counterexample: possibilities and limits,
Proceedings of the EUSFLAT conference (Gijón 2015) (pdf, opens an external URL in a new window).

 

[P16], opens an external URL in a new window (with M. Petrík) An algorithm for generating finite totally ordered monoids,
in: J.P. Carvalho, M.-J. Lesot, U. Kaymak, S. Vieira, B. Bouchon-Meunier, R.R. Yager, Information Processing and Management of Uncertainty in Knowledge-Based Systems,
Proceedings of IPMU (Juni 2016, Eindhoven), Springer-Verlag 2016; 532 - 543 (pdf, opens an external URL in a new window).

 

[P17], opens an external URL in a new window Orthogonality spaces allowing gradual transitions,
Proceedings of the EUSFLAT conference (Prague 2019), 192 - 197 (pdf, opens an external URL in a new window).

 

[P18] (with J. Paseka) Hilbert spaces reduced to their orthogonality relation,
Extended abstract for the International Conference on Quantum Physics and Logic (Paris/online 2020) (pdf, opens an external URL in a new window).

 

[P19], opens an external URL in a new window (with F. Esteva, Ll. Godo, R.O. Rodriguez) On Ruspini's Models of Similarity-Based Approximate Reasoning,
Proceedings of IPMU (Lisbon/online 2020) (pdf, opens an external URL in a new window).

 

[P20], opens an external URL in a new window (with K. Emir, D. Kruml, J. Paseka) Linear orthogonality spaces as a new approach to quantum logic,
Proceedings of the ISMVL (Nursultan/online 2021) (pdf, opens an external URL in a new window).
 

[LN1] t-normbasierte mehrwertige Logiken (t-norm based many-valued logics), University of Dortmund, 2004.

 

[LN2] Algebraische Aspekte der Logik (Algebraic aspects of logics), Johannes Kepler University, 2006.

 

[LN3] Fuzzysysteme (Fuzzy systems), Medical University of Vienna, 2008.

 

[LN4] Verbandstheorie (Lattice Theory), Johannes Kepler University, 2011.

 

[LN5] (with E. P. Klement and S. Saminger-Platz) Mathematische Grundlagen (Mathematical Foundations), Johannes Kepler University, 2011.

 

[LN6] (with S. Saminger-Platz) Diskrete Strukturen (Discrete Structures), Johannes Kepler University, 2013.

 

[LN7] Lattice Theory and Projective Geometry, Johannes Kepler University, 2019.

 

[LN8] Mathematik für die Statistik, part I--II, Johannes Kepler University, 2016.

 

[LN9] Mathematik für die Physik und Nawitec, part I--III, Johannes Kepler University, 2019-2022.

 

FoDOK entries