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Thomas Vetterlein, publications


Peer-reviewed journal articles

My PhD thesis (supervisor: Prof. A. Dvurečenskij) consists of the articles [J2], [J3], [J5], [J6], [J8], [J9], [J10], and [B1].

(The articles' numbers are linked to the journals' online publication, if existent.)
[J1] Pseudoeffect algebras,
J. Electr. Eng. 51 (2000), 96 - 98.
(Zbl 0972.03061)
[J2] (with A. Dvurečenskij) Pseudoeffect algebras. I. Basic properties,
Int. J. Theor. Phys. 40 (2001), 685 - 701.
(Zbl 0994.81008, MR1831592)
[J3] (with A. Dvurečenskij) Pseudoeffect algebras. II. Group representations,
Int. J. Theor. Phys. 40 (2001), 703 - 726.
(Zbl 0994.81009, MR1831593)
[J4] Generalized pseudoeffect algebras and related quantum structures,
J. Electr. Eng. 52 (2001), 71 - 73.
(Zbl 1048.81014)
[J5] (with A. Dvurečenskij) Congruences and states on pseudoeffect algebras,
Found. Phys. Letters 14 (2001), 425 - 446.
[J6] (with A. Dvurečenskij) Algebras in the positive cone of po-groups,
Order 19 (2002), 127 - 146.
(Zbl 1012.03064, MR1922915)
[J7] Nearly commutative pseudoeffect algebras,
J. Electr. Eng. 53 (2002), 94 - 96.
(Zbl 1037.03053)
[J8] (with A. Dvurečenskij) Infinitary lattice and Riesz properties for pseudoeffect algebras and po-groups,
J. Aust. Math. Soc. 75 (2003), 295 - 311.
(Zbl 1044.06008, MR2015319)
[J9] Existence of states on PE-algebras,
Int. J. Theor. Phys. 42 (2003), 673 - 695.
(Zbl 1044.81011, MR2003096)
[J10] (with A. Dvurečenskij) Archimedeaness and the MacNeille completion of pseudoeffect algebras and po-groups,
Algebra Univers. 50 (2003), 207 - 230.
(Zbl 1092.03034MR2037527)
[J11] (with A. Dvurečenskij) On pseudoeffect algebras which can be covered by pseudo-MV algebras,
Demonstr. Math. 36 (2003), 261 - 282.
(Zbl 1039.03049, MR1984338)
[J12] Weak effect algebras,
J. Electr. Eng. 54 (2003), 61 - 64.
(Zbl 1062.03065)
[J13] (with A. Dvurečenskij) Non-commutative algebras and quantum structures,
Int. J. Theor. Phys. 43 (2004), 1599-1612.
(Zbl 1075.81010, MR2108297)
[J14] BL-algebras and quantum structures,
Math. Slovaca 54 (2004), 127 - 141.
(Zbl 1065.03049, MR2074210, pdf)
[J15] BL-algebras and effect algebras,
Soft Comput. 9 (2005), 557 - 564.
(Zbl 1094.0305, pdf)
[J16] Partial algebras for Łukasiewicz logics and its extensions,
Arch. Math. Logics 44 (2005), 913 - 933.
(Zbl 1081.03067, MR2192162, pdf)
[J17] t-norms induced by metrics on boolean algebras,
Soft Comput. 10 (2006), 995 - 1000.
(Zbl 1108.03054, pdf)
[J18] Spline interpolation between hyperspaces of convex of fuzzy sets,
Fuzzy Sets Syst. 157 (2006), 2472 - 2481.
(Zbl 1101.41009, MR2254176, pdf)
[J19] (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.
(Zbl 1137.93308, MR2224971, pdf)
[J20] (with M. Navara) Defuzzification using Steiner points,
Fuzzy Sets Syst. 157 (2006), 1455 - 1462.
(Zbl 1104.03057, MR2234553, pdf)
[J21] Weak effect algebras,
Algebra Univers. 58 (2008), 129 - 143.
(Zbl 1143.0334, MR2386526, pdf)
[J22] Fuzzy logic as a logic of the expressive strength of information,
Soft Comput. 12 (2008), 479 - 485.
(Zbl 1140.03011, pdf)
[J23] Boolean algebras with an automorphism group: a framework for Łukasiewicz logic,
J. Mult.-Val. Log. Soft Comput. 14 (2008), 51 - 67.
(MR2456707, pdf)
[J24] Residuated lattices arising from equivalence relations on Boolean and Brouwerian algebras,
Math. Log. Q. 54 (2008), 350 - 367.
(Zbl 1182.03110, MR2435899, pdf)
[J25] A way to interpret Łukasiewicz Logic and Basic Logic,
Studia Logica 90 (2008), 407 - 423.
(Zbl 1216.03044, MR2470083, pdf)
[J26] Analytic calculi for logics of ordinal multiples of standard t-norms,
J. Log. Comput. 18 (2008), 35 - 57.
(Zbl 1139.03018MR2391428, pdf)
[J27] Regular left-continuous t-norms,
Semigroup Forum 77 (2008), 339 - 379.
(Zbl 1172.03039, MR2457325, pdf)
[J28] MTL-algebras arising from partially ordered groups,
Fuzzy Sets and Systems 161 (2010),  433 - 443.
(Zbl 1194.03056, MR2566252, pdf)
[J29] Pseudo-BCK algebras as partial algebas,
Information Sciences 180 (2010), 5101 - 5114.
(Zbl 1194.03056, MR2726680, pdf)
[J30] (with A. Ciabattoni) On the (fuzzy) logical content of CADIAG-2,
Fuzzy Sets and Systems, 161 (2010), 1941 - 1958.
(Zbl 1192.68680, MR2639422, pdf)
[J31] (with H. Mandl and K.-P. Adlassnig) Fuzzy Arden Syntax: a fuzzy programming language for medicine,
Artificial Intelligence in Medicine 49 (2010), 1 - 10.
(PMID 20167457, pdf)
[J32] Partial quantum logics revisited,
International Journal of General Systems 40 (2011), 23 - 38.
(Zbl 1210.81010, MR2747548, pdf)
[J33] Plausible reasoning and graded information: a unified approach,
Fuzzy Sets Syst. 197 (2012), 71 - 94.
(Zbl 1251.68249, MR2911341, pdf)
[J34] (with F. Esteva, R. Rodríguez, and Ll. Godo) Logics for approximate and strong entailment,
Fuzzy Sets Syst. 197 (2012), 59 - 70.
(Zbl 1251.03034, MR2911340, pdf)
[J35] Vagueness: where degree-based approaches are useful, and where we can do without,
Soft Computing 16 (2012), 1833 - 1844.
(Zbl 1275.03064, pdf)
[J36] (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.
(Zbl 1266.68174, MR3001225, pdf)
[J37] The construction of left-continuous t-norms: a geometric approach in two dimensions,
Fuzzy Sets Syst. 252 (2014), 1 - 24.
[J38] The approximation of left-continuous t-norms,
Fuzzy Sets Syst. 292 (2016), 411 - 423.
[J39] On positive commutative tomonoids,
Algebra Univers. 75 (2016), 381 - 404.
[J40] Totally ordered monoids based on triangular norms,
Commun. Algebra 43 (2015), 2643 - 2679.
[J41] (with M. Petrík) Rees coextensions of finite, negative tomonoids,
J. Log. Comput. 27 (2017), 337 - 356.
[J42] (with A. Zamansky) Reasoning with graded information: the case of diagnostic scales in healthcare,
Fuzzy Sets Syst. 298 (2016), 411 - 423.
[J43] Logic of approximate entailment in quasimetric spaces,
Int. J. Approx. Reasoning 64 (2015), 39 - 53.
[J44] Real coextensions as a tool for constructing triangular norms,
Information Sciences 348 (2016), 357 - 376.
[J45] A representation of finite, positive, commutative tomonoids,
J. of Mult.-Valued Logic & Soft Computing, to appear.
[J46] (with F. Esteva and Ll. Godo) Logic for approximate entailment in ordered universes of discourse,
Int. J. Approx. Reasoning 71 (2016), 50 - 63.
[J47] Logic of approximate entailment in quasimetric and in metric spaces,
Soft Comput. 21 (2017), 4953 - 4961.
[J48] (with J. Janda) The coextension of pomonoids and its application to triangular norms,

Book chapters

[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.
(Zbl 1012.03063, MR1865061)
[B2] Vagueness - a mathematician's perspective,
in: P. Cintula, C. Fermüller, Ll. Godo, P. Hájek (eds.), "Understanding vagueness"; 65 - 91.


[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.
[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.
[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.


Articles in conference proceedings

[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.
[P2] (with M. Navara) The Steiner centroid of fuzzy sets,
in: Proceedings IFSA 2005, 28. - 31. 7. 2005 in Peking; 1256 - 1258.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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).
[P11] 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.
[P12] A logic for approximate reasoning with a comparative connective,
Proceedings of the Workshop WL4AI at the 20th ECAI conference (Montpellier 2012); 77 - 81.
[P13] Tomonoid extensions: the key for the construction of t-norms,
Proceedings of the EUSFLAT conference (Milano 2013); 48 - 55.
[P14] (with M. Petrík) Algorithm to generate the Archimedean, finite, negative tomonoids,
Proceedings of the SCIS & ISIS conference (Fukuoka 2014).

[P15] Logic of prototypes and counterexample: possibilities and limits,
Proceedings of the EUSFLAT conference (Gijón 2015).
[P16] (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.

Technical Reports

[R1] (with H. Mandl and K.-P. Adlassnig) Vorschläge zur Spezifikation der Programmiersprache FuzzyArden, Technical Report, Medical University of Vienna 2009.


Lecture notes 

[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.

Reviews, referee reports

Up to now, I wrote >50 reviews for the Mathematical Reviews and >10 for the Mathematisches Zentralblatt.

Furthermore, I provided numerous reports on articles suggested for publication in international journals, namely for Fuzzy Sets and Systems, Soft Computing, Artificial Intelligence in Medicine, Information Sciences, Tatra Mountains Mathematical Publications, Mathematica Slovaca, two IEEE journals, Neural Computing and Applications, Archives for Mathematical Logics, Studia Logica, Journal of Logic and Computation, Acta Scientiarum Mathematicarum, Algebra Universalis, Semigroup Forum, Mathware and Soft Computing, International Journal of Theoretical Physics, Journal of the Australian Mathematical Society, and Kuwait Journal of Science and Engineering. In addition, there were reports on suggested book chapters, web articles, and numerous further reports on submitted conference contributions.