Abstract:
The aim of this paper is to survey a class of logical formalizations of similarity-based reasoning models where similarity is understood as a graded notion of truthlikeness. We basically identify two different kinds of logical approaches that have been used to formalize fuzzy similarity reasoning: syntacticelly-oriented approaches based on a notion of approximate proof, and semantically-oriented approaches based on several notions of approximate entailments. In particular, for these approximate entailments we provide four different formalisations in terms of suitable systems of modal and conditional logics, including for each class a system of graded operators with classical semantics, as well as a system with many-valued operators. Finally, we also explore some nonmonotonic issues of similarity-based reasoning. © 2008, Springer International Publishing. All rights reserved.
Registro:
Documento: |
Artículo
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Título: | Logical approaches to fuzzy similarity-based reasoning: An overview |
Autor: | Godo, L.; Rodríguez, R.O. |
Filiación: | AI Research Institute, IIIA, Spanish National Research Council, CSIC, Bellaterra, 08193, Spain Computer Science Department, FCEyN, University of Buenos Aires, UBA, Buenos Aires, 1428, Argentina
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Año: | 2008
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Volumen: | 504
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Página de inicio: | 75
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Página de fin: | 128
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DOI: |
http://dx.doi.org/10.1007/978-3-211-85432-7_4 |
Título revista: | CISM International Centre for Mechanical Sciences, Courses and Lectures
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Título revista abreviado: | CISM Int. Cent. Mech. Sci. Courses Lectures
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ISSN: | 02541971
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02541971_v504_n_p75_Godo |
Referencias:
- Alchourrón, C., Gärdenfors, P., Makinson, D., On the logic of theory change: Partial meet contraction and revision function (1985) Journal Symbolic Logic, 50, pp. 510-530
- Apt, R.K., Logic Programming (1990) Handbook of Theoretical Computer Science, B, pp. 492-574. , In J. van Leeuwen (Ed.), Elsevier, Amsterdam
- Biacino, L., Gerla, G., Generated necessities and possibilities (1992) International Journal of Intelligent Systems, 7, pp. 445-454
- Biacino, L., Gerla, G., Logics with approximate premises (1998) International Journal of Intelligent Systems, 13, pp. 1-10
- Biacino, L., Gerla, G., Ying, M., Approximate Reasoning based on Similarity (2000) Mathematical Logic Quaterly, 46 (1), pp. 77-86
- Blandi, L., Godo, L., Rodríguez, R., A connection between similarity logic programming and Gödel modal logic (2005) Proc of EUSFLATLFA 2005, pp. 775-780. , Barcelona, Sept
- Bloch, I., Lang, J., Towards mathematical morpho-logics (2002) Proc of IPMU’2000. Revised Version in Technologies for Constructing Intelligent Systems, 2, pp. 367-380. , Springer-Verlag
- Bodenhofer, U., A note on approximate equality versus the Poincar paradox (2003) Fuzzy Sets and Systems, 133 (2), pp. 155-160
- Boixader, D., On the relationship between T-transitivity and approximate equality (2003) Fuzzy Sets and Systems, 133 (2), pp. 161-169
- Boixader, D., Jacas, J., ; Boixader, D., Jacas, J., Extensionality based approximate reasoning (1998) International Journal of Approximate Reasoning, 19, pp. 221-230
- Bou, F., Esteva, F., Godo, L., Rodríguez, R., On many-valued modal logics over finite residuated lattices. Manuscript in preparation (2007) Abstract Presented in TANCL’07 (Oxford, August 2007) and in IX Congreso Dr. Antonio Monteiro, , Bahía Blanca, May
- Bouchon-Meunier, B., Dubois, D., Godo, L., Prade, H., Fuzzy sets and possibility theory in approximate and plausible reasoning (1999) Fuzzy Sets in Approximate Reasoning and Information Systems, pp. 15-190. , J. Bezdek, D. Dubois, and H. Prade, editors, The Handbooks of Fuzzy Sets Series, Chapter 1
- Caicedo, X., Rodríguez, R., A Gödel similarity-based modal logic. Manuscript. A shortened version was published as “A Gödel modal logic” (2007) Proc of Logic, Computability and Randomness, p. 2004. , Córdoba, Argentina
- Carnap, R., Treatability and meaning (1937) Philosophy of Science, (3-4)
- Carnap, R., (1950) The Logical Foundations of Probability, , University Chicago Press, Chicago
- Chatalic, P., Froidevaux, C., Lattice-based graded logic: A multimodal approach (1992) Proceedings 8Th Conference on Uncertainty in Artificial Intelligence, pp. 33-40. , Stanford, CA
- Cignoli, R., D’Ottaviano, I.M.L., Mundici, D., (2000) Algebraic Foundations of Many-Valued Reasoning, Volume 7 of Trends in Logic — Studia Logica Library, , Kluwer Academic Publishers, Dordrecht
- De Cock, M., Kerre, E., On (Un)suitable fuzzy relations to model approximate equality (2003) Fuzzy Sets and Systems, 133 (2), pp. 137-153
- De Cock, M., Kerre, E., Why fuzzy-equivalence relations do not resolve the Poincar paradox, and related issues (2003) Fuzzy Sets and Systems, 133 (2), pp. 181-192
- Driankov, D., Doherty, P., A nonmonotonic fuzzy logic (1992) Fuzzy Logic for the Management of Uncertainty, , Eds. L. Zadeh and J. Kacprzyk, John Wiley & Sons
- Dubois, D., Belief structures, possibility theory and decomposable confidence measures (1986) Computers and Artificial Intelligence, 5, pp. 403-416
- Dubois, D., Esteva, F., Garcia, P., Godo, L., Lopez De Mántaras, R., Prade, H., Fuzzy set modelling in case-based reasoning (1998) International Journal of Intelligent Systems, pp. 345-373
- Dubois, D., Esteva, F., Garcia, P., Godo, L., Prade, H., Similarity-based consequente relations (1995) Symbolic and Quantitative Approaches to Reasoning and Uncertainty, Volume 946 of Lecture Note in Artificial Intelligence, pp. 168-174. , In Christine Froidevaux and Jürg Kohlas, editors, Fribourg, Switzerland, Springer
- Dubois, D., Esteva, F., Garcia, P., Godo, L., Prade, H., A logical approach to interpolation based on similarity relations (1997) International Journal of Approximate Reasoning, 17, pp. 1-36
- Dubois, D., Lang, J., Prade, H., Possibilistic logic (1994) Handbook of Logic in Artificial Intelligence and Logic Programming. Volume 3: Nonmonotonic Reasoning and Uncertain Reasoning, pp. 439-513. , D.M. Gabbay, C.J. Hogger, and J.A. Robinson, editors, Oxford University Press
- Dubois, D., Prade, H., An introduction to possibilistic and fuzzy logics (1988) Non-Standard Logics for Automatic Reasoning, , P. Smets, A. Mamdani, D. Dubois, and H. Prade, editors, Academic Press
- Dubois, D., Prade, H., Fuzzy sets in approximate reasoning, part 1: Inference with possibility distributions (1991) Fuzzy Sets Ans Systems, 40, pp. 143-202
- Dubois, D., Prade, H., Fuzzy sets in approximate reasoning, part 2: Logical approaches (1991) Fuzzy Sets and Systems, 40, pp. 203-244
- Dubois, D., Prade, H., Possibilistic logic, preferencial models, non-monotonicity and related issues (1991) Proc of IJCAI’91, pp. 419-424
- Dubois, D., Prade, H., Belief change and possibility theory (1992) Peter Gärdenfors, Editor, Belief Revision, Volume 29 of Cambridge Tracts in Theoretical Computer Science, pp. 142-182. , Cambridge University Press
- Dubois, D., Prade, H., Fuzzy sets and probability: Misunderstandings, bridges and gaps (1993) Second IEEE International Conference on Fuzzy Systems, Volume II, pp. 501-506. , San Francisco, California
- Dubois, D., Prade, H., Similarity-based approximate reasoning (1994) Computacional Intelligence: Imitating Life, pp. 69-80. , In J.M. Zurada, R.J. MarksII, and C.J. Robinson, editors, IEEE Press, New York
- Dubois, D., Prade, H., ; Dubois, D., Prade, H., Possibility theory, probability theory and multiple-valued logics: A clarification (2001) Annals of Mathematics and Artificial Intelligence, 32, pp. 35-66
- Dubois, D., Prade, H., Bezdek, J., Introduction: Fuzzy sets in approximate reasoning and intelligent information systems technology (1999) Fuzzy Sets in Approximate Reasoning and Information Systems, the Handbooks of Fuzzy Sets Series, pp. 1-13. , J. Bezdek, D. Dubois, and H. Prade, editors, Kluwer Academic Publishers
- Esteva, F., Garcia, P., Godo, L., ; Esteva, F., Garcia, P., Godo, L., Rodriguez, R., A modal account of similarity-based reasoning (1997) International Journal of Approximate Reasoning, 16 (3-4), pp. 235-261
- Esteva, F., Gispert, J., Godo, L., Noguera, C., Adding truthconstants to continuous t-norm based logics: Axiomatization and completeness results (2007) Fuzzy Sets and Systems, 158, pp. 597-618
- Esteva, F., Godo, L., Putting Lukasiewicz and product logic together (1999) Mathware and Soft Computing, 4 (2-3), pp. 219-234
- Esteva, F., Godo, L., Hájek, P., Navara, M., Residuated fuzzy logics with an involutive negation (2000) Archive for Mathematical Logic, 39, pp. 103-124
- Esteva, F., Godo, L., Montagna, F., Equational characterization of the subvarieties of BL generated by t-norm algebras (2004) Studia Logica, 76, pp. 161-200
- Esteva, F., Godo, L., Noguera, C., On Rational Weak Nilpotent Minimum Logics (2006) Journal of Multiple-Valued Logic and Soft Computing, 12 (1-2), pp. 9-32
- Fariñas Del Cerro, L., Herzig, A., (1991) A Modal Analysis of Possibility Theory. Volume 535 of Lecture Notes in Computer Sciences, pp. 11-18. , Springer Verlag, Berlin
- Fariñas Del Cerro, L., Herzig, A., Lang, J., From ordering-based nonmonotonic reasoning to conditional logics (1994) Artificial Intelligence, 66, pp. 375-394
- Fattorosi-Barnaba, M., De Caro, F., Graded modalities (1985) Studia Logica, 2, pp. 197-221
- Fine, K., So many possible worlds (1972) Notre Dame Journal of Formal Logic, 13 (4), pp. 516-520
- Fitting, M., Many-valued modal logics (1991) Fundamenta Informaticae, 15, pp. 235-254
- Fitting, M., Many-valued modal logics, II (1992) Fundamenta Informaticae, 17, pp. 55-73
- Fitting, M., Tableaus for many-valued modal logic (1995) Studia Logica, 55 (1), pp. 63-87
- Formato, F., Gerla, G., Sessa, M.I., (2000) Similarity-Based Unification.Fundamenta Informaticae, 40, pp. 1-22
- Gärdenfors, P., (1988) Knowledge in Flux: Modeling the Dynamics of Epistemic States, , The MIT Press, Cambridge
- Gärdenfors, P., ; Gärdenfors, P., Makinson, D., Relations between the logic of theory change and nonmonotonic logic (1991) Lecture Notes in Artificial Intelligence, 465, pp. 185-205. , A. Furman and M. Morreau, editors, Springer Verlag
- Gärdenfors, P., Makinson, D., Nonmonotonic inference based on expections (1994) Artificial Intelligence, 65, pp. 197-245
- Geffner, H., On the logic of defaults (1988) Proc of the 7Th. AAAI National Conference on Artificial Intelligence, pp. 449-454. , St. Paul
- Gerla, G., ; Gerla, G., Sessa, M.I., Similarity Logic and Similarity PROLOG Proc. Joint EUROFUSE-SIC99 International Conference, pp. 367-372. , 25-28 May 1999, Budapest, Hungary
- Gerla, G., Sessa, M.I., Similarity in Logic Programming (1999) Fuzzy Logic and Soft Computing, pp. 19-31. , G. Chen, M. Ying, K.-Y. Cai (Eds.), Kluwer Acc. Pub., Norwell
- Goble, F.L., Grades of modality (1970) Logique Et Analyse, 51, pp. 323-334
- Gödel, K., Zum intuitionistischen aussgenkalkül (1932) Klasse, 69, pp. 65-66
- Godo, L., Hájek, P., Esteva, F., A fuzzy modal logic for belief functions (2003) Fundamenta Informaticae, 57 (2-4), pp. 127-146
- Godo, L., Rodríguez, R., A Fuzzy Modal Logic for Similarity Reasoning (1999) Fuzzy Logic and Soft Computing, Guoqing Chen, pp. 33-48. , Mingsheng Ying and Kai-Yuan Cai eds., Kluwer
- Godo, L., Rodríguez, R., Graded similarity-based semantics for nonmonotonic inferences (2002) Annals of Mathematics and Artificial Intelligence, 34, pp. 89-105
- Gottwald, S., (2001) A Treatise on Many-Valued Logics, Studies in Logic and Computation, 9. , Research Studies Press Ltd., Baldock, UK
- Gottwald, S., Hájek, P., Triangular norm based mathematical fuzzy logic (2005) Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular Norms, pp. 275-300. , In Erich Peter Klement and Radko Mesiar, editors, Elsevier, Amsterdam
- Hájek, P., (1998) Metamathematics of Fuzzy Logic., Volume 4 of Trends in Logic-Studia Logica Library, , Kluwer Academic Publishers, The Netherlands
- Hájek, P., Making fuzzy description logic more general (2005) Fuzzy Sets and Systems, 154, pp. 1-15
- Hájek, P., Godo, L., Esteva, F., Fuzzy logic and probability (1995) Proceedings of the 11Th. Conference of Uncertainty in Artificial Intelligence, pp. 237-244. , Morgan Kaufmann
- Hájek, P., Harmancová, D., A many-valued modal logic (1996) Proc. IPMU’96, pp. 1021-1024
- Halpern, J., (2003) Reasoning about Uncertainty, , The MIT Press
- Hansoul, G., Teheux, B., (2006) Completeness Results for Many-Valued Lukasiewicz Modal Systems and Relational Semantics, , http://arvix.org/abs/math/0612542
- Harmanec, D., Klir, G.J., On the modal logic interpretation of dempster-sshafer theory of evidence (1994) International Journal Uncertainty Fuzzyness Knowledge Based Systems, 9, pp. 941-951
- Hilpinen, R., Approximate truth and truthlikeness (1976) Formal Methods in the Methodology of the Empirical Sciences, pp. 19-42. , In M. Przelecki, K. Szaniawski and R. Wojcicki (eds.), Dordrecht: Reidel
- Van Der Hoek, W., Meyer, J.J., Modalities and (Un-)certainties (1992) Lectures Notes for School Summer of Linköping’92
- Van Der Hoek, W., De Rijke, M., (1991) Quantifiers and Modal Logic. ITLI Publ. Series LP-91-01, , University of Amsterdam, Netherlands
- Hüllermeier, E., Similarity-based inference as evidential reasoning (2001) Int. J. Approx. Reasoning, 26 (2), pp. 67-100
- Jani, V., Resemblance is a nearness (2003) Fuzzy Sets and Systems, 133 (2), pp. 171-173
- Klawonn, F., Fuzzy sets and vague environment (1994) Fuzzy Sets and Systems, 66, pp. 207-221
- Klawonn, F., Similarity based reasoning (1995) Proceedings of EUFIT’95, pp. 34-38. , Aachen (Germany), August 28-31
- Klawonn, F., Should fuzzy equality and similarity satisfy transitivity? Comments on the paper by M. De Cock and E. Kerre (2003) Fuzzy Sets and Systems, 133 (2), pp. 175-180
- Klawonn, F., Castro, J.L., Similarity in fuzzy reasoning (1995) Mathware & Soft Computing, (2), pp. 197-228
- Klawonn, F., Gebhardt, J., Kruse, R., Fuzzy control on the basis of equality relations with an example from idle speed control (1995) IEEE Transactions on Fuzzy Systems, 3 (3), pp. 336-350
- Klawonn, F., Kruse, R., Equality relations as a basis for fuzzy control (1993) Fuzzy Sets and Systems, 54, pp. 147-156
- Klawonn, F., Novák, V., The relation between inference and interpolation in the framework of fuzzy systems (1996) Fuzzy Sets and Systems, 81, pp. 331-354
- Konikowska, B., A logic for reasoning about relative similarity (1997) Studia Logica, 58, pp. 185-226
- Kripke, S., A completeness theorem in modal logic (1959) Journal of Symbolic Logic, 24, pp. 1-14
- Kripke, S., Semantical analysis of modal logic (1959) Journal of Symbolic Logic, 24, pp. 323-324
- Lehmann, D., Stereotypical reasoning: Logical properties (1998) Logic Journal of the IGPL, 6 (1), pp. 49-58
- Lewis, D., (1973) Contrafactuals, , Oxford Basil Blackwell, London
- Liau, C.-J., Possibilistic residuated implication logics with applications (1998) International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 6 (4), pp. 365-385
- Liau, C.-J., Lin, B.I.-P., Qualitative modal logic and possibilistic reasoning (1992) Proceedings of ECAI’92, pp. 43-47. , B. Newmann, editor, John Willey & Sons ltd
- Liau, C.-J., Lin, B.I.-P., A theoretical investigation into possibilistic reasoning (1995) Fuzzy Sets and Systems, 75, pp. 355-363
- Liau, C.-J., Lin, B.I.-P., Possibilistic reasoning—a minisurvey and uniform semantics (1996) Artificial Intelligence, 88, pp. 163-193
- Lindström, S., Rabinowicz, W., ; Makinson, D., General patterns in nonmonotnic reasoning (1994) Handbook of Logic in Artificial Inteligence and Logic Programming, Volume 4 of Nonmonotonic Reasoning and Uncertain Reasoning, pp. 35-110. , In D.M. Gabbay, C.J. Hogger, J.A. Robinson, and D. Nute, editors, Clarendon Press, Oxford
- McDermott, D., A critic of pure reason (1987) Computational Intelligence, 3 (3), pp. 151-160
- Miller, D., On the comparison of false theories by their bases (1974) The British Journal for the Philosophy of Science, 25 (2), pp. 178-188
- Minsky, M., A framework for representation knowledge (1985) Reading in Knowledge Representation, pp. 246-262. , In R.J. Brachman and H.J. Levesque, editors, Morgan Kaufman, Los Altos
- Nicod, J., (1970) Geometry and Induction, , Routledge Press, London
- Niiniluoto, I., (1987) Truthlikeness, Volume 185 of Synthese Library, , D. Reidel Publishing Company, 1rt. edition
- Novák, V., (1990) On the Syntactico-Semantical Completeness of First-Order Fuzzy Logic (I) and (II). Kybernetika, (26), pp. 47-66
- Novák, V., Perfilieva, I., Močkoř, J., (1999) Mathematical Principles of Fuzzy Logic, , Kluwer, Dordrecht
- Oddie, G., Truthlikeness. The Stanford Encyclopedia of Philosophy, , http://plato.stanford.edu/archives/spr2007/entries/truthlikeness/, (Spring 2007 Edition) Edward N. Zalta (ed.)
- Ostermann, P., Many-valued modal propositional calculi (1988) Zeitschrift für Mathematische Logik Und Grundlagen Der Mathematik, 34 (4), pp. 343-354
- Panti, G., Multi-valued logics (1998) Quantified Representation of Uncertainty, Volume 1 of the Handbook of Defeasible Reasoning and Uncertainty Management Systems, pp. 25-74. , D. Gabbay and P. Smets, editors, Kluwer
- Pavelka, J., On the fuzzy logic I: Many valued rules and inference (1979) Math. Logik Grundlag. Math, (25), pp. 45-52
- Pearl, J., (1988) Probabilistic Reasoning in Intelligent Systems: Network of Plausible Inference. Morgan Kauffman, , Los Altos, Ca
- Resconi, G., Klir, G.J., Clair, U.S., Hierarchical uncertainty metatheory based upon modal logic (1992) International Journal of General Systems, (21), pp. 23-50
- Resconi, G., Klir, G.J., Clair, U., Harmanec, D., On the integration of uncertainty theories (1993) International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 1 (1), pp. 1-18
- Rodríguez, R.O., (2002) Aspectos Formales En El Razonamiento Basado En Relaciones De Similitud Borrosas, , Ph. D. Thesis, Technical University of Catalonia (UPC
- Rott, H., A nonmonotonic conditional logic for belief revision. Part 1: Semantics and logic of simple conditionals (1991) The Logic of Theory Change, Workshop, Lecture Notes in Artificial Intelligence, 465. , In Fuhrmann A. and M. Morreau, editors, Konstanz, FRG, Springer Verlag
- Ruspini, E., (1987) The Logical Foundations of Evidential Reasoning, , Technical Report 408, Artificial Inteligence Center, SRI International, Merlo Park, California
- Ruspini, E., On the semantics of fuzzy logic (1991) International Journal of Approximate Reasoning, 5, pp. 45-88
- Schlechta, K., (1997) Nonmonotonic Logics. Basic Concepts, Results, and Techniques, Lecture Notes in Artifical Intelligence, 1187. , Springer
- Sessa, M.I., ; Sessa, M.I., Approximate Reasoning by Similarity-based SLD Resolution (2002) Theoretical Computer Science, 275, pp. 389-426
- Suzuki, N.-Y., Kripke frame with graded accesibility and fuzzy possible world semantics (1997) Studia Logica, 59 (2), pp. 249-269
- Tarski, A., Methodology of deductive sciences (1956) Logics, Semantics, Metamathematics. Oxford University Press
- Thiele, H., On the definition of modal operators in fuzzy logic (1993) Proceedings of the 23Rd IEEE International Symposium on Multiple-Valued Logic, pp. 269-276. , In IEEE Computer Society Press, editor, Sacramento, California
- Tichý, P., On Popper’s definitions of verisimilitude (1974) The British Journal for the Philosophy of Science, 25, pp. 155-160
- Weston, T., Approximate truth (1987) Journal of Philosophical Logic, 16 (4), pp. 203-227
- Williamson, T., First order logics for comparative similarity (1988) Notre Dame Journal of Formal Logic, 29 (4), pp. 457-481
- Ying, M.-S., On standard models of fuzzy modal logics (1988) Fuzzy Sets and Systems, 26, pp. 357-363
- Ying, M.-S., A logic for approximate reasoning (1994) The Journal of Symbolic Logic, 53 (3), pp. 830-837
- Zadeh, L., Fuzzy sets (1965) Information and Control, (8), pp. 338-353
- Zadeh, L., Similarity relations and fuzzy orderings (1971) Information Sciences, 3, pp. 177-200
- Zadeh, L., Is probability theory sufficient for daeling with uncertainty in ia: A negative view (1986) Uncertainty in Artificial Intelligence, 9, pp. 103-116. , L.N. Karnal and J.F. Lemmer, editors, Elsevier Science Publishers
- Zadeh, L.,
Citas:
---------- APA ----------
Godo, L. & Rodríguez, R.O.
(2008)
. Logical approaches to fuzzy similarity-based reasoning: An overview. CISM International Centre for Mechanical Sciences, Courses and Lectures, 504, 75-128.
http://dx.doi.org/10.1007/978-3-211-85432-7_4---------- CHICAGO ----------
Godo, L., Rodríguez, R.O.
"Logical approaches to fuzzy similarity-based reasoning: An overview"
. CISM International Centre for Mechanical Sciences, Courses and Lectures 504
(2008) : 75-128.
http://dx.doi.org/10.1007/978-3-211-85432-7_4---------- MLA ----------
Godo, L., Rodríguez, R.O.
"Logical approaches to fuzzy similarity-based reasoning: An overview"
. CISM International Centre for Mechanical Sciences, Courses and Lectures, vol. 504, 2008, pp. 75-128.
http://dx.doi.org/10.1007/978-3-211-85432-7_4---------- VANCOUVER ----------
Godo, L., Rodríguez, R.O. Logical approaches to fuzzy similarity-based reasoning: An overview. CISM Int. Cent. Mech. Sci. Courses Lectures. 2008;504:75-128.
http://dx.doi.org/10.1007/978-3-211-85432-7_4