Additive generators of overlap functions

Advances in Soft Computing

Volumn 228, Issue , 2013, Pages 167-178

  Dimuro, Graçaliz Pereira ^a   Bedregal, Benjamín ^b  

^a FEDERAL UNIVERSITY OF RIO GRANDE   (Brazil)

^b FEDERAL UNIVERSITY OF RIO GRANDE DO NORTE   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

DECISION MAKING; EDUCATION; IMAGE PROCESSING;

ADDITIVE GENERATORS; AGGREGATION FUNCTIONS; BIVARIATE FUNCTIONS; FUZZY PREFERENCE RELATIONS; OVERLAP FUNCTIONS; SYSTEMATIC METHODOLOGY; UNIT SQUARES;

MATHEMATICAL OPERATORS;

EID: 84914163587     PISSN: 16153871     EISSN: 18600794     Source Type: Book Series    
DOI: 10.1007/978-3-642-39165-1_19     Document Type: Article

References (44)

1. Alsina, C., Frank, M.J., Schweizer, B.: Associative Functions: Triangular Norms and Copulas. World Scientific Publishing Company, Singapore (2006)
2. Beattie, A.R., Landsberg, P.T.: One-dimensional overlap functions and their application to auger recombination in semiconductors. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 258(1295), 486–495 (1960)
3. Bedregal, B.C., Dimuro, G.P., Bustince, H., Barrenechea, E.: New results on overlap and grouping functions (to appear, 2013)
4. Bedregal, B.C., Dimuro, G.P., Reiser, R.H.S.: An approach to interval-valued R-implications and automorphisms. In: Carvalho, J.P., Dubois, D., Kaymak, U., da Costa Sousa, J.M. (eds.) Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, IFSA/EUSFLAT, pp. 1–6 (2009)
5. Bedregal, B.C., Dimuro, G.P., Santiago, R.H.N., Reiser, R.H.S.: On interval fuzzy S-implications. Information Sciences 180(8), 1373–1389 (2010)
6. Beliakov, G., Bustince, H., Goswami, D.P., Mukherjee, U.K., Pal, N.R.: On averaging operators for Atanassov’s intuitionistic fuzzy sets. Information Sciences 181(6), 1116–1124 (2011)
7. Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners. STUDFUZZ, vol. 221. Springer, Heidelberg (2007)
8. Bustince, H., Fernández, J., Mesiar, R., Montero, J., Orduna, R.: Overlap index, overlap functions and migrativity. In: Proceedings of IFSA/EUSFLAT Conference, pp. 300–305 (2009)
9. Bustince, H., Fernandez, J., Mesiar, R., Montero, J., Orduna, R.: Overlap functions. Nonlinear Analysis 72(3-4), 1488–1499 (2010)
10. Bustince, H., Pagola, M., Mesiar, R., Hüllermeier, E., Herrera, F.: Grouping, overlaps, and generalized bientropic functions for fuzzy modeling of pairwise comparisons. IEEE Transactions on Fuzzy Systems 20(3), 405–415 (2012)
11. Deschrijver, G.: Additive and multiplicative generators in interval-valued fuzzy set theory. IEEE Transactions on Fuzzy Systems 15(2), 222–237 (2007)
12. Dimuro, G.P., Bedregal, B.C., Santiago, R.H.N., Reiser, R.H.S.: Interval additive generators of interval t-norms and interval t-conorms. Information Sciences 181(18), 3898–3916 (2011)
13. Dimuro, G.P., Bedregal, B.R.C., Reiser, R.H.S., Santiago, R.H.N.: Interval additive generators of interval T-norms. In: Hodges, W., de Queiroz, R. (eds.) WoLLIC 2008. LNCS (LNAI), vol. 5110, pp. 123–135. Springer, Heidelberg (2008)
14. Eskola, K.J., Vogt, R., Wang, X.N.: Nuclear overlap functions. International Journal of Modern Physics A 10(20-21), 3087–3090 (1995)
15. Faucett, W.M.: Compact semigroups irreducibly connected between two idempotents. Proceedings of the American Mathematical Society 6, 741–747 (1955)
16. Jurio, A., Bustince, H., Pagola, M., Pradera, A., Yager, R.R.: Some properties of overlap and grouping functions and their application to image thresholding. In: Fuzzy Sets and Systems (in press, corrected proof, 2013) (available online in January 2013)
17. Klement, E.P., Mesiar, R., Pap, E.: Quasi- and pseudo-inverses of monotone functions, and the construction of t-norms. Fuzzy Sets and Systems 104(1), 3–13 (1999)
18. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publisher, Dordrecht (2000)
19. Klement, E.P., Mesiar, R., Pap, E.: Triangular norms: Basic notions and properties. In: Klement, E.P., Mesiar, R. (eds.) Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, pp. 17–60. Elsevier, Amsterdam (2005)
20. Leventides, J., Bounas, A.: An approach to the selection of fuzzy connectives in terms of their additive generators. Fuzzy Sets and Systems 126(2), 219–224 (2002)
21. Ling, C.H.: Representation of associative functions. Publicationes Mathematicae Debrecen 12, 189–212 (1965)
22. Mayor, G., Monreal, J.: Additive generators of discrete conjunctive aggregation operations. IEEE Transactions on Fuzzy Systems 15(6), 1046–1052 (2007)
23. Mayor, G., Trillas, E.: On the representation of some aggregation functions. In: Proceedings of IEEE International Symposium on Multiple-Valued Logic, pp. 111–114. IEEE, Los Alamitos (1986)
24. Menger, K.: Statistical metrics. Proceedings of the National Academic of Sciences 28(12), 535–537 (1942)
25. Mesiarová, A.: Generators of triangular norms. In: Klement, E.P., Mesiar, R. (eds.) Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, pp. 95–111. Elsevier, Amsterdam (2005)
26. Mesiarová, A.: H-transformation of t-norms. Information Sciences 176(11), 1531–1545 (2006)
27. Mesiarová-Zemánková, A.: Ranks of additive generators. Fuzzy Sets and Systems 160(14), 2032–2048 (2009)
28. Monreal, E.P., Mesiar, R., Pap, E.: Additive generators of t-norms which are not necessarily continuous. In: Proceddings of the Fourth European Congress on Intelligent Techniques and Soft Computing – EUFIT 1996, vol. 1, pp. 60–73. ELITE-Foundation, Aachen (1996)
29. Mostert, P.S., Shields, A.L.: On the structure of semigroups on a compact manifold with boundary. Annals of Mathematics 65(1), 117–143 (1957)
30. Nguyen, H.T., Walker, E.A.: A First Course in Fuzzy Logic. Chapman & Hall/CRC, Boca Raton (2006)
31. Ouyang, Y.: On the construction of boundary weak triangular norms through additive generators. Nonlinear Analysis 66(1), 125–130 (2007)
32. Ouyang, Y., Fang, J., Zhao, Z.: A generalization of additive generator of triangular norms. International Journal of Approximate Reasoning 49(2), 417–421 (2008)
33. Povey, A.C., Grainger, R.G., Peters, D.M., Agnew, J.L., Rees, D.: Estimation of a lidar’s overlap function and its calibration by nonlinear regression. Applied Optics 51(21), 5130–5143 (2012)
34. Reiser, R.H.S., Bedregal, B.C., Santiago, R.N., Dimuro, G.P.: Analyzing the relationship between interval-valued D-implications and interval-valued QL-implications. TEMA – Tendencies in Computational and Applied Mathematics 11(1), 89–100 (2010)
35. Reiser, R.H.S., Dimuro, G.P., Bedregal, B.R.C., Santiago, R.H.N.: Interval valued QL-implications. In: Leivant, D., de Queiroz, R. (eds.) WoLLIC 2007. LNCS, vol. 4576, pp. 307–321. Springer, Heidelberg (2007)
36. Schweizer, B., Sklar, A.: Statistical metric spaces. Pacific Journal of Mathematics 10(1), 313–334 (1960)
37. Schweizer, B., Sklar, A.: Associative functions and statistical triangle inequalities. Publicationes Mathematicae Debrecen 8, 168–186 (1961)
38. Schweizer, B., Sklar, A.: Associative functions and abstract semigroups. Publicationes Mathematicae Debrecen 10, 69–81 (1963)
39. Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland, New York (1983)
40. Viceník, P.: Additive generators of non-continuous triangular norms. In: Rodabaugh, S.E., Klement, E.P. (eds.) Topological and Algebraic Structures in Fuzzy Sets, pp. 441–454. Kluwer, Dordrecht (2003)
41. Viceník, P.: Additive generators of associative functions. Fuzzy Sets and Systems 153(2), 137–160 (2005)
42. Viceník, P.: Additive generators of border-continuous triangular norms. Fuzzy Sets and Systems 159(13), 1631–1645 (2008)
43. Viceník, P.: Intersections of ranges of additive generators of associative functions. Tatra Mountains Mathematical Publications 40, 117–131 (2008)
44. Viceník, P.: On a class of generated triangular norms and their isomorphisms. Fuzzy Sets and Systems 161(10), 1448–1458 (2010)