Negation and affirmation: The role of involutive negators

Soft Computing

Volumn 11, Issue 7, 2007, Pages 647-654

  Maes, Koen C ^a   De Baets, Bernard ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

Affirmation; Automorphism; Coxeter group; Involutive negator; Negation; Strict negator

Indexed keywords

EID: 33847232551     PISSN: 14327643     EISSN: 14337479     Source Type: Journal    
DOI: 10.1007/s00500-006-0127-x     Document Type: Article

References (27)

1. Batyrshin I (2003) On the structure of involutive, contracting and expanding negations. Fuzzy Sets Syst 139:661-672
2. Batyrshin I, Wagenknecht M (1997) Noninvolutive negations on [0,1]. J Fuzzy Math 5:997-1010
3. Batyrshin I, Wagenknecht W (1998) Contracting and expanding negations on [0,1]. J Fuzzy Math 6:133-140
4. Calvo T, Kolesárová A, Komorníková M, Mesiar R (2002) Aggregation operators: Properties, classes and construction methods, ser. studies in fuzziness and soft computing, vol 97. Physica-Verlag, Heidelberg, pp 3-104
5. Choquet G (1954) Theory of capacities. Annales de l'Institut Fourier 5:131-295
6. De Baets B (1999) Idempotent uninorms. Eur J Oper Res 118:631-642
7. De Cooman G, Kerre EE (1994) Order norms on bounded partially ordered sets. J Fuzzy Math 2:281-310
8. Dubois D, Prade H (1988) Possibility theory: An approach to computerised processing of uncertainty. Plenum Press, New York
9. Esteva F, Domingo X (1980) Sobre funciones de negación en [0,1]. Stochastica 4:141-166
10. Fodor J (1993) A new look at fuzzy connectives. Fuzzy Sets Syst 57:141-148
11. Hájek P (1998) Metamathematics of fuzzy logic, ser. trends in logic, vol 4. Kluwer, Dordrecht
12. Higashi M, Klir G (1982) On measures of fuzziness and fuzzy complements. Int J Gen Syst 8:169-180
13. Klement E-P, Mesiar R, Pap E (2000) Triangular norms, ser. trends in logic, vol 8. Kluwer, Dordrecht
14. Maes K, De Baets B (2005) Isomorphic continuous connectives in fuzzy logic. J Intell Fuzzy Syst 16:273-279
15. Maes KC, De Baets B (2006) Orthosymmetrical monotone functions. B Belg Math Soc Sim (in press)
16. Mayor G (1994) Sugeno's negations and t-norms. Mathware Soft Comput 1:93-98
17. Mayor G, Calvo T (1994) Fractal negations. Mathware Soft Comput 3:277-283
18. Mesiar R, Rückschlossová T (2004) Characterization of invariant aggregation operators. Fuzzy Sets Syst 142:63-73
19. Nguyen H, Walker E (2000) A first course in fuzzy logic, 2nd edn. Chapman & Hall/CRC, London
20. Ovchinnikov S (1983) General negations in fuzzy set theory. J Math Anal Appl 92:234-239
21. Ovchinnikov S, Dukhovny A (2000) Integral representation of invariant functionals. J Math Anal Appl 244:228-232
22. Trillas E (1979) Sobre funciones de negación en la teoría de conjuntos difusos. Stochastica 3:47-59
23. Trillas E, Rodríguez A, Cubillo S (1994) Ovchinnikov's automorphisms revisited. Mathware Soft Comput 1:83-92
24. Wagenknecht M, Batyrshin I (1998a) On negations generated by compensations. J Fuzzy Math 6:141-150
25. Wagenknecht M, Batyrshin I (1998b) Fixed point properties of fuzzy negations. J Fuzzy Math 6:975-981
26. Wangming W (1994) Commutative implications on complete lattices. Int J Uncertainty Fuzziness Knowl Based Syst 2:333-341
27. Yager R (1980) On measures of fuzziness and negation. II. Lattices. Inform Control 44:236-260