Generation of interval-valued fuzzy and Atanassov's intuitionistic fuzzy connectives from fuzzy connectives and from Kα operators: Laws for conjunctions and disjunctions, amplitude

International Journal of Intelligent Systems

Volumn 23, Issue 6, 2008, Pages 680-714

  Bustince, H ^a   Barrenechea, E ^a   Pagola, M ^a  

^a PUBLIC UNIVERSITY OF NAVARRE   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ABSORPTION; FUZZY SETS; SET THEORY; TRANSIENTS;

(I ,J) CONDITIONS; (PL) PROPERTIES; (U ,V) OPERATOR; EXCLUDED-MIDDLE; FUZZY CONNECTIVES; IDEMPOTENCY; INTERVAL-VALUED; INTERVAL-VALUED FUZZY SETS; INTUITIONISTIC FUZZY SETS (IFS);

FUZZY LOGIC;

EID: 44649161293     PISSN: 08848173     EISSN: 1098111X     Source Type: Journal    
DOI: 10.1002/int.20292     Document Type: Article

References (42)

1. Zadeh LA. Outline of a new approach to analysis of complex systems and decision processes. IEEE Trans. Syst Man Cybern 1973;3:28-44.
2. Zadeh LA. Theory of approximate reasoning. In: Hayes EJ, Michie D, Mikulich LI, editors Machine intelligence Chichester, UK: Ellis Horwood Ltd; 1970. pp 149-194.
3. Sambuc R. Function φ-flous, application a 1'aide au diagnostic en pathologie thyroidienne. These de Doctorat en Medicine, Marseille, 1975.
4. Kohout LJ, Bandler W. Fuzzy interval inference utilizing the checklist paradigm and BK-relational products. In: Kearfort RB et al., editors. Application of interval computations, Dordrecht:Kluwer; 1996. pp 291-335.
5. Gorzalczany MB. A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 1987;21: 1-17.
6. Turksen IB. Interval-valued fuzzy sets and compensatory AND. Fuzzy Sets Syst 1992;51:295-307.
7. Arnauld T, Tano S. Interval-valued fuzzy backward reasoning. IEEE Trans Fuzzy Syst 1995;3(4):425-437.
8. Atanassov K. Intuitionistic fuzzy sets. In VII ITKR's Session, Deposed in Central Sci. Technol. Library of Bulg. Acd. of Sci., Sofia June 1983. pp 1684-1697.
9. Atanassov K. Intuitionistic fuzzy sets. Theory and applications. Heidelberg: Physica-Verlag; 1999.
10. Burillo P, Bustince H. Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst 1996;78:305-3016.
11. Burillo P, Bustince H. Orderings in the referential set induced by an intuitionistic fuzzy relation. Notes on IFS, 1995;1:93-103.
12. Burillo P, Bustince H. Construction theorems for intuitionistic fuzzy sets. Fuzzy Sets Syst l996;84:271-281.
13. Bustince H. Indicator of inclusion grade for interval-valued fuzzy sets. Application to approximate reasoning based on interval-valued fuzzy sets. Int J Approx Reason 2000;23(3):137-209.
14. Bustince H, Burillo P. Mathematical analysis of interval-valued fuzzy relations: Application to approximate reasoning. Fuzzy Sets Syst 2000;1 13:205-219.
15. Bustince H, Burillo P. Structures on intuitionistic fuzzy relations. Fuzzy Sets Syst 1996;78:293-303.
16. Bustince H, Kacprzyk J, Mohedano V. Intuitionistic fuzzy generators. Application to intuitionistic fuzzy complementation. Fuzzy Sets Syst, 2000; 114:485-504.
17. Bustince H, Montero J, Pagola M, Barrenechea E, Gómez D. A survey on interval-valued fuzzy sets. In: Pedrycz W, Skowron A, Kreinovich V, editors. Handbook of granular computing. New York: Wiley 2008. pp 489-515.
18. Bustince H, Herrera F, Montero J, editors. Fuzzy sets and their extensions: Representation, aggregation and models. Berlin; Springer-Verlag; 2007.
19. Chen SM, Hsiao WH, Jong WT. Bidirectional approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 1997;91:339-353.
20. Jenei S. A more efficient method for defining fuzzy connectives. Fuzzy Sets Syst 1997;90:25-35.
21. Kehagias A, Konstantinidou M. L-fuzzy valued inclusion measure, L-fuzzy similarity and L-fuzzy distance. Fuzzy Sets Syst 2003;136:313-332.
22. Klir G, Yuan B. Fuzzy sets and fuzzy logic: Theory and applications. Upper Saddle River, NJ; Prentice-Hall; 1995.
23. Mendel JM, Robert I. Bob John, Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 2002;10(2):117-127.
24. Roy MK, Biswas R. I-V fuzzy relations and Sanchez's approach for medical diagnosis. Fuzzy Sets Syst 1992;47:35-38.
25. Goguen JA. L-fuzzy sets. J Math Anal Appl 1967;18(1):623-668.
26. Montero J, Gómez D, Bustince H. On the relevance of some families of fuzzy sets. Fuzzy Sets Syst 2007;158(2):2429-2442.
27. Alsina C, Trillas E, Valverde L. On some logical connectives for fuzzy sets theory. J Math Anal Appl l983;93:15-26.
28. (a) Dubois D, Prade H. Fuzzy sets and systems: Theory and applications. New York: Academic Press; 1980.
29. (b) Fuzzy Sets Syst 1991;40:143-202.
30. Esteva F, Trillas E, Domingo X. Weak and strong negation function for fuzzy set theory. In: Proc. Eleventh IEEE Intern. Symp. on Multivalued Logic, Norman, OK 1981; pp 23-27.
31. Fodor J, Roubens M. Fuzzy preference modelling and multicriteria decision support. In: Theory and decision library. Boston, MA: Kluwer Academic Publishers; 1994.
32. Fodor J. On fuzzy implication operators. Fuzzy Sets Syst 1991;42:293-300.
33. Trillas E. Sobre funciones de negación en la teoría de conjuntos difusos. Stochastica, III-1 (1979) 47-59, (in Spanish). Reprinted (English version) in Advances of fuzzy logic Barro S. et al. tri-Universidad de Santiago de Compostela; 1998. pp 31-43.
34. Trillas E, Alsina C, Terricabras JM, editors. Introducción a la lógica borrosa. Madrid: Ariel Matemática; 1995.
35. Trillas E, Valverde L. On mode and implication in approximate reasoning. In: Gupta MM, Kandel A, Bandler W, Kiszka JB, editors, Approximate reasoning in expert systems. Amsterdam: North-Holland; 1985. pp 157-166.
36. Weber S. A general concept of fuzzy connectives, negations and implications based on t-norms and t-conorms. Fuzzy Sets Syst 1983;11:115-134.
37. Cornelis C, Deschrijver G, Kerre E. Classification of intuitionistic fuzzy implicators: An algebraic approach. In: Proceedings of the 6th Joint Conference on Information Sciences, Research Triangle Park, NC, March 8-13, 2002. pp 105-108.
38. Cornelis C, Deschrijver G, Kerre E. Intuitionistic Fuzzy Connectives Revisited. Proceedings of the Ninth International Conference IPMU 2002, Annecy-France July 1-5,2002. pp 1839-1844.
39. Deschrijver G, Cornelis C, Kerre EE. On the representation of intuitionistic fuzzy T-norms and T-conorms. IEEE Trans Fuzzy Syst 2004;12(1):45-61.
40. Mayor G, Trillas E. On the representation of some aggregation functions. In Proc. 16th ISMVL, Blacksburg, VA; 1986. pp 110-114.
41. Dombi J. A general class of fuzzy operators, the De Morgan class of fuzzy operators and fuzziness measures induced by fuzzy operators. Fuzzy Sets Syst 1982;8:149-163.
42. Ovchinnikov SV, Roubens M. On strict preference relations. Fuzzy Sets and Syst 1991;43:319-326.