Balanced fuzzy sets

Information Sciences

Volumn 176, Issue 17, 2006, Pages 2467-2506

  Homenda, Władysław ^a  

^a WARSAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Balanced norms; Fuzzy sets; Membership functions; Negative information; Triangular norms; Uninorms and nullnorms

Indexed keywords

DATA PROCESSING; FUNCTIONS; HIERARCHICAL SYSTEMS; LINEAR SYSTEMS; MATHEMATICAL OPERATORS; SET THEORY;

BALANCED NORMS; NEGATIVE INFORMATION; TRIANGULAR NORMS; UNINORMS AND NULLNORMS;

FUZZY SETS;

EID: 33746877534     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2005.12.003     Document Type: Article

References (42)

1. Alsina C., Trillas E., and Valverde L. On some logical connectives for fuzzy sets. Journal of Mathematical Analysis and Applications 93 (1983) 15-22
2. Atanassov K.T. Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20 (1986) 87-96
3. De Baets B. Uninorms: the known classes. In: Ruan D., et al. (Ed). Fuzzy Logic and Intelligent Technologies for Nuclear Science and Industry (1998), World Scientific Publishing Company, Singapore 21-28
4. B. De Baets, J. Fodor, On the structure of uninorms and their residual implicators, in: Proceedings of the 18th Linz Seminar on Fuzzy Set Theory, Linz, Austria, 1997, pp. 81-87.
5. Bezdek J.C. Computing with uncertainty. IEEE Communication Magazine September (1992) 24-36
6. Birkhoff G. Lattice Theory vol. XXV, third ed. (1995), AMS, Providence, RI (eight printing)
7. Buchanan B., and Shortliffe E. Ruled Based Expert Systems, The MYCIN Experiment of the Stanford Heuristic Programming Project (1984), Addison-Wesley, Reading, MA
8. Calvo T., et al. Aggregation operators: properties, classes and construction methods. In: Calvo T., Mayor G., and Mesiar R. (Eds). Aggregation Operators (2002), Physica-Verlag, Heidelberg 3-104
9. Calvo T., De Baets B., and Fodor J.C. The functional equations of Frank and Alsina for uninorms and nullnorms. Fuzzy Sets and Systems 120 (2001) 15-24
10. Dubois D., and Prade H. Twofold fuzzy sets: an approach to the representation of sets with fuzzy boundaries based on possibility and necessity measures. Journal of Fuzzy Mathematics 3 4 (1983) 53-76
11. Fodor J.C., Yager R.R., and Rybalov A. Structure of uninorms. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems 5 (1997) 411-427
12. M. Detyniecki, Mathematical Aggregation Operators and their Application to Video Querying, PhD Thesis, l'UNIVERSITE PARIS VI, Paris, 2000.
13. Elkan C. The paradoxical success of fuzzy logic. IEEE Expert August (1994) 3-8
14. Fodor J., and Roubens M. Fuzzy Preference Modeling and Multicriteria Decision Support (1994), Kluwer Academic Publisher, Dordrecht
15. Grabisch M., Nguyen H.T., and Walker E.A. Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference (1995), Kluwer Academics Publishers, Dordrecht
16. M. Grabisch, B. De Baets, J. Fodor, On symmetric pseudo-additions and pseudo-multiplications: Is it possible to built rings on [-1, +1]? in: The 9th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2002, 1-5 July, Annecy, France.
17. Gau W.L., and Buehrer D.J. Vague sets. IEEE Transactions on Systems, Man, and Cybernetics 23 (1993) 610-614
18. Gupta M.M., and Rao D.H. On the principles of Fuzzy Neural Networks. Fuzzy Sets and Systems 61 (1994) 1-18
19. W. Homenda, Fuzzy relational equations with cumulative composition operator as a form of fuzzy reasoning, in: Proceedings of the International Fuzzy Engineering Symposium'91, Yokohama, November 1991, pp. 277-285.
20. Homenda W. Algebraic operators: an alternative approach to fuzzy sets. Applied Mathematics and Computer Science 6 3 (1996) 505-527
21. Homenda W., and Pedrycz W. Processing of uncertain information in linear space of fuzzy sets. Fuzzy Sets and Systems 44 (1991) 187-198
22. W. Homenda, W. Pedrycz, Fuzzy neuron modelling based on algebraic approach to fuzzy sets, in: Proceedings of the SPIE's International Symposium on Applications of Fuzzy Logic Technology II, Orlando, FL, April 1995, pp. 71-82.
23. W. Homenda, Triangular norms, uni- and nullnorms, balanced norms: the cases of the hierarchy of iterative operators, in: Proceedings of the 24th Linz Seminar on Fuzzy Set Theory, Linz, 4-8 February 2003, pp. 27-35.
24. Kahneman D., and Tversky A. Prospect theory: an analysis of decision under risk. Econometrica XVLII (1979) 263-291
25. Klement E.P., Mesiar R., and Pap E. On the relationship of associative compensatory operators to triangular norms and conorms. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems 4 (1996) 129-144
26. Klement E.P., Mesiar R., and Pap E. A characterization of the ordering of continuous t-norms. Fuzzy Sets and Systems 86 (1997) 189-195
27. Klement E.P., Mesiar R., and Pap E. Triangular Norms (2000), Kluwer Academic Publishers, Dordrecht
28. Kosko B. Fuzzy cognitive maps. International Journal of Man-Machine Studies 24 January (1986) 65-75
29. G. Mayor, E. Trillas, On the representation of some aggregation functions, in: Proceeding of ISMVL, 1986, pp. 111-114.
30. Mesiar R., and Pap E. Different interpretations of triangular norms and related operations. Fuzzy Sets and Systems 96 (1998) 183-189
31. Mesiar R., and Komorníková M. Aggregation operators. In: Herceg D., and Surla K. (Eds). Proceeding of the XI Conference on Applied Mathematics PRIM'96 (1997), Institute of Mathematics, Novi Sad 193-211
32. Mesiar R., and Komornikova M. Triangular norm-based aggregation of evidence under fuzziness. In: Bouchon-Meunier B. (Ed). Aggregation and Fusion of Imperfect Information (1998), Physica-Verlag, Heidelberg 11-35
33. Ovchinnikov S. On robust aggregation procedures. In: Bouchon-Meunier B. (Ed). Aggregation Operators for Fusion under Fuzziness (1998) 3-10
34. Silvert W. Symmetric summation: a class of operations on fuzzy sets. IEEE Transactions on Systems, Man, and Cybernetics 9 (1979) 659-667
35. Schweizer B., and Sklar A. Probabilistic Metric Spaces (1983), North Holland, New York
36. Yager R.R. On ordered weighted averaging aggregation operators. IEEE Transactions on Systems, Man, and Cybernetics 18 (1988) 183-190
37. Yager R.R. Families of OWA operators. Fuzzy Sets and Systems 59 (1993) 125-148
38. Yager R.R., and Filev D. Induced ordered weighted averaging operators. IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics 29 (1999) 141-150
39. Yager R.R., and Rybalov A. Uninorm aggregation operators. Fuzzy Sets and Systems 80 (1996) 111-120
40. Yager R.R., and Rybalov A. Full reinforcement operators in aggregation techniques. IEEE Transactions on Systems, Man and Cybernetics 28 (1998) 757-769
41. Zadeh L.A. Fuzzy sets. Information and Control 8 (1965) 338-353
42. Zhang W.R., et al. Pool2: A generic system for cognitive map development and decision analysis. IEEE Transactions on Systems, Man, and Cybernetics 19 January-February (1989) 31-39