Concave type-2 fuzzy sets: Properties and operations

Soft Computing

Volumn 14, Issue 7, 2010, Pages 749-756

  Tahayori, Hooman ^a   Tettamanzi, Andrea G B ^a   Antoni, Giovanni Degli ^a   Visconti, Andrea ^a   Moharrer, Masoomeh ^b  

^a UNIVERSITY OF MILAN   (Italy)

^b POLITECNICO DI MILANO   (Italy)

Author keywords

Concave fuzzy sets; Join; Meet; Type 2 fuzzy sets

Indexed keywords

JOIN; SEMI-RING; T - NORM; T-CONORMS; TYPE-2 FUZZY SET;

MATHEMATICAL OPERATORS;

FUZZY SETS;

EID: 77952880134     PISSN: 14327643     EISSN: 14337479     Source Type: Journal    
DOI: 10.1007/s00500-009-0462-9     Document Type: Article

References (31)

1. Bustince H, Burillo P (2000) Mathematical analysis of interval-valued fuzzy relations: application to approximate reasoning. Fuzzy Sets Syst 113: 205-219.
2. Chaudhuri BB (1991) Some shape definitions in fuzzy geometry of space. Pattern Recognit Lett 12: 531-535.
3. Chaudhuri BB (1992) Concave fuzzy set: a concept complementary to the convex fuzzy set. Pattern Recognit Lett 13: 103-106.
4. Coupland S, John RI (2004) A new and efficient method for the type-2 meet operation. In: Proceedings of the IEEE FUZZ conference. Budapest, Hungary, pp 959-964.
5. Coupland S, John RI (2005) Towards more efficient type-2 fuzzy logic systems. In: Proceedings of the IEEE FUZZ conference. Reno, NV, pp 236-241.
6. Coupland S, John RI (2007) Geometric type-1 and type-2 fuzzy logic systems. IEEE Trans Fuzzy Syst 15(1): 3-15.
7. Dubois D, Prade H (1978) Operations on fuzzy numbers. Int J Syst Sci 9: 613-626.
8. Dubois D, Prade H (1979) Operations in a fuzzy-valued logic. Inf Control 43: 224-240.
9. Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New York.
10. Karnik NN, Mendel JM (1998) Type-2 fuzzy logic systems: type-reduction. In: Proceedings of the IEEE system, man, and cybernetics conference. San Diego, CA.
11. Karnik NN, Mendel JM (2001a) Operations on type-2 fuzzy sets. Fuzzy Sets Syst 122: 327-348.
12. Karnik NN, Mendel JM (2001b) Centroid of a type-2 fuzzy set. Inf Sci 132: 195-220.
13. Karnik NN, Mendel JM, Liang Q (1999) Type-2 fuzzy logic systems. IEEE Trans Fuzzy Syst 7: 643-658.
14. Kaufmann A, Gupta MM (1991) Introduction to fuzzy arithmetic: theory and applications. van Nostrand Reinhold, New York.
15. Liang Q, Mendel JM (2000) Interval type-2 fuzzy logic systems: theory and design. IEEE Trans Fuzzy Syst 8: 535-550.
16. Mendel JM (2001) Uncertain rule-based fuzzy logic systems: introduction and new directions. Prentice-Hall, Upper-Saddle River.
17. Mendel JM (2003) Type-2 fuzzy sets: some questions and answers. IEEE Connections, Newsletter of the IEEE Neural Networks Society, pp 10-13.
18. Mendel JM (2007a) Advances in type-2 fuzzy sets and systems. Inf Sci 177: 84-110.
19. Mendel JM (2007b) Type-2 fuzzy sets and systems: an overview. IEEE Comput Intell Mag, pp 20-29.
20. Mendel JM, John RI (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2): 117-127.
21. Mendel JM, John RI, Liu F (2006) Interval Type-2 fuzzy logic systems made simple. IEEE Trans Fuzzy Syst 14(6): 808-821.
22. Mizumoto M, Tanaka K (1976) Some properties of fuzzy sets of type-2. Inf Control 31: 312-340.
23. Mizumoto M, Tanaka K (1981) Fuzzy sets of type-2 under algebraic product and algebraic sum. Fuzzy Sets Syst 5: 277-290.
24. Nieminen J (1977) On the algebraic structure of fuzzy sets of type-2. Kybernetica 13(4): 261-273.
25. Tahayori H, Degli Antoni G (2008) Operations on concavoconvex type-2 fuzzy sets. Int J Fuzzy Syst 10(4): 276-286.
26. Tahayori H, Tettamanzi AGB, Degli Antoni G (2006) Approximated type-2 fuzzy set operations. IEEE World Congress on Computational Intelligence, pp 1910-1917.
27. Turksen I (1986) Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst 20: 191-210.
28. Walker Carol L, Walker Elbert A (2005) The algebra of fuzzy truth values. Fuzzy Sets Syst 149: 309-347.
29. Walker Carol L, Walker Elbert A (2006) T-norms for type-2 fuzzy sets. In: IEEE international conference on fuzzy systems, pp 1235-1239.
30. Zadeh LA (1965) Fuzzy sets. Inf Control 8: 338-353.
31. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-1. Inf Sci 8: 199-249.