No Access

ON CONNECTION BETWEEN UNCERTAINTY ALGEBRAIC HYPERSYSTEMS AND PROBABILITY SPACES

B. DAVVAZ

Department of Mathematics, Yazd University, Yazd, Iran

https://doi.org/10.1142/S0218488505003497Cited by:6 (Source: Crossref)

Abstract

Using the concept of triangular norm, we define T-fuzzy subalgebraic hypersystems, we examine a number of extended uncertainty algebraic hypersystems and study a few results in this respect. In fact, we define a probabilistic version of algebraic hypersystems using random sets. We show that fuzzy algebraic hypersystems defined in triangular norms are consequences of probabilistic algebraic hypersystems under certain conditions.

Keywords:

References

F. Marty, Sur une generalization de la notion de group, Proc. 8nd Congress Math. Scandenaves (1934) pp. 45–49. Google Scholar
S. D. Comer, J. Algebra 89, 397 (1984), DOI: 10.1016/0021-8693(84)90225-4. Crossref, Web of Science, Google Scholar
P. Corsini , Prolegomena of hypergroup theory , 2nd edn. ( Aviani Editor , 1993 ) . Google Scholar
T. Vougiouklis , Hyperstructures and their representations ( Hadronic Press, Inc , Palm Harber, USA , 1994 ) . Google Scholar
L. A. Zadeh, Inform. Control 8, 338 (1965), DOI: 10.1016/S0019-9958(65)90241-X. Crossref, Google Scholar
A. Rosenfeld, J. Math. Anal. Appl. 35, 512 (1971), DOI: 10.1016/0022-247X(71)90199-5. Crossref, Web of Science, Google Scholar
J. M. Anthony and H. Sherwood, J. Math. Anal. Appl. 69, 124 (1979), DOI: 10.1016/0022-247X(79)90182-3. Crossref, Web of Science, Google Scholar
B. Schweizer and A. Sklar, Pacific J. Math. 10, 313 (1960). Crossref, Google Scholar
M. Akgul, J. Math. Anal. Appl. 133, 93 (1988), DOI: 10.1016/0022-247X(88)90367-8. Crossref, Web of Science, Google Scholar
L. Biacino and G. Gerla, Inform. Sci. 32, 181 (1984), DOI: 10.1016/0020-0255(84)90027-6. Google Scholar
Lu Tu and Wen-xiang Gu, Fuzzy sets and systems 61, 313 (1994), DOI: 10.1016/0165-0114(94)90174-0. Crossref, Web of Science, Google Scholar
Zhudeng Wang, Fuzzy sets and systems 65, 59 (1994), DOI: 10.1016/0165-0114(94)90247-X. Crossref, Web of Science, Google Scholar
S. K. Tan, P. Z. Wang and E. S. Lee, J. Math. Anal Appl. 174, 242 (1993), DOI: 10.1006/jmaa.1993.1114. Crossref, Web of Science, Google Scholar
Xue-hai Yuan and E. Stanly Lee, J. Math. Anal. Appl. 208, 243 (1997), DOI: 10.1006/jmaa.1997.5331. Crossref, Web of Science, Google Scholar
B. Davvaz, Fuzzy sets and systems 101, 191 (1999), DOI: 10.1016/S0165-0114(97)00071-7. Crossref, Web of Science, Google Scholar
B. Davvaz, J. Fuzzy Math. 8(1), 43 (2000). Web of Science, Google Scholar
B. Davvaz, Pure Math. Appl. 12, 137 (2001). Google Scholar
B. Davvaz, Korean J. Comput. Appl. Math. 6, 197 (1999). Crossref, Web of Science, Google Scholar
M. M. Zahedi, M. Bolurian and A. Hasankhani, J. Fuzzy Math. 3, 1 (1995). Web of Science, Google Scholar
P. Z. Wang , Fuzzy sets and falling shadows of random sets ( Beijing Normal University Press , China , 1985 ) . Google Scholar
I. R. Goodman, Recent Development in Fuzzy Sets and Possibility Theory, ed. R. Yager (Pergamona, New York, 1982) pp. 327–342. Google Scholar
Q. D. Li and E. S. Lee, J. Math. Anal. Appl. 190, 546 (1995), DOI: 10.1006/jmaa.1995.1090. Crossref, Web of Science, Google Scholar