Browse > Article
http://dx.doi.org/10.5391/IJFIS.2013.13.3.208

Fuzzy relation equations in pseudo BL-algebras  

Kim, Yong Chan (Department of Mathematics, Gangneung-Wonju National University)
Publication Information
International Journal of Fuzzy Logic and Intelligent Systems / v.13, no.3, 2013 , pp. 208-214 More about this Journal
Abstract
Bandler and Kohout investigated the solvability of fuzzy relation equations with inf-implication compositions in complete lattices. Perfilieva and Noskova investigated the solvability of fuzzy relation equations with inf-implication compositions in BL-algebras. In this paper, we investigate various solutions of fuzzy relation equations with inf-implication compositions in pseudo BL-algebras.
Keywords
Pseudo BL-algebras; inf-implication compositions; fuzzy relation equations;
Citations & Related Records
연도 인용수 순위
  • Reference
1 E. Sanchez, "Resolution of composite fuzzy relation equations," Information and Control, vol. 30, no. 1, pp. 38-48, Jan. 1976.   DOI   ScienceOn
2 S. Gottwald, "On the existence of solutions of systems of fuzzy equations," Fuzzy Sets and Systems, vol. 12, no. 3, pp. 301-302, Apr. 1984.   DOI   ScienceOn
3 W. Pedrycz, "s-t fuzzy relational equations," Fuzzy Sets and Systems, vol. 59, no. 2, pp. 189-195, Oct. 1993.   DOI   ScienceOn
4 I. Perfilieva, "Fuzzy function as an approximate solution to a system of fuzzy relation equations," Fuzzy Sets and Systems, vol. 147, no. 3, pp. 363-383, Nov. 2004.   DOI   ScienceOn
5 I. Perfilieva and L. Noskova, "System of fuzzy relation equations with inf- composition: complete set of solutions," Fuzzy Sets and Systems, vol. 159, no. 17, pp. 2256- 2271, Sep. 2008.   DOI   ScienceOn
6 W. Bandler and L. J. Kohout, "Semantics of implication operators and fuzzy relational products," International Journal of Man-Machine Studies, vol. 12, no. 1, pp. 89- 116, Jan. 1980. http://dx.doi.org/10.1016/S0020-7373(80) 80055-1   DOI   ScienceOn
7 G. Birkhoff, Lattice Theory, 3rd ed., Providence, RI: American Mathematical Society, 1967.
8 A. Dvurecenskij, "Pseudo MV-algebras are intervals in l-groups," Journal of the Australian Mathematical Society, vol. 72, no. 3, pp. 427-445, Jun. 2002.   DOI
9 A. Dvurecenskij, "On pseudo MV-algebras," Soft Computing, vol. 5, no. 5, pp. 347-354, Oct. 2001. http://dx.doi. org/10.1007/s005000100136   DOI
10 N. Galatos and C. Tsinakis, "Generalized MV-algebras," Journal of Algebra, vol. 283, no. 1, pp. 254-291, Jan. 2005. http://dx.doi.org/10.1016/j.jalgebra.2004.07.002   DOI   ScienceOn
11 G. Georgescu and L. Leustean, "Some classes of pseudo- BL algebras," Journal of the Australian Mathematical Society, vol. 73, no. 1, pp. 127-154, Aug. 2002. http: //dx.doi.org/10.1017/S144678870000851X   DOI
12 G. Georgescu and A. lorgulescu, "Pseudo MV-algebras," Multiple-Valued Logics, vol. 6, pp. 193-215, 2001.
13 G. Georgescu and A. Popescu, "Non-commutative fuzzy Galois connections," Soft Computing, vol. 7, no. 7, pp. 458-467, Jun. 2003. http://dx.doi.org/10.1007/ s00500-003-0280-4
14 G. Georgescu and A. Popescu, "Non-commutative fuzzy structures and pairs of weak negations," Advances in Fuzzy Logic, vol. 143, no. 1, pp. 129-155, Apr. 2004.
15 U. Hoohle and E. P. Klement, Non-Classical Logics and Their Applications to Fuzzy Subsets: A Handbook of the Mathematical Foundations of Fuzzy Set Theory, Boston: Kluwer Academic Publishers, 1995.