Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
권호 표지
DOI QR코드

DOI QR Code

A Note on the Fuzzy Linear Maps

  • Received : 2011.06.14
  • Accepted : 2011.07.25
  • Published : 2011.08.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we investigate some situations in connection with two exact sequences of fuzzy linear maps. Also we obtain a generalization of the work [Theorem4] of Pan [5], and we study the analogies of The Four Lemma and The Five Lemma of homological algebra. Finally we obtain a special exact sequence.

Keywords

References

  1. C. V. Negoita and D. A. Ralescu, "Applicationsof Fuzzy Setsto System Analysis", Birkhauser, Basel, Chap. 1, pp.18-24,1975.
  2. A. K. Katsaras and D. B. Liu, "Fuzzy Vector Spaces and Fuzzy Topological Vector Spaces", J. of Math. Anal. Appl., 58,pp.135-146,1977. https://doi.org/10.1016/0022-247X(77)90233-5
  3. R. Lowen, "Convex Fuzzy Sets", Fuzzy Setsand Systems, vol. 3, no. 3, pp. 291-310, 1980. https://doi.org/10.1016/0165-0114(80)90025-1
  4. F. Z. Pan, "Fuzzy Finitely Gernerated Modules", Fuzzy Sets and Systems, vol. 21, no. 1, pp. 105-113, 1987.
  5. F. Z. Pan,"Exact Sequences of Fuzzy Linear Maps", Fuzzy Sets and Systems, vol. 27, no. 3, pp. 317-325, 1988. https://doi.org/10.1016/0165-0114(88)90057-7
  6. C. B. Kim, "The Fuzzy Linear Maps", J.of Fuzzy Logic and Intelligent Systems, vol. 15, no. 4, pp. 511-513, 2005. https://doi.org/10.5391/JKIIS.2005.15.4.511
  7. S. T. Hu, Introduction to Homological Algebra, Holden-day, Inc. San Francisco, 1968.
  8. N. G. Northcott, An Introduction to Homological Al-gebra, Cambridge Univ. press, London,1960.
  9. J. J. Rotman, An Introduction to Homological Algebra, Academic press, New York, 1972.