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Fuzzy lattices as fuzzy relations

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We define a fuzzy lattice as a fuzzy relation, develop some basic properties of the fuzzy lattice, show that the operations of join and meet in fuzzy lattices are isotone and associative, characterize a fuzzy lattice by its level set, and show that the direct product of two fuzzy lattices is a fuzzy lattice.

Abstract

We define a fuzzy lattice as a fuzzy relation, develop some basic properties of the fuzzy lattice, show that the operations of join and meet in fuzzy lattices are isotone and associative, characterize a fuzzy lattice by its level set, and show that the direct product of two fuzzy lattices is a fuzzy lattice.

참고문헌 (6)

  1. N. Ajmal, "Fuzzy lattices", Inform. Sci, 79, pp.271~291 (1994)
  2. 전인흥, "Fuzzy partial order relations and fuzzy lattices", 한국수학논문집, 17(4), pp.361~374 (2009), 강원경기수학회
  3. J. A. Goguen, "L-fuzzy sets", J. Math. Anal. Appl, 18, pp.145~174 (1967)
  4. E. Sanchez, "Resolution of composite fuzzy relation equation", Inform. and Control, 30, pp.38~48 (1976)
  5. L. A. Zadeh, "Fuzzy sets", Inform. and Control, 8, pp.338~353 (1965)
  6. L. A. Zadeh, "Similarity relations and fuzzy orderings", Inform. Sci, 3, pp.177~200 (1971)

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