On the vague DeMorgan complemented partially ordered sets and lattices
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Lattice theory is a basic topic of mathematics and many application areas. It is important and useful to fuzzily de¯ne the concepts in lattice theory. Therefore, this work contributes to mathematics in the following way: In this work, fuzzy partially ordered sets and fuzzy lattices that are many-valued logical counterparts to partially ordered sets and lattices in classical lattice theory have been studied on the basis of many-valued equivalence relations. Fuzzy DeMorgan complemented partially ordered sets and lattices are introduced by using many- valued equivalence relations. Furthermore, various non-trivial examples for these concepts are provided.
Abstract
Lattice theory is a basic topic of mathematics and many application areas. It is important and useful to fuzzily de¯ne the concepts in lattice theory. Therefore, this work contributes to mathematics in the following way: In this work, fuzzy partially ordered sets and fuzzy lattices that are many-valued logical counterparts to partially ordered sets and lattices in classical lattice theory have been studied on the basis of many-valued equivalence relations. Fuzzy DeMorgan complemented partially ordered sets and lattices are introduced by using many- valued equivalence relations. Furthermore, various non-trivial examples for these concepts are provided.
참고문헌 (23)
- R. Belohlavek, "Fuzzy Relational Systems: Foundations and Principles", pp.2002, Kluwer Academic
- G. Birkhoff, "Lattice Theory" (1967), Amer. Math. Soc. Colloquium Publications
- U. Bodenhofer, "Representations and Constructions of Similarity-Based Fuzzy Orderings", Fuzzy Sets and Systems, 137, pp.113~136 (2003)
- D. Boixader, "Fuzzy Equivalence Relations: Advanced Material in Fundamentals of Fuzzy Sets, The handbooks of fuzzy sets series", pp.261~290 (2000), Kluwer Academic Publishers
- U. Cerruti, "An Approach to Uncertainty Using Algebras Over a Monoidal Closed Category", Suppl. Rend. Circ. Matem. Palermo Ser. II, 12, pp.47~63 (1986)
- M. Demirci, "Fuzzy Functions and Their Applications", J. Math. Anal. Appl., 252, pp.495~517 (2000)
- M. Demirci, "Fundamentals of M-Vague Algebra and M-Vague Arithmetic Operations", Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems, 10(1), pp.25~75 (2002)
- M. Demirci, "Foundations of Fuzzy Functions and Vague Algebra Based on Many-Valued Equivalence Re- lations, Part I: Fuzzy Functions and Their Applications", Int. J. General Systems, 32(2), pp.123~155 (2003)
- M. Demirci, "Foundations of Fuzzy Functions and Vague Algebra Based on Many-Valued Equivalence Re- lations, Part II:Vague Algebraic Notions", Int. J. General Systems, 32(2), pp.157~175 (2003)
- M. Demirci, "On many-valued Partitions and Many-valuedEquivalence relations", Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems, 11(2), pp.235~253 (2003)
- M. Demirci, "A Theory of Vague Lattices Based on Many-Valued Equivalence Relations-I: General Representation Results", Fuzzy Sets and Systems, 151(3), pp.437~472 (2005)
- Demirci M, "An Introduction to Vague Complemented Ordered Sets", Information Science, 177, pp.150~160 (2007)
- U. Hohle, "Partial Ordering in L-Underdeterminate Sets", Inform. Sci., 35, pp.133~144 (1985)
- U. Hohle, "Non-Classical Logics and Their Applications to Fuzzy Subsets", pp.53~106 (1995), Kluwer Academic Publishers
- U. Hohle, "Axiomatic Foundations of Fixed-Basis Fuzzy Topology in Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, The hand books of fuzzy sets series, Vol.3", pp.123~273 (1999), Kluwer Academic Publishers
- J. Jacas, "Fuzzy Numbers and Equality Relations", Proc. FUZZ'IEEE 93, pp.1298~1301 (1993)
- G. Kalmbach, "Orthomodular Lattices" (1983), Academic Press
- F. Klawonn, "Similarity in Fuzzy Reasoning", Mathware and Soft Computing, 2, pp.197~228 (1995)
- F. Klawonn, "Fuzzy Points, Fuzzy Relations and Fuzzy Functions in Discovering World with Fuzzy Logic", pp.431~453 (2000), Physica-Verlag
- Klement E.P, "Triangular Norms", ~ (2000)
- V. Novak, "Fuzzy Sets and Their Applications" (1989), Adam Hilger
- L. Valverde, "On the Structure of F-Indistinguishability Operators", Fuzzy Sets and Systems, 17, pp.313~328 (1985)
- L. A. Zadeh, "Similarity Relations and Fuzzy Orderings", Inform. Sci., 3, pp.177~200 (1971)