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On nearness measures in fuzzy relational data models. (English) Zbl 0676.68077
Summary: It has been widely recognized that the imprecision and incompleteness inherent in real-world data suggests a fuzzy extension for information management systems. Various attempts to enhance these systems by fuzzy extensions can be found in the literature. Varying approaches concerning the fuzzification of the concept of a relation are possible, two of which are referred to in this article as the generalized fuzzy approach and the fuzzy-set relation approach. In these enhanced models, items can no longer be retrieved by merely using equality-check operations between constants; instead, operations based on some kind of nearness measures have to be developed. In fact, these models require such a nearness measure to be established for each domain for the evaluation of queries made upon them. An investigation of proposed nearness measures, often fuzzy equivalences, is conducted. The unnaturalness and impracticality of these measures leads to the development of a new measure: the resemblance relation, which is defined to be a fuzzified version of a tolerance relation. Various aspects of this relation are analyzed and discussed. It is also shown how the resemblance relation can be used to reduce redundancy in fuzzy relational database systems.

MSC:
68P20 Information storage and retrieval of data
03B52 Fuzzy logic; logic of vagueness
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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[1] Codd, E.F., A relational model of data for large shared data banks, Commun. ACM, 13, 6, 337-387, (1970) · Zbl 0207.18003
[2] Zadeh, L.A., Fuzzy sets, Inf. control, 8, 338-353, (1965) · Zbl 0139.24606
[3] Kacprzyk, J.; Ziolkowski, A., Database queries with fuzzy linguistic quantifiers, IEEE trans. syst. man, cybern., SMC-16, 3, 474-479, (1986)
[4] Prade, H.; Testemale, C., Generalizing database relational algebra for the treatment of incomplete/uncertain information and vague queries, Inf. sci., 34, 115-143, (1984) · Zbl 0552.68082
[5] Buckles, B.P.; Petry, F.E.; Sachar, H.S., Retrieval and design concepts for similarity-based (fuzzy) relational databases, (), 243-251 · Zbl 0633.68105
[6] Rundensteiner, E.A.; Hawkes, L.W.; Bandler, W., A set-valued temporal knowledge representation for fuzzy temporal retrieval in ICAI, (), 37-65
[7] Zemankova, M.; Kandel, A., Fuzzy relational database—A key to expert systems, (1984), Verlag TÜV Rheinland Cologne · Zbl 0567.68056
[8] Rundensteiner, E.A.; Bandler, W.; Kohout, L.; Hawkes, L.W., An investigation of fuzzy nearness measures, ()
[9] Schreider, J.A., Equality, resemblance, and order, (1971), Mir Publishers Moscow, Russian translation
[10] Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets syst., 1, 1, 3-28, (1979) · Zbl 0377.04002
[11] Zvieli, A., On complete fuzzy relational query languages, (), 704-726
[12] Dubois, D.; Prade, H., The treatment of uncertainty in knowledge-based systems using fuzzy sets and possibility theory, Int. J. intell. syst., 3, 2, 141-165, (1988) · Zbl 0647.68084
[13] Zemankova, M.; Kandel, A., Implementing imprecision in information systems, Inf. sci., 37, 3, 107-141, (1985) · Zbl 0583.68053
[14] Buckles, B.P.; Petry, F.E., A fuzzy representation of data for relational databases, Fuzzy sets syst., 7, 213-226, (1982) · Zbl 0475.68059
[15] Oezsoyoglu, G.; Oezsoyoglu, Z.M.; Matos, V., Extending relational algebra and relational calculus with set-valued attributes and aggregate functions, ACM trans. database syst., 12, 4, 566-592, (1987)
[16] Umano, M., Freedom-O: a fuzzy database system, (), 339-347
[17] Raju, K.V.S.V.N.; Majumdar, A.K., Fuzzy functional dependencies and lossless join decomposition of fuzzy relational database systems, ACM trans. database syst., 13, 2, 129-166, (1988)
[18] Anvari, M.; Rose, G.F., Fuzzy relational databases, ()
[19] Rundensteiner, E.A., The development of a fuzzy temporal relational database (FTRDB): an artificial intelligence application, ()
[20] Potoczny, H.B., On similarity relations in fuzzy relational databases, Fuzzy sets syst., 12, 231-235, (1984) · Zbl 0547.68097
[21] Tversky, A., Features of similarity, Psychol. rev., 84, 4, 327-353, (1977)
[22] Zadeh, L.A., Similarity relations and fuzzy orderings, Inf. sci., 3, 177-200, (1971) · Zbl 0218.02058
[23] Garey, M.R.; Johnson, D.S., Computers and intractability. A guide to the theory of NP-completeness, (1979), Freeman San Francisco · Zbl 0411.68039
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