On nearness measures in fuzzy relational data models.

*(English)*Zbl 0676.68077Summary: 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) |

##### Keywords:

fuzzy relational data model; fuzzy relations; nearness measure; tolerance relation; resemblance relation
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\textit{E. A. Rundensteiner} et al., Int. J. Approx. Reasoning 3, No. 3, 267--298 (1989; Zbl 0676.68077)

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