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Deriving fuzzy topological relations from incomplete observations

Author

Listed:
  • Subhankar Jana

    (National Institute of Technology Silchar)

  • Anjali Patel

    (National Institute of Technology Silchar)

  • Juthika Mahanta

    (National Institute of Technology Silchar)

Abstract

Spatial objects in a geographical information system are often vague. Fuzzy topology-based intersection methods were introduced to obtain the topological relation between such vague objects by considering the objects as fuzzy sets. The elements of the intersection matrices express the nature of the intersections between topological parts of the objects. In reality, it may only be possible to calculate some of the required intersections due to the unavailability of data. This paper introduces a method to construct a fuzzy 9-intersection matrix under incomplete observations. Further, it computes the possible fuzzy topological relation using a quantitative fuzzy 9-intersection method based on fuzzy similarity measure. Some special cases of the incomplete observations and fuzzy topological relation under such situations are discussed. Finally, few applications are presented, where the proposed method is used to obtain relation between two uncertain objects under the condition that the topological properties of the objects are partially known.

Suggested Citation

  • Subhankar Jana & Anjali Patel & Juthika Mahanta, 2024. "Deriving fuzzy topological relations from incomplete observations," Journal of Geographical Systems, Springer, vol. 26(1), pages 117-147, January.
    • Handle: RePEc:kap:jgeosy:v:26:y:2024:i:1:d:10.1007_s10109-023-00432-x
    DOI: 10.1007/s10109-023-00432-x
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    Keywords

    Fuzzy 9-intersection matrix; GIS; Fuzzy modeling; Fuzzy topology; Uncertain object modeling; Incomplete observation;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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