Intuitionistic Fuzzy Sets for Spatial and Temporal Data Intervals

Abstract

Spatial and temporal uncertainties are found in data for many critical applications. This paper describes the use of interval-based representations of some spatial and temporal information. Uncertainties in the information can arise from multiple sources in which degrees of support and non-support occur in evaluations. This motivates the use of intuitionistic fuzzy sets to permit the use of the positive and negative memberships to capture these uncertainties. The interval representations will include both simple and complex or nested intervals. The relationships between intervals such as overlapping, containing, etc. are then developed for both the simple and complex intervals. Such relationships are required to support the aggregation approaches of the interval information. Both averaging and merging approaches to interval aggregation are then developed. Furthermore, potential techniques for the associated aggregation of the interval intuitionistic fuzzy memberships are provided. A motivating example of maritime depth data required for safe navigation is used to illustrate the approach. Finally, some potential future developments are discussed.