Fuzzy Metric Space Induced by Intuitionistic Fuzzy Points and its Application to the Orienteering Problem

摘要

In this paper, a new definition for Atanassov intuitionistic fuzzy metric space is presented using the concept of Atanassov intuitionistic fuzzy point and Atanassov intuitionistic fuzzy scalars. The distance metric introduced here is then applied to an interesting problem called the orienteering problem that finds application in several industries, such as the home delivery system, robot path planning, tourism industry etc., and in each of these practical applications, the two parameters involved, i.e., score and distance travelled as well as the position of locations cannot be predicted precisely. To tackle these uncertainties, we use trapezoidal Atanassov intuitionistic fuzzy numbers for representing the parameter score. The uniqueness of this paper is the consideration of uncertainty in the position of a city or a location and handling this type of uncertainty using the idea of Atanassov intuitionistic fuzzy points and the distance metric between Atanassov intuitionistic fuzzy points. Further, a method for ranking trapezoidal Atanassov intuitionistic fuzzy numbers has been presented and used for modeling the scores.