A Hypervolume Based Approach to Rank Intuitionistic Fuzzy Sets and Its Extension to Multi-criteria Decision Making Under Uncertainty

Ranking intuitionistic fuzzy sets with distance based ranking methods requires to calculate the distance between intuitionistic fuzzy set and a reference point which is known to have either maximum (positive ideal solution) or minimum (negative ideal solution) value. These group of approaches assume that as the distance of an intuitionistic fuzzy set to the reference point is decreases, the similarity of intuitionistic fuzzy set with that point increases. This is a misconception because an intuitionistic fuzzy set which has the shortest distance to positive ideal solution does not have to be the furthest from negative ideal solution for all circumstances when the distance function is nonlinear. This paper gives a mathematical proof of why this assumption is not valid for any of the non-linear distance functions and suggests a hypervolume based ranking approach as an alternative to distance based ranking. In addition, the suggested ranking approach is extended as a new multicriteria decision making method, HyperVolume based ASsessment (HVAS). HVAS is applied for multicriteria assessment of Turkey's energy alternatives. Results are compared with three well known distance based multicriteria decision making methods (TOPSIS, VIKOR, and CODAS).Comment: 8 pages, 3 figure

Neighborhood rough filter and intuitionistic entropy in unsupervised tracking

This paper aims at developing a novel methodology for unsupervised video tracking by exploring the merits of neighborhood rough sets. A neighborhood rough filter is designed in this process for initial labeling of continuous moving object(s) even in the presence of several variations in different feature spaces. The locations and color models of the object(s) are estimated using their lower-upper approximations in spatio-color neighborhood granular space. Velocity neighborhood granules and acceleration neighborhood granules are then defined over this estimation to predict the object location in the next frame and to speed up the tracking process. A novel concept, namely, intuitionsistic entropy is introduced here, which consists of two new measures: neighborhood rough entropy and neighborhood probabilistic entropy to deal with the ambiguities that arise due to occurrence of overlapping/ occlusion in a video sequence. The unsupervised method of tracking is equally good even when compared with some of the state-of-the art partially supervised methods while showing superior performance during total occlusion