Crouch gait is one of the most common gait abnormalities; it is usually caused by cerebral palsy. There are few works related to the modeling of crouch gait kinematics, crouch gait analysis, and visualization in both the workspace and joint space. In this work, we present a quaternion-based method to solve the forward kinematics of the position of the lower limbs during walking. For this purpose, we propose a modified eight-DoF human skeletal model. Using this model, we present a geometric method to calculate the gait inverse kinematics. Both methods are applied for gait analysis over normal, mild, and severe crouch gaits, respectively. A metric-based comparison of workspace and joint space for the three gaits for a gait cycle is conducted. In addition, gait visualization is performed using Autodesk Maya for the three anatomical planes. The obtained results allow us to determine the capabilities of the proposed methods to assess the performance of crouch gaits, using a normal pattern as a reference. Both forward and inverse kinematic methods could ultimately be applied in rehabilitation settings for the diagnosis and treatment of diseases derived from crouch gaits or other types of gait abnormalities.

This paper presents an account of fuzzy similarity metrics that have been proposed to quantify consensus in Multi Criteria Group Decision Making. Fuzzy similarity metrics are indispensable to determine consensus when experts evaluate alternatives in fuzzy terms, which capture experts’ uncertainty and hesitancy. Furthermore, factors such as the level of expertise or cognitive bias lead to disagreements within the group. The fuzzy similarity metrics described in this article are used to measure the similarity between type 1 and type 2 fuzzy sets, and fuzzy numbers. Consensus can be quantified at three different levels: criteria judgement, alternative judgement, or expert preferences. Promising future work includes the incorporation of social fuzzy measures under the umbrella of multi-agent systems as well as the analysis of fuzzy intuitionistic sets.

Crouch gait, also referred to as flexed knee gait, is an abnormal walking pattern, characterized by an excessive flexion of the knee, and sometimes also with anomalous flexion in the hip and/or the ankle, during the stance phase of gait. Due to the fact that the amount of clinical data related to crouch gait are scarce, it is difficult to find studies addressing this problem from a data-based perspective. Consequently, in this paper we propose a gait recognition strategy using synthetic data that have been obtained using a polynomial based-generator. Furthermore, though this study, we consider datasets that correspond to different levels of crouch gait severity. The classification of the elements of the datasets into the different levels of abnormality is achieved by using different algorithms like k-nearest neighbors (KNN) and Naive Bayes (NB), among others. On the other hand, to evaluate the classification performance we consider different metrics, including accuracy (Acc) and F measure (FM). The obtained results show that the proposed strategy is able to recognize crouch gait with an accuracy of more than 92%. Thus, it is our belief that this recognition strategy may be useful during the diagnosis phase of crouch gait disease. Finally, the crouch gait recognition approach introduced here may be extended to identify other gait abnormalities.