A Fuzzy Indiscernibility Based Measure of Distance between Semantic Spaces Towards Automatic Evaluation of Free Text Answers

Quantitative models built as tools for evaluating human language performance, can prove useful for both theoretical and applied areas of discourse comprehension, assessment, and education. The current paper offers a test case focused on mathematical articulation of a model and a test of that model with existing corpora. The model presented has been developed to evaluate free text answers of students based on the fuzzy indiscernibility between the semantic spaces created by the model answer and the learners' response. The model semantic space represented as a knowledge matrix can be constructed out of one or more model answers prepared by human experts and closely resemble the knowledge of the human evaluator. The proposed model finds out the indiscernibility between the types of word usage and scores the answer based on the fuzzy indiscernibility measures stored in a graded thesaurus prepared specifically for this purpose. The results returned on experimental data correlates well with human evaluators. This simulated learner-friendly atmosphere, inspired by a teacher's intelligent benevolence, ensures effective attainment of learning objective in e-learning environment.