Solving Zadeh´s Magnus challenge problem on linguistic probabilities via Linguistic Weighted Averages

In this paper, we present a solution to Zadeh´s Magnus challenge problem on linguistic probabilities. First, we implement Zadeh´s solution to this problem. Then, we use the intersection-product syllogism and a syllogism based on the entailment principle to interpret the problem so that it can be solved via Linguistic Weighted Averages. We show that the problem can be solved by calculation of pessimistic (lower) and optimistic (upper) probabilities via Linguistic Weighted Averages. Then, we choose vocabularies for quantifiers and linguistic probabilities that are involved in the problem statement. The vocabularies are modeled using interval type-2 fuzzy sets. We calculate optimistic (upper) and pessimistic (lower) probabilities, which naturally would be interval type-2 fuzzy sets. Finally, we map the pessimistic and optimistic probabilities to linguistic probabilities present in the vocabularies, so that the results can be comprehended by a human.