Solving Zadeh's Swedes and Italians challenge problem

摘要

In this paper, we present a solution to Zadeh's Swedes and Italians challenge problem which involves linguistic quantifiers and linguistic attributes. First, we argue that Zadeh's solution to this problem via the Generalized Extension Principle is very difficult to implement. Then, we use 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 the expected values of two belief structures via Linguistic Weighted Averages. Then, we choose vocabularies for height differences and linguistic quantifiers that are involved in the problem statement. The vocabularies are modeled using interval type-2 fuzzy sets. We calculate the expected values of two belief structures, which naturally would be interval type-2 fuzzy sets. Finally, we map the solution to linguistic height differences present in the vocabularies, so that the results can be comprehended by a human.