A simple theoretical model to understand fuzzy objects

Fuzzy objects are objects that have crisp and linguistic variables. Therefore, they have crisp and linguistic states and transit over the states during life cycle. In this paper, a simple theoretical model is proposed to understand the fuzzy objects for easier analysis and specification of the integrated computation by using the object-oriented approach. By introducing a hypothetical device that converts crisp information to linguistic form, this new framework shows the following properties: 1) the operations on fuzzy sets can be refined by using linguistic expressions, and a proof of non-preservation on the law of contradiction and excluded middle is given as representative; 2) an extension to the extension principle is derived and the interpretation of overlapping sub-images shown in still-image pictures is made possible; 3) an explicit formulation and reasoning of Sugeno fuzzy rule evaluation are given; and 4) the design of fuzzy objects is given.