Indicator of inclusion grade for interval-valued fuzzy sets. Application to approximate reasoning based on interval-valued fuzzy sets

We begin the paper studying the axioms that the indicators of the grade of inclusion of a fuzzy set in another fuzzy set must satisfy. Next, we presen t an expression of such indicator, first for fuzzy sets and then for interv al-valued fuzzy sets, analyzing in both cases their main properties. Then, we suggest an expression for the similarity measure between interval-valued fuzzy sets. Besides, we study two methods for inference in approximate rea soning based on interval-valued fuzzy sets, the inclusion grade indicator a nd the similarity measure. Afterwards, we expose some of the most important properties of the methods of inference presented and we compare these meth ods to Gorzalczany's. Lastly, we use the indicator of the grade of inclusio n for interval-valued fuzzy sets as an element that selects from the differ ent methods of inference studied, the one that will be executed in each cas e. (C) 2000 Elsevier Science Inc. All rights reserved.