Decision makers in reality always behave characteristics of bounded ra-tionalities and satisficed decisions. Individual internal rationalities are modeled based on the logical consistency relations of internal preferences and revealed preferences. Definitions of perception preferences, local relations and compatible decisions etc are given and discussed according to a type of bounded rational decisions with “upward” consisent preferences. Based on the models and the concepts, existence of a compat- ible decision under kind of ordinal preferences are proved, and bounded rationality characteristics are studied of weak expansions, adjunct expansions and strong expan- sions. Some satisficed phenomenon and rational features of compatible decisions are
analyzed and discussed by use of interval ordinal numbers. This paper is intended to probe into theoretical bases of satisficed decisions such as fuzzy ones and incomplete information ones.