Abstract
Today we are living in a state where the same commodity is available in the offline as well as online markets. In presence of the two markets the agent considers the two as an union and an extended decision space. The characteristics of the commodity spaces differ from market to market, state to state and place to place. The paper identifies three types of commodity spaces/decision spaces/domains and explains how a decision maker is moving from one space to another and forms a new decision rule. These are conlinear space, fuzzy space and a linear space. The paper gives an idea and the road maps where if the domain has been extended to the union of these three spaces then what would be the preference and mapping behavior on this extended space. This mapping depends on the characteristics of the space and acts as a source of the identification of the agent's risk behavior. The paper first derives three important criteria to move from one domain to another. Thereafter, as an example, derives a value function for a domain and analyze the criteria.
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