The Interval Parameter Optimization Model Based on Three-Way Decision Space and Its Application on “Green Products Recommendation”

Algorithm 1

Decision optimization algorithm under given interval parameters (GPOA).

	Input: decision formal context ;
	Interval parameters ;
	Object and its condition attribute set ;
	Output: the decision rules of object .
	Step 1: according to the given formal context , interval three-way decision space will be built by interval three-way decision concepts:  and parent-children relationship (Definitions 7–9);
	Step 2: find intension in interval three-way decision concepts , turn to Step 3; else and , and turn to Step 6;
	Step 3: if there are n concepts like , n decision rules will be obtained, namely, , and they can constitute n-dimensional decision space, ;
	Step 4: if there is only meeting will become the final decision rules of , namely, making the accept or reject decision of the smallest loss as the final decision;
	Step 5: if there are some meeting , search the subconcepts of and . And on the basis of intension of those subconcepts, add related attribute of , until get the only decision meeting condition;
	Step 6: according to the parent-children relationship in the three-way decision space, search concepts whose intension is . meets the conditions of and , and turn to Step 3; else turn to Step 7;
	Step 7: search the concepts whose intension is , meets the conditions of and and turn to Step 3 to continue making decision, until the end node whose intension is .
	End.