Healthcare Facilities Redesign Using Multicriteria Decision-Making: Fuzzy TOPSIS and Graph Heuristic Theories

Algorithm 1

Hospitals’ departments evaluated: ranking using the fuzzy TOPSIS method.

	Step 1: create the evaluation matrix.
	(1.1) From the evaluation process of the selected department [39], each answer will be presented with its fuzzy number according to Table 3 for each evaluated hospital.
	Step 2: normalize the evaluation matrix using the normalization formula [40].
	Step 3: resolve the weighted standardized evaluation matrix (inclusion of weight).
	where wj is weight of criterion j
	Step 4: resolve the perfect positive solution and perfect negative solution using, ,
	Where positive ideal solution (A^+) and negative ideal solution (A^−) are acquired as weighted and normalized values from matrix and is the best alternative value in criterion j, is the worst alternative value in criterion j.
	Step 5: determine the separation value. ,
	Where the distance of alternatives from the positive ideal solution is , and the distance of alternatives from the negative ideal solution is
	Step 6: determine the nearness coefficients and rank the alternatives.
	Where () is relative closeness of each alternative to the ideal solution value is in the 0 ≤ C^+i ≤ 1 interval. As gets closer to 1, alternative i gets closer to A^+, whereas if gets closer to 0, alternative i gets closer to A^−
	Step 7: arrange the alternative choices. Alternatives are arranged according to the decreasing order of