A Modified TODIM Based on Compromise Distance for MAGDM with q-Rung Orthopair Trapezoidal Fuzzy Numbers

Algorithm 1

Algorithm of the modified TODIM method.

	Input: q-ROTrFNs matrices
	Output: ranking result according to the value of
	Process
	Step 1: to eliminate the influence of different physical dimensions on decision-making, transform the evaluation matrix into a standard matrix .
	Step 2: decision maker chooses the value of according to the risk preference and gets the value of q by the observation method or the traversal method. The value of q needs to hold in matrix .
	Step 3: aggregate by equation (34), represents q-ROTrFNs in the decision matrix given by the tth expert, and get the collective matrix .
	Step 4: get the relative weight of each attribute using equation (35).
	Step 5: obtain the positive-ideal alternative and the negative-ideal alternative of according to equations (36) and (38) and using equations (39) and (40) to get the distance between them and each element in .
	Step 6: the compromise distances of elements in are obtained via equations (41) and (42).
	Step 7: get the dominance of alternative relative to alternative by equations (45) and (46).
	Step 8: calculate the overall dominance by equation (47).
	Step 9: according to the value of , the ranking result of the alternatives is the same as rank of , and the alternative with the largest is the optimal.