By Ching-Lai Hwang, Abu Syed Md. Masud (auth.)

Decision making is the method of choosing a potential plan of action from the entire to be had possible choices. In just about all such difficulties the multiplicity of standards for judging the choices is pervasive. that's, for lots of such difficulties, the choice maker (OM) desires to reach multiple target or aim in picking out the plan of action whereas fulfilling the limitations dictated through surroundings, tactics, and assets. one other attribute of those difficulties is that the targets are it seems that non commensurable. Mathematically, those difficulties might be represented as: (1. 1 ) topic to: gi(~) ~ zero, ,', . . . ,. ! the place ~ is an n dimensional selection variable vector. the matter includes n selection variables, m constraints and ok targets. all or any of the services might be nonlinear. In literature this challenge is usually often called a vector greatest challenge (VMP). commonly there are methods for fixing the VMP. one in all them is to optimize one of many ambitions whereas appending the opposite pursuits to a constraint set in order that the optimum resolution may fulfill those pursuits at the least as much as a predetermined point. the matter is given as: Max f. ~) 1 (1. 2) topic to: the place at is any applicable predetermined point for target t. the opposite process is to optimize a super-objective functionality created by way of multiplying each one 2 target functionality with an appropriate weight after which through including them together.

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**Extra resources for Multiple Objective Decision Making — Methods and Applications: A State-of-the-Art Survey**

**Example text**

9) for f * j , the Otherwise the procedure is repeated until all k objectives have been considered. t. gj (~) < 0, fR, (~) * fR,' j R, 1, 2, = 1, ... 10) Since the procedure is terminated when a unique solution is obtained at the ith problem, the solution will be the preferred solution to the entire problem; the objectives ranked less important than this method. fi(~) are ignored by The rationale for this method is that individuals tend to make decisions in this manner. 47 Let us consider an example with two objectives and one decision variable as illustrated in Fig.

Prior to assessing the manager's preference, note that Y cannot exceed $130 and that Z cannot exceed 250 dolls; these values are obtained by optimizing max Y XEX = max fl(~ XEX and max Z = max XEX space is limited by (Cy, z) I °2- Y 2- 130, f2(~. Thus the consequence XEX 02- z 2- 250}. It is necessary to check whether Y is utility independent of Z. Given U (y,z), we shall say Y is utility independent of Z if the DM's preference over any lotteries on Y for a fixed Zo in Z are the same regardless of the amount of zoo Thus if Z is the same for all possible consequences, the DM's relative preferences for lotteries involving these consequences depend only on Y.

1) for generating a nondominated solution set by this set the DM then selects the preferred solution. varying~. 1. the solutions are on the line segment of Be From in Fig. 3. 1 The nondominated solutions set of Example 1. xl x2 fl f2 Location* of f O. 250. 0 100. 25 250. 0 100. 67 250. 0 100. 5 250. 0 100. 2 -4. 250. 0 100. 0 O. wI w2 O. 2 * ** -w 1/w2 Segment BC 100. 300. 130. 100 B Locations in Fig. 3 It is equal to the slope of BC in Fig. 3, hence the solutions set has infinite pOints. 3x 2 = '" I I I \ , "- \ \ I - - - - - - - - - '-\ c __ 1 ___ _ ~W /w 'I 1 ',I 1', I , " I I 200 2 " I I 100 s 50 FiS.