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# Multi attribute decision making

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### Multi attribute decision making

1. 1. Name: Shriraam Madanagopal<br />Distance Student<br />TERM PAPER<br />Engineering Economy –IE 5304<br />Topic: Multi Attribute Decision Making<br />Multi Attribute Decision Making<br />Introduction:<br />Multi-attribute decision making method, has its base for the decision making model, is one of the decision-making support methods. The decision making model is based on a chosen list of criteria, parameters, variables or factors, which we wish to monitor in the decision making process. The formal base for the establishment of a model-Multi attribute decision making, in which the key criteria is the interconnectedness of assessments according to the individual parameters that result in an integrated assessment. From the observations of the case study, a better understanding of the advancement in Multi Attribute Decision Making model and cognitive techniques underlining the observed effects and precise information with respect to the analysis of a project uses task variants. The Multi Attribute Decision support can be best explained as a procedure aimed at the evaluation of options that occur in decision making process. This procedure will take us through a description of the scenario and a study of the results.<br />Decision Models:<br />One of the basic approaches to the decision support is the multi attribute decision making with the basic principle of decomposing the decision problem into smaller, less complex sub-problems. Options are decomposed onto various dimensions X, usually called the attributes, parameters or criteria. After decomposing, each option O is defined by a vector value v for the corresponding attributes. These vectors are evaluated by a Utility Function F. The Utility Function should be well defined by the decision maker(s), by defining his or her or their main objectives or goals. When these rules or protocol is applied to the particular option O, the function F yields to a Utility F(O). According to this value, the options can be ranked as per the decision maker’s goals and the best one is selected. The attributes X and the Utility Function F are the two main factors which determines the decision maker’s knowledge about a particular decision problem. Added to this there is a data base of options, consisting of vectors v. The procedure of hierarchical models has been developed and extensively applied in relation to the decision support. <br />The attributes are represented in the form of a tree which gives the outline for the decision problem. These attributes are designed according to their interdependence. The leaves of the tree are referred as basic attributes, which solely depend on the characteristic of options. The internal nodes of the tree are called the aggregate attributes and their values are determined by the basis of the Utility Functions. The root of the tree is the most important aggregate attribute. These roots represent the overall Utility of options.<br />These Utility functions define the process of aggregation of lower level attributes into the corresponding higher –level fathers. Every aggregate attribute X, a Utility function F that maps the values of sons of X into values of X, must be defined by the person who makes decision. <br />Utility functions are represented by elementary decision rules.<br />Let X1, X2, X3…..Xk be the predecessor of an aggregate attribute Y. Then the Function Y= F( X1, X2,X3….. Xk) be defined by a set of rules of the form:<br />X1= x1 and Xk = xk and<br />Y = ym : yM, where xi, ym and yM represent the values of the Corresponding attributes. “ym : yM” stands for an interval of values between ym and yM, inclusive.<br />The most commonly, ym:yM is a single-value interval. In this case, the rule is simplified to<br />if X1 = x1 ….. Xk = xk then Y = y. <br />Tables are formed by grouping set of elementary decision rules. When more decision making groups with different objectives are involved on the decision process, each group can define their own set of utility functions.<br />Figure a: General Concept of multi attribute Decision making<br />Utility<br /> F(O1)…F(Ok)<br /> F<br />Utility Functions<br /> Attributes<br />X1 X2 …Xk <br /> O1= ( V11 V12 … V1n) Options<br /> Ok= ( Vk1 Vk2 .... Vkn)<br /> <br /> Multi Attribute Decision Model: <br />Multi Attribute Decision Model can be developed with qualitative hierarchical decision model which is based on the DEX shell. This helps to create the decision models that consist of non-numerical qualitative criteria. The criteria are hierarchically ordered into a tree structure. The weights are replaced by rules that define the interdependence of the criteria and their influence on the final evaluation. Thus the influence of criteria can depend on its value, which corresponds in Utility theory to the variability of weights. The qualitative hierarchical decision model is based on a chosen list of criteria, parameters, variables or factors, which we are going to monitor in the decision making process.<br />The Decision making process is divided into five phases:<br /><ul><li>Identification of the problem
2. 2. Criteria identification and criteria structuring
3. 3. Utility function(decision rules)
4. 4. Description of variants