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On solving stochastic MADM problems

The paper examines a MADM problem with stochastic attributes. The transformation of a stochastic MADM problem into a cardinal problem is done by the standardization of the probability distribution of each attribute X and calculating the information of each attribute as Shannon's entropy or Onicescu's informational energy. | Yugoslav Journal of Operations Research Vol 19 (2009), Number 1, 75-83 DOI:10.2298/YUJOR0901075V ON SOLVING STOCHASTIC MADM PROBLEMS Ion VĂDUVA University of Bucharest, Faculty of Maths and Computer Science, Romania vaduva@fmi.unibuc.ro Cornel RESTEANU National Institute for Research and Development in Informatics, Bucharest Romania resteanu@ici.ro Received: December 2007 / Accepted: May 2009 Abstract: The paper examines a MADM problem with stochastic attributes. The transformation of a stochastic MADM problem into a cardinal problem is done by the standardization of the probability distribution of each attribute X and calculating the information of each attribute as Shannon's entropy or Onicescu's informational energy. Some well known (performant) methods to solve a cardinal MADM problem are presented and a method for combining results of several methods to give a final MADM solution is discussed. Keywords: Multiple attribute decision making, stochastic MADM problems, stochastic entries, entropy, informational energy. 1. INTRODUCTION A MADM (i.e. Mulltiple Attribute Decision Making) problem can be formulated as follows [2,4,6,12,14,15]: there are n decision alternatives to be taken and there are m criteria or attributes used to determine the best (optimun) alternative decision. In order to make a decision, a “sense” for selecting decisions is associated with each criterion, namely, the best decision is selected if its attribute has a minimum or a maximum value. The problem is to select the “best” decision alternative with respect to all the criteria combined with sense requirements. I. Vaduva, C. Resteanu / On Solving Stohastic 76 The data of a MADM problem can be represented as in the following table [2,9]: A table representing decision data. C1 C2 CM A1 a11 a12 a1m A2 An P a21 an1 a22 an 2 p1 p2 pm sense sense1 sense2 sensem a2m anm The entries aij ,1 ≤ i ≤ n,1 ≤ j ≤ m define the n × m decision matrix. The .