Abstract—Group decision making is investigated using ordinal interval number ranking. The closed interval preference is given independently by each decision maker and for every course of action. Genetic algorithms are employed for establishing the mutually preferred course(s) of action. The combination of crossover and adjusted mutation is found efficient in terms of problem representation and genetic- algorithm operation/convergence to (one of) the preferred course(s) of action. I. INTRODUCTION roup decision making is performed by an ensemble of decision makers who collectively decide upon the preferred course of action (solution) to a problem, as selected out of a number of alternative courses of action which are available at the time of decision making. Although more time consuming than individual decision making, a group decision allows the combination of the strengths and the expertise of each decision maker in the group in order to maximize the joint agreement upon the selected course of action. A variety of group decision making methods exist [1-2] for reaching the final decision, with each method having advantages and disadvantages in terms of speed and decision maker satisfaction/agreement with the mutually preferred course of action. Group decision making methods include – among others - decision by authority, decision by majority, decision by negative minority, decision by unanimity, decision by consensus and decision via preference ranking. In this piece of research, group decision making is investigated using ordinal interval number preference ranking. The closed intervals of preference are given independently by each decision maker, who provides an interval for every available course of action. Genetic algorithms [3] are employed for establishing the preferred course(s) of action. The combination of crossover and adjusted mutation is proved efficient in terms of problem representation and genetic-algorithm operation/convergence to a preferred course of action. This paper is organized as follows: Section II introduces the group decision making and ranking methods while also Manuscript received March 10, 2011. T. Tambouratzis is with the Department of Industrial Management & Technology, University of Piraeus, 107 Deligiorgi St, Piraeus 185 34, Greece, and the Department of Nuclear Engineering, Chalmers University of Technology, SE-412 Göteborg, Sweden (phone: +30-210-4142423; fax: +30-210-4142392; e-mail: tatianatambouratzis@gmail.com). detailing its operation under the ordinal interval number representation of the decision makers’ preferences; Section III describes the inspiration, structure and mode of operation of genetic algorithms; Section IV demonstrates the application of genetic algorithms to ordinal interval number preference ranking and group decision making while also evaluating their performance on a number of problems from the existing literature; finally, Section V concludes the paper. II. GROUP DECISION MAKING AND RANKING Ranking aggregates the preferred courses of action of the different decision makers in order to select the mutually preferred course of action. Ranking has a number of advantages: it is robust to the composition and size of the group of decision makers as well as to the familiarity of each decision maker with the problem at hand; different evaluation criteria that are related to each decision maker’s background and outlook towards the problem can be simultaneously accommodated; finally, the assignment of relative importance values to the preferences of the various decision makers is allowed. A number of formats are available for ranking. These formats include nominal [4], ordinal [5-18] and ordinal interval [19-20] numbers; the choice of format depends (a) on the way in which the constraints between alternative courses of action are expressed and (b) on the means of aggregating and, subsequently, evaluating the alternative courses of action. In the following it is assumed that n possible courses of action exist and that m decision makers are involved in the group decision making process. When performing ranking using ordinal interval numbers, the cth course of action (1≤c≤n) is attributed an interval [x cd y cd ] by the dth decision maker (1≤x cd ,y cd ≤n, x cd ≤y cd and 1≤d≤m) which expresses the preference that the dth decision maker assigns to the cth course of action when compared to the entire set of courses of action. Since interval creation is performed independently by each decision maker and for every course of action, nm intervals are needed in order to cover all courses of action as well as all decision makers. These intervals state the constraints/preferences between courses of action in a purely implicit manner, thus providing (i) a straightforward and uncomplicated means of expressing the preference(s) for each course of action, and (ii) an efficient way of performing course of action comparison, aggregation and ranking. To date, group decision making via Genetic Algorithms for Group Decision Problems Using Ordinal Interval Numbers Tatiana Tambouratzis G