A Decision Rule for Uncertain Multi-Criteria Pure Decision Making and Independent Criteria

Abstract

SummaryThe paper is concerned with multi-criteria decision-making under uncertainty with scenario planning. This topic has been explored by many researchers since almost all real-world decision problems contain multiple conflicting criteria and a deterministic evaluation of criteria is often impossible. We propose a procedure for uncertain multi-objective optimization which can be applied when seeking a pure strategy. A pure strategy, as opposed to a mixed strategy, allows the decision-maker to select and perform only one accessible alternative. The new approach takes into account the decision-maker's preference structure (importance of particular goals) and nature (pessimistic, moderate or optimistic attitude towards a given problem). It is designed for one-shot decisions made under uncertainty with unknown probabilities (frequencies), see decision-making under complete uncertainty or decision-making under strategic uncertainty. The novel approach can be used in the case of totally independent payoff matrices for particular targets.

A decision rule based on goal programming and one-stage models for uncertain multi-criteria mixed decision making and games against nature

“…There are many classical and extended decision rules designed for multi-criteria decision making under uncertainty, e.g. [1], [2], [7], [8], [11], [13], [20], [24], [25], [28], [29], [34], [36], [40], [41], [42], [45], [48], [49], [50], [51], [56], [57], [58], [61], [62], [63], [65], [66], [71], [74], [75], [76], however the majority of the methods refer to probability calculus. Hence, those contributions are not directly related to the topic investigated in this paper, since here we concentrate on totally new decision problems for which frequencies are not known.…”

“…A mixed strategy implies that the DM selects and performs a weighted combination of several accessible alternatives, see e.g. bonds portfolio construction, cultivation of different plants [24], [52], [55], [60]. This paper will deal with the latter case.…”

“…Therefore, in such contexts it is useful to construct scenarios that describe possible ways in which the future might unfold and to combine MDMU (multi-criteria decision making under uncertainty) with SP (scenario planning). The result of the choice made under uncertainty with scenario planning depends on two factors: which decision will be selected and which scenario will occur [24]. Instead of using probabilities, here we apply probabilitylike quantities, i.e.…”

“…Conclusions are gathered in the last Section. The paper is a continuation of several articles, where uncertain one-criterion procedures [16], [18], [22] and multi-criteria decision rules for 2-stage models [20], [24], [25] were investigated.…”

On two applications of the Omega ratio: max?min and Omega(H+B) / O dwóch zastosowaniach wskaźnika Omega: max?min i Omega(H+B)

“…The literature offers numerous decision rules for DMPI [Guo 2013;Kmietowicz, Pearman 1984;Kofler, Zweifel 1993;Michalska, Pośpiech 2010;, Michalska 2012Weber 1987] and for DMCU [Gaspars 2007;GasparsWieloch 2013;2014a;2014b;2014c;2014d;2014e;2015a;2015b;2015c;2015d;2015e;2016;Hayashi 2008;Hurwicz 1952;Ioan, Ioan 2011;Piasecki 1990;Savage 1961;Wald 1950], but here we only investigate the use of the Ω ratio in these two decision cases.…”