A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package

The application of multi-attribute utility theory whose aggregation process is based on the Choquet integral requires the prior identification of a capacity. The main approaches to capacity identification proposed in the literature are reviewed and their advantages and inconveniences are discussed. All the reviewed methods have been implemented within the Kappalab R package. Their application is illustrated on a detailed example.     

Estimating the population utility function: A parametric Bayesian approach

In this paper we consider the health utility index mark II for quantifying and describing a population’s health related quality of life over health states composed of multiple attributes. This measure can be used for various purposes such as evaluating the severity of the effect of a disease or comparing different treatment methods. We present a Bayesian framework for population utility estimation and health policy evaluation by introducing a probabilistic interpretation of the multi-attribute utility theory (MAUT) used in health economics. In doing so, our approach combines ideas from the MAUT and Bayesian statistics and provides an alternative method of modeling preferences and utility estimation.     

An ordinal sorting method for group decision-making

Several group decision-making methods were proposed with the aim to establish, from individual opinions, a collective one. However, the literature review of such methods show that, until now, few of them accept individual preferences expressed in partial pre-orders or, more generally, in preferences relational systems (p.r.s.). In addition, the majority of these methods produce a ranking on the alternative set, i.e. they concern the ranking decision-making problematic. In fact, the efforts provided to develop methods which treat, for example, the sorting problematic, remain insufficient. For these reasons, we propose in this paper an ordinal sorting method which determines, from individual p.r.s., at least one collective assignment which takes into account the relative importance of the members. If there is more than one collective assignment, an interactive procedure to reach a consensus assignment is proposed.     

A flexible framework for Group Decision Support: WINGDSS version 3.0

A flexible framework for Group Decision Support on PCs in Microsoft Windows environment is presented. WINGDSS does not replace human judgment but highly supports the entire process of decision making, from problem structuring to post-decision analysis. The latest version of WINGDSS is a modular, open system with a dynamical connection to relational databases, an interpreter for defining problem specific evaluation procedures, a lot of interactive features from setting up the tree of criteria until the sensitivity analysis on individual/group ranking. By providing tools for recursively redefining the decision problem, WINGDSS helps the decision makers in achieving a result satisfactory to the whole group.Research supported in part by the Hungarian Foundation for Scientific Research, Grant No. 2568 and by the Hungarian National Committee for Technical Research and Development, Grant No. 93-97-67-0553.     

Aggregation of monotone reciprocal relations with application to group decision making

This paper is composed of two complementary parts. The first part is a formal investigation into the interplay of properties of reciprocal relations, how monotonicity relates to some natural and intuitive properties, including stochastic transitivity. The goal is to aggregate monotone reciprocal relations on a given set of alternatives. Monotonicity is expressed w.r.t. a linear order on the set of alternatives. The second part is a practical protocol to both determine the best fitting linear order underlying the alternatives, and construct a reciprocal relation monotone w.r.t. it. We formulate the problem as an optimization problem, where the aggregated linear order is that for which the implied stochastic monotonicity conditions are closest to being satisfied by the distribution of the input monotone reciprocal relations. We show that if stochastic monotonicity conditions are satisfied, a monotone reciprocal relation is easily found on the basis of the (possibly constructed) stochastically monotone reciprocal distributional relation.     

A decisional framework system for computer network intrusion detection

This paper presents a multi-attribute decisional framework for computer network intrusion detection. First, a cost model that allows to estimate accurately the damage resulting from a security incident is described. Then, a multi-attribute optimization algorithm is applied to select the optimal decision based on alternatives to remedy such incidents.     

群体多指标决策的偏好集结方法

研究多个指标条件下,利用个体决策结果形成群体一致偏好的方法、假设个体有加性效用函数,将个体多指标效用函数表示成单个指标评价函数的加权和,群体指标评价函数表示成个体指标评价函数的加权和.通过协商指标权重、指标评价函数、支付意愿三个参数,成对个体达成双方一致.提出了(n-1)对个体之间达成双方一致,从而得出群体效用函数的决策方法,这种分析框架同样可以扩展到联盟协商一致中.     

Normalizing rank aggregation method for priority of a fuzzy preference relation and its effectiveness

The aim of this paper is to show that the normalizing rank aggregation method can not only be used to derive the priority vector for a multiplicative preference relation, but also for the additive transitive fuzzy preference relation. To do so, a simple functional equation between fuzzy preference’s element and priority weight is derived firstly, then, based on the equation, three methods are proposed to prove that the normalizing rank aggregation method is simple and effective for deriving the priority vector. Finally, a numerical example is used to illustrate the proposed methods.     

Utility efficiency and its approximation

Summary We assume a multi-attribute decision making problem under uncertainty with partial information on the decision maker's preferences, by a vector utility function with two components and imprecision over their scaling constants. We propose an approximation set whose determination may be easier than the one of the utility efficient set and we consider an interactive procedure which uses such approximation to decision aid. We study some nesting and convergence properties based on the interactive reduction of the approximation set. Finally, we illustrate the procedure with a numerical example.     

Fuzzy Ideal Based Computational Approach for Group Decision Making Problems

In this paper, we present a computational method to fuzzy group decision making problems. A function that satisfies the properties of fuzzy ideal of semiring of positive integers is also investigated in the present paper and is used for idealizing the group preference matrix obtained by different decision makers. The proposed method appears in form of simple computational algorithms to idealize the group preference matrix and calculating total order of preference relation. Finally, the suitability of the proposed method is shown by taking an example of a human resource development (HRD) event, where it is used to select the best possible candidate by different decision makers.     

A collective choice method based on individual preferences relational systems (p.r.s.)

In group decision-making literature, several procedures are proposed in order to establish a collective preference from the different individual ones. The majority of these procedures, however, reveal that the individual preferences are always expressed in total pre-orders (or ranking). Indeed, until now very few have considered individual preferences which are expressed in partial pre-orders or, more generally, in preferences relational systems (p.r.s.). Moreover, many of these procedures generate collective preferences which are expressed in total pre-orders (ranking decision-making problematic). The efforts reported in the literature to develop procedures which treat other decision-making problematics—such as choice problematic—remain insufficient. In this paper, we propose a method which would determine from individual p.r.s. at least one collective subset containing the “best” alternatives. Each of these collective subsets results from the exploitation—according to the choice problematic—of a collective p.r.s. obtained from the aggregation of the individual p.r.s. Furthermore, each collective p.r.s. has two main characteristics: (i) it is at a minimum distance from all individual p.r.s. and (ii) it takes into account the members’ relative importance.     

Second-order preferences in group decision making

We propose an aggregation method based on the concept of second-order preferences, which is capable of assigning a value function on the finite set of alternatives for each group member. This study incorporates a criterion of equity among individuals, in which everybody influences the group ranking to the same degree.     

Quadratic distances for capacity and bi-capacity approximation and identification

The application of multi-attribute utility theory based on the Choquet integral requires the prior identification of a capacity if the utility scale is unipolar, or of a bi-capacity if the utility scale is bipolar. In order to implement a minimum distance principle for capacity or bi-capacity approximation or identification, quadratic distances between capacities and bi-capacities are studied. The proposed approach, consisting in solving a strictly convex quadratic program, has been implemented within the GNU R kappalab package for capacity and nonadditive integral manipulation. Its application is illustrated on two examples.      

A multi-attribute group decision-making method based on weighted geometric aggregation operators of interval-valued trapezoidal fuzzy numbers

With respect to the multiple attribute group decision making problems in which the attribute values take the form of generalized interval-valued trapezoidal fuzzy numbers (GITFN), this paper proposed a decision making method based on weighted geometric aggregation operators. First, some operational rules, the distance and comparison between two GITFNs are introduced. Second, the generalized interval-valued trapezoidal fuzzy numbers weighted geometric aggregation (GITFNWGA) operator, the generalized interval-valued trapezoidal fuzzy numbers ordered weighted geometric aggregation (GITFNOWGA) operator, and the generalized interval-valued trapezoidal fuzzy numbers hybrid geometric aggregation (GITFNHGA) operator are proposed, and their various properties are investigated. At the same time, the group decision methods based on these operators are also presented. Finally, an illustrate example is given to show the decision-making steps and the effectiveness of this method.     

When conflict induces the expression of incomplete preferences

Multicriteria conflict arises in pairwise comparisons, where each alternative outperforms the other one on some criterion, which imposes a trade-off. Comparing two alternatives can be difficult if their respective advantages are of high magnitude (the attribute spread is large). In this paper, we investigate to which extent conflict in a comparison situation can lead decision makers to express incomplete preferences, that is, to refuse to compare the two alternatives, or to be unable to compare them with confidence. We report on an experiment in which subjects expressed preferences on pairs of alternatives involving varying conflicts. Results show that depending on whether the participants are allowed to express incomplete preferences or not, attribute spread has a different effect: a large attribute spread increases the frequency of incomparability statements, when available, while it increases the use of indifference statements when only indifference and preference answers are permitted. These results lead us to derive some implications for preference elicitation methods involving comparison tasks.     

Inferring consensus weights from pairwise comparison matrices without suitable properties

Pairwise comparison is a popular method for establishing the relative importance of n objects. Its main purpose is to get a set of weights (priority vector) associated with the objects. When the information gathered from the decision maker does not verify some rational properties, it is not easy to search the priority vector. Goal programming is a flexible tool for addressing this type of problem. In this paper, we focus on a group decision-making scenario. Thus, we analyze different methodologies for getting a collective priority vector. The first method is to aggregate general pairwise comparison matrices (i.e., matrices without suitable properties) and then get the priority vector from the consensus matrix. The second method proposes to get the collective priority vector by formulating an optimization problem without determining the consensus pairwise comparison matrix beforehand.     

Linguistic group decision-making: opinion aggregation and measures of consensus

Group decision-making is a crucial activity, necessary in many aspects of our civilization. In many cases, due to inherent complexity, experts cannot express their opinion or preferences using exact numbers, thus resorting to a qualitative preference such as linguistic labels. Another complicating factor is the fact that very seldom all individuals in a group share the same opinion about the alternatives. This creates the need to aggregate all the differing individual opinions into a group opinion. Moreover, it is desirable to be able to assess the level of agreement among the experts; termed consensus. This paper presents a methodology for aggregating experts’ judgements, presented as linguistic labels, into a group opinion with a measure of the group consensus. The aggregation model allows weighted experts to express a degree of optimism or upward bias in their opinions. Then the paper presents two models of calculating the consensus based on the individual expert opinions and the group aggregated opinion.     

An integrated operation module for individual risk management

In this study, we used the cumulative prospect theory to propose the individual risk management process (IRM) which includes risk analysis and risk response stages. According to an individual’s preferential structure, the process has been developed into an operational module which includes two sub-modules. From this, the individual’s risk level for the confronted risk can be identified from the risk analysis, while the response strategies can be assessed at the risk response stage. Therefore, optimal response strategies can be recommended based on individual risk tolerance levels.