Performance evaluation: An integrated method using data envelopment analysis and fuzzy preference relations

In a multi-attribute decision-making (MADM) context, the decision maker needs to provide his preferences over a set of decision alternatives and constructs a preference relation and then use the derived priority vector of the preference to rank various alternatives. This paper proposes an integrated approach to rate decision alternatives using data envelopment analysis and preference relations. This proposed approach includes three stages. First, pairwise efficiency scores are computed using two DEA models: the CCR model and the proposed cross-evaluation DEA model. Second, the pairwise efficiency scores are then utilized to construct the fuzzy preference relation and the consistent fuzzy preference relation. Third, by use of the row wise summation technique, we yield a priority vector, which is used for ranking decision-making units (DMUs). For the case of a single output and a single input, the preference relation can be directly obtained from the original sample data. The proposed approach is validated by two numerical examples.     

g-dominance: Reference point based dominance for multiobjective metaheuristics

One of the main tools for including decision maker (DM) preferences in the multiobjective optimization (MO) literature is the use of reference points and achievement scalarizing functions [A.P. Wierzbicki, The use of reference objectives in multiobjective optimization, in: G. Fandel, T. Gal (Eds.), Multiple-Criteria Decision Making Theory and Application, Springer-Verlag, New York, 1980, pp. 469–486.]. The core idea in these approaches is converting the original MO problem into a single-objective optimization problem through the use of a scalarizing function based on a reference point. As a result, a single efficient point adapted to the DM’s preferences is obtained. However, a single solution can be less interesting than an approximation of the efficient set around this area, as stated for example by Deb in [K. Deb, J. Sundar, N. Udaya Bhaskara Rao, S. Chaudhuri, Reference point based multiobjective optimization using evolutionary algorithms, International Journal of Computational Intelligence Research, 2(3) (2006) 273–286]. In this paper, we propose a variation of the concept of Pareto dominance, called g-dominance, which is based on the information included in a reference point and designed to be used with any MO evolutionary method or any MO metaheuristic. This concept will let us approximate the efficient set around the area of the most preferred point without using any scalarizing function. On the other hand, we will show how it can be easily used with any MO evolutionary method or any MO metaheuristic (just changing the dominance concept) and, to exemplify its use, we will show some results with some state-of-the-art-methods and some test problems.     

Using box indices in supporting comparison in multiobjective optimization

Because of the conflicting nature of criteria or objectives, solving a multiobjective optimization problem typically requires interaction with a decision maker who can specify preference information related to the objectives in the problem in question. Due to the difficulties of dealing with multiple objectives, the way information is presented plays a very important role. Questions posed to the decision maker must be simple enough and information shown must be easy to understand. For this purpose, visualization and graphical representations can be useful and constitute one of the main tools used in the literature. In this paper, we propose to use box indices to represent information related to different solution alternatives of multiobjective optimization problems involving at least three objectives. Box indices are an intelligible and easy to handle way to represent data. They are based on evaluating the solutions in a natural and rough enough scale in order to let the decision maker easily recognize the main characteristics of a solution at a glance and to facilitate comparison of two or more solutions in an easily understandable way.     

Risk preference modeling with conditional average: an application to portfolio optimization

The paper introduces a new risk measure called Conditional Average (CAVG), which was designed to cover typical attitudes towards risk for any type of distribution. It can be viewed as a generalization of Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), two commonly used risk measures. The preference structure induced by CAVG has the interpretation in Yaari’s dual theory of choice under risk and relates to Tversky and Kahneman’s cumulative prospect theory. The measure is based on the new stochastic ordering called dual prospect stochastic dominance, which can be considered as a dual stochastic ordering to recently developed prospect stochastic dominance. In general, CAVG translates into a nonconvex quadratic programming problem, but in the case of a finite probability space it can also be expressed as a mixed-integer program. The paper also presents the results of computational studies designed to assess the preference modeling capabilities of the measure. The experimental analysis was performed on the asset allocation problem built on historical values of S&P 500 sub-industry indexes. The research was supported by the grant PBZ-KBN-016/P03/99 from the State Committee for Scientific Research.     

Preference modeling experiments with surrogate weighting procedures for the PROMETHEE method

One of the main tasks in a multi-criteria decision-making process is to define weights for the evaluation criteria. However, in many situations, the decision-maker (DM) may not be confident about defining specific values for these weights and may prefer to use partial information to represent the values of such weights with surrogate weights. Although for the additive model, the use of surrogate weighting procedures has been already explored in the literature, there is a gap with regard to experimenting with such kind of preference modeling in outranking based methods, such as PROMETHEE, for which there already are applications with surrogate weights in the literature. Thus, this paper presents an experimental study on preference modeling based on simulation so as to increase understanding and acceptance of a recommendation obtained when using surrogate weights within the PROMETHEE method. The main approaches to surrogate weights in the literature (EW, RS, RR and ROC) have been evaluated for choice and ranking problematics throughout statistical procedures, including Kendall's tau coefficient. The surrogate weighting procedure that most faithfully represents a DM's value system according to this analysis is the ROC procedure.     

犹豫直觉模糊偏好关系积性一致性及其在群决策中的应用

模糊偏好关系在群决策中得到了广泛研究,针对犹豫直觉模糊集既能反映决策者偏好和非偏好的信息,又能描述其犹豫心理的特点,提出了犹豫直觉模糊偏好关系及其积性一致性的定义。为了修复不一致的犹豫直觉模糊偏好关系,先构建积性一致性指标,然后提出两种修复方法。最后,将犹豫直觉模糊偏好关系应用到群决策中,通过实例和比较说明了两种修复方法的有效性和合理性。     

Kernel-based learning methods for preference aggregation

The mathematical representation of human preferences has been a subject of study for researchers in different fields. In multi-criteria decision making (MCDM) and fuzzy modeling, preference models are typically constructed by interacting with the human decision maker (DM). However, it is known that a DM often has difficulties to specify precise values for certain parameters of the model. He/she instead feels more comfortable to give holistic judgements for some of the alternatives. Inference and elicitation procedures then assist the DM to find a satisfactory model and to assess unjudged alternatives. In a related but more statistical way, machine learning algorithms can also infer preference models with similar setups and purposes, but here less interaction with the DM is required/allowed. In this article we discuss the main differences between both types of inference and, in particular, we present a hybrid approach that combines the best of both worlds. This approach consists of a very general kernel-based framework for constructing and inferring preference models. Additive models, for which interpretability is preserved, and utility models can be considered as special cases. Besides generality, important benefits of this approach are its robustness to noise and good scalability. We show in detail how this framework can be utilized to aggregate single-criterion outranking relations, resulting in a flexible class of preference models for which domain knowledge can be specified by a DM.      

An extension to data envelopment analysis with preference structure for estimating overall inefficiency

This paper extends data envelopment analysis (DEA) with preference structure by fully considering the substitution effects among different inputs or outputs. When the unit cost and price information on inputs and outputs are available, the generalized weighted CCR (GWCCR) models proposed in this paper can provide some scalar values for measuring the overall inefficiency. It is found that the GWCCR models focus on the relative aspects of overall inefficiency instead of the absolute aspects focused on by the weighted additive DEA model.     

Learning intransitive reciprocal relations with kernel methods

In different fields like decision making, psychology, game theory and biology, it has been observed that paired-comparison data like preference relations defined by humans and animals can be intransitive. Intransitive relations cannot be modeled with existing machine learning methods like ranking models, because these models exhibit strong transitivity properties. More specifically, in a stochastic context, where often the reciprocity property characterizes probabilistic relations such as choice probabilities, it has been formally shown that ranking models always satisfy the well-known strong stochastic transitivity property. Given this limitation of ranking models, we present a new kernel function that together with the regularized least-squares algorithm is capable of inferring intransitive reciprocal relations in problems where transitivity violations cannot be considered as noise. In this approach it is the kernel function that defines the transition from learning transitive to learning intransitive relations, and the Kronecker-product is introduced for representing the latter type of relations. In addition, we empirically demonstrate on two benchmark problems, one in game theory and one in theoretical biology, that our algorithm outperforms methods not capable of learning intransitive reciprocal relations.     

Toward eudaimonology: notes on a quantitative framework for the study of happiness

After noting factors (concern for others, ignorance, irrationality) accounting for the divergences between preference and happiness, the question of representing the preference of an individual by a utility function is discussed, taking account of lexicographic ordering, imperfect discrimination and the corresponding concepts of semiorder and sub-semiorder. Methods to improve upon the interpersonal comparability of measures of happiness such as pinning down the dividing line of zero happiness and the use of a just perceivable increment of happiness are discussed. The relation of social welfare to individual welfare (i.e. happiness) is then considered. Some reasonable set of axioms ensuring that social welfare is a separable function of and indeed an unweighted sum of individual welfares are reviewed. Finally, happiness is regarded as a function of objective, institutional and subjective factors; an interdisciplinary approach is needed even for an incomplete analysis.