Kazimierz Zaras

Rough approximation of a preference relation by a multi-attribute dominance for deterministic, stochastic and fuzzy decision problems

Abstract The case of mixed data in which attributes have a different nature is not well known in current literature, although it is essential from a practical point of view. This situation is particularly frequent in risk management modelling which incorporates various degrees of precision of the variables measured, and can also be noted in a planning context for project evaluation problems taking into account information of a mixed (qualitative and quantitative) type. For a set of alternatives evaluated by a set of attributes, three kinds of evaluations are considered in this paper: deterministic, stochastic, or fuzzy with relation to each attribute. The mixed-data multi-attribute dominance for a reduced number of attributes (MMD R ) is proposed to model the preferences in this kind of problem. The approach is based on the dominance-based rough set approach proposed by Greco, Matarazzo and Slowinski.

Multiattribute Analysis Based on Stochastic Dominance

This paper presents a multiattribute analysis using Stochastic Dominances. These Dominances are proposed in relation with Separate Utility Models for gains and for losses. Two classes of utility functions, DARA-INARA, will be suggested for each of these domains on each attribute. These models allow us to identify the “transparent” category of stochastic dominances and to establish for each of these attributes the preferences of a decision maker. In practice, the essential characteristic of a multiattribute problem is that we have several conflicting attributes. Consequently, the Multiattribute Stochastic Dominance relationship risk being poor, thus resulting in uselessness to the decision maker. This is why we propose to weaken the unanimity condition of classic dominance. We will use Roy’s Preference Aggregation Rule which allows us to build a global outranking relation. Very often we can build a global outranking relation based only on the “transparent” category of stochastic dominances, because this category is satisfied in a high percentage of cases.

Stochastic dominance in multicriterion analysis under risk

Traditionally, in the literature on the modelling of decision aids one notes the propensity to treat expected utility models and outranking relation models as rivals. It may be possible, however, to benefit from the use of both approaches in a risky decision context. Stochastic dominance conditions can be used to establish, for each criterion, the preferences of a decision maker and to characterise them by a concave or convex utility function.Two levels of complexity in preference elicitation, designated as clear and unclear, are distinguished. Only in the case of unclear preferences is it potentially interesting to attempt to estimate the value function of the decision maker, thus obtaining his (her) preferences with a reduced number of questions. The number of questions that must be asked of the decision maker depends upon the level of the concordance threshold that he(she) requires in the construction of the outranking relations using the ELECTRE method.

Rough approximation of a preference relation by a multi-attribute stochastic dominance for determinist and stochastic evaluation problems

Abstract Let A be a set of actions evaluated by a set of attributes. Two kinds of evaluations will be considered in this paper: determinist or stochastic in relation to each attribute. The multi-attribute stochastic dominance (MSD r ) for a reduced number of attributes will be suggested to model the preferences in this kind of problem. The case of mixed data, where we have the attributes of different natures is not well known in the literature, although it is essential from a practical point of view. To apply the MSD r the subset R of attributes from which approximation of the global preference is valid should be known. The theory of Rough Sets gives us an answer on this issue allowing us to determine a minimal subset of attributes that enables the same classification of objects as the whole set of attributes. In our approach these objects are pairs of actions. In order to represent preferential information we shall use a pairwise comparison table. This table is built for subset B ⊂ A described by stochastic dominance (SD) relations for particular attributes and a total order for the decision attribute given by the decision maker (DM). Using a Rough Set approach to the analysis of the subset of preference relations, a set of decision rules is obtained, and these are applied to a set A ⧹ B of potential actions. The Rough Set approach of looking for the reduction of the set of attributes gives us the possibility of operating with MSD r .

Multicriteria optimization and decision engineering of an extrusion process aided by a diploid genetic algorithm

In many, if not most, optimization problems, industrialists are often confronted with multiobjective decision problems. For example, in manufacturing processes, it may be necessary to optimize several criteria to take into account all the market constraints. So, the purpose is to choose the best tradeoffs among all the defined and conflicting objectives. In multicriteria optimization, after the decision maker has chosen all his objectives, he has to determine the multicriteria optimal zone by using the concept of domination criterion called Pareto domination. Two points in the research domain are compared. If one is better for all attributes, it is a nondominating solution. All the nondominating points form the Paretos region. In this paper, several multiobjective optimization algorithms are used to obtain this zone. These methods are based on a diploid genetic algorithm and are compared to an industrial application: food granulation. In the optimal zone, the decision maker has to choose the best solution after he has made a ranking with all potential solutions. A partition is made and the decision maker has more information on the process. Finally, a decision support system shell is developed in order to classify all solutions.

Comparison of two multicriteria decision aid methods: Net Flow and Rough Set Methods in a high yield pulping process

Abstract This investigation presents a synthesis of two multicriteria analysis methods, Rough Set Method (RSM) and Net Flow Method (NFM), applied to the multicriteria optimisation for the manufacture of paper using jack pine as the source of fibres. This work is the result of a collaboration between different Canadian and French laboratories. The two optimisation methods, based on different approaches, are applied to the same Pareto domain of non-dominated operating conditions. The Rough Set Method (RSM) uses a set of decision rules that are based on the preferences of experts, when presented with a small set of diverse conditions extracted from the Pareto domain. These rules are then applied to the entire Pareto domain to determine the preferred zone of operation. In the Net Flow Method (NFM), the preferences of experts are defined with three threshold values and one set of weights that are used to classify the entire Pareto domain. The NFM is a hybrid of two methods between ELECTRE and PROMETHEE. To compare these two methods, they were used to optimise the identical process. Results clearly show that the two methods gave nearly identical optimal solutions and well within inherent experimental errors.

Multicriteria optimization of a high yield pulping process with rough sets

Abstract The optimization of complex processes usually involves many competing objectives; in this case there is typically no solution that yields optimal values for all of the objective criteria and the decision-maker must therefore find a reasonable compromise. In recent years, new multicriteria methods have been developed to assist the practitioner in achieving a judicious compromise among the various competing objectives. One method, the rough set method (RSM), is able to encapsulate the preferences of an expert within a simple set of logical rules that are used to rank a large number of feasible solutions according to these preferences. The RSM was used in this investigation to determine the optimal operating region of a high yield pulping process. This pulping process has seven input variables that can be manipulated to optimize four objective criteria characterizing the product: brightness, specific refining energy, extractive content, and rupture length. Results show that an optimal solution zone can be easily defined and zones of decreasing preference can be drawn. This information is very useful to the practitioner for choosing the desired operating conditions and for analyzing the robustness of the preferred operating scenarios from a process control point of view.

The value of additional information in multicriteria decision making choice problems with information imperfections

Processing information is a key ingredient for decision making. In most decision-making cases, information is distributed across various sources that may differ in reliability and accuracy. Various sources and kinds of uncertainty are encountered in the same decision situation. “Information imperfections” is a general term that encompasses all kinds of “deficiencies” (such as uncertainty, imprecision, ambiguity, incompleteness) that may affect the quality of information at hand. In discrete multicriteria decision making, where several alternatives are assessed according to heterogeneous and conflicting criteria, information used to assess such alternatives can also be imperfect. It is rather natural, in such a context, to seek additional information to reduce these imperfections. This paper aims at extending the Bayesian model for assessing the value of additional information to multicriteria decision analysis in a context of imperfect information. A unified procedure for processing additional information has been proposed in a previous work. It leads to prior and posterior global preference relational systems. It will be extended here to include pre-posterior analysis where concepts such as the expected value of perfect information and the expected value of imperfect information are adapted to multicriteria decision making choice problems.

Rough Approximation of a Preference Relation by a Multi-Attribute Stochastic Dominance for a Reduced Number of Attributes

Let A be a set of actions evaluated by a set of attributes. Two kinds of evaluations will be considered in this paper: determinist or stochastic in relation to each attribute. The Multi-Attribute Stochastic Dominance (MSDr) for a reduced number of attributes will be suggested to model the preferences in this kind of problem. To apply the MSDr the subset R of attributes from which approximation of the global preference is valid should be known. The theory of Rough Sets gives us an answer on this issue allowing us to determine a minimal subset of attributes that enables the same classification of objects as the whole set of attributes. In our approach these objects are pairs of actions. In order to represent preferential information we shall use a pairwise comparison table (PCT). This table is built for subset B⊂ A described by Stochastic Dominance relations for particular attributes and a total order for the decision attribute given by the decision maker (DM). Using a Rough Sets approach for the analysis of the subset of preference relations, a set of decision rules is obtained, and these are applied to a set A\B of potential actions. The Rough Sets approach of looking for the reduction of the set of attributes gives us the possibility of operating on Multi-Attribute Stochastic Dominance for a reduced number of attributes.

Ranking by rough approximation of preferences for decision engineering applications

A pulping process is studied to illustrate a new methodology in the field of decision engineering, which relies on the Dominance Rough-Set-based Approach (DRSA) to determine the optimal operating region. The DRSA performs a rough approximation of preferences on a small set of Pareto-optimal experimental points to infer the decision rules with and without considering thresholds of indifference with respect each attribute in the decision table. With thresholds of indifference, each rule can be represented by three discrete values (i.e. 0; 0.5; 1). A value of (1) indicates the first point, in a pair wise comparison, is strictly preferred to the second point from the Pareto domain. A value of (0) indicates the opposite relation whereas a value of (0.5) indicates that the two points are equivalent from an engineering point of view. These decision rules are then applied to the entire set of points representing the Pareto domain. The results show that the rules obtained with the indifference thresholds improve the quality of approximation.