Eiji Takeda

A method for multiple pseudo-criteria decision problems

Abstract Most complex decision problems involve conflicting multicriteria to be reconciled. It is not uncommon that the numerical values of alternatives of some criteria are subject to imprecision, uncertainty, and indetermination. The concept of pseudo-criterion and its two thresholds allow them to be taken into account. So far, outranking relation methods, which are called ELECTRE I–IV and others, in which an outranking relation between alternatives is constructed from pseudo-criteria have been developed. Among others, ELECTRE III is the most familiar and has been widely used. The purpose of this paper is to propose a new procedure for treating the pseudo-criterion based on the ternary AHP. This procedure differs from ELECTRE III and requires only the incomplete information on the weights but not precise weights. Strict preference, weak preference, and indifference relations associated with a pseudo-criterion are formulated by a ternary comparison. In general, the procedures for dealing with the pseudo-criterion necessarily involve a certain amount of arbitrariness. Therefore, it is preferable to derive the rankings of alternatives from several procedures for the pseudo-criterion in order to promote complementary viewpoints. Comparing our procedure with ELECTRE III, the strengths and weaknesses of the proposed procedure are discussed. Scope and purpose Most decision problems involve multiple and conflicting objectives, goals, or attributes. In the past three decades, many approaches have been developed. These include decision analysis based on multiattribute utility theory and interactive approaches based on the progressive articulation of preferences. They are built on sound theoretical foundations but rely on strict assumptions about the underlying preference structure. It is not uncommon that the numerical values of alternatives of some criteria are imprecise and ambiguous in complex decision problems. In such cases, the above approaches may not be appropriate. To cope with them, the concept of pseudo-criterion was introduced. So far, the outranking relation methods based on the pseudo-criterion which do not require the assumption of transitivity nor the complete comparability in the underlying preference structure have been developed. In this paper, we propose a new procedure for treating the pseudo-criterion based on the ternary AHP that differs from the outranking relation methods. In general, the procedures for dealing with the pseudo-criterion necessarily involve a certain amount of arbitrariness. Therefore, it is preferable to derive the rankings of alternatives from several procedures based on the pseudo-criterion in order to promote complementary viewpoints.

Assessing priority weights from subsets of pairwise comparisons in multiple criteria optimization problems

Using a set covering concept we explore the possibility and flexibility of selecting a subset of all possible pairs of comparisons to assess priority weights of the decision criteria. Different techniques offer different priority weights with different properties. They are, however, interrelated when special subsets such as basic coverings, elementary cycles and complete covering are considered. This paper provides a framework for unifying existing assessment methods, and offers some fundamental theorems which reveal the intricate relationships among the methods over the subsets.

An extended DEA model: Appending an additional input to make all DMUs at least weakly efficient

Abstract This paper proposes an extended Data Envelopment Analysis (DEA) model in which an additional input is appended to the original DEA model. For each DMU, the additional input takes the value of (0,1] as close as possible to one under the condition that all efficient DMUs in the original CCR model remain efficient and that all DMUs which are not efficient be at least weakly efficient in the extended CCR model. It is shown that the additional input value of any inefficient DMU is the reciprocal of the radial distance to the boundary of a production possibility set in the original BCC model.

Exploitation Procedure Based on Eigenvector Revisited: The Concept of Weighted Preference Flows in Multicriteria Outranking Analysis

The outranking analysis has been frequently used to deal with the complex decisions involving qualitative criteria and imprecise data. So far, various versions of ELECTRE have been proposed for ranking alternatives in the outranking analysis. Among others, ELECTRE III has been widely used. A distillation procedure using a qualification index is proposed to rank alternatives from the fuzzy outranking relation. A weakness of ELECTRE III, however, is to involve the arbitrariness in the selection of the discrimination threshold function for the distillation procedure. On the other hand, various variants of PROMETHEE has also been proposed for the outranking analysis. PROMETHEE intends to be simple and easy to understand. A deficiency of PROMETHEE is that it does not take discordance into account when the outranking relation matrix is constructed. This note revisits an exploitation procedure based on eigenvector using the “weighted” preference in-and out-flows of each alternative in the outranking analysis. The basic idea is that it should be better to outrank a “strong” alternative than a “weak” one and, conversely, it is less serious to be outranked by a “strong” alternative than by a “weak” one in a PROMETHEE context. It has a completely different interpretation with the AHP (Analytic Hierarchy Process) since the components of the fuzzy (valued) outranking relation matrix are neither ratios nor reciprocal as in the AHP.

MCDA in Analyzing the Recycling Strategies in Malaysia

The outranking analysis has been frequently used to deal with the complex decisions involving qualitative criteria and imprecise data (see [5]).

A Generalized Procedure in PROMETHEE Analysis, with an Application to the Evaluation of Recycling Strategies in Malaysia

At present, the per capita generation of solid waste in Malaysia varies from 0.45 to 2kg/day depending on the economic status of an area. In general, the per capita generation rate is about 1kg/day. Even though 17,000 tonnes/day of solid waste is being generated, only 5% is being recycled. If this particular scenario continues without appropriate mitigation, Malaysia will be facing a serious problem in municipal solid waste management. Hence, government has targeted 22% of waste to be recycled by 2020. Various strategies have been formulated in achieving this figure. In Malaysia, research is being done vastly on recycling but very few related to multicriteria. The purpose of this paper is to propose an eigenvector procedure using the ”weighted” preference flows in the PROMETHEE multicriteria analysis. It is illustrated by an application to the evaluation of the recycling strategies to provide an insight on inspiring the recycling activities among residents.

EIGENVECTOR METHOD IN MULTICRITERIA OUTRANKING RELATIONS

Most complex decision problems involve conflicts among multiple criteria and uncertain and imprecise data. The (fuzzy) outranking relation model that was introduced by Roy can tackle such complex situations. The present paper proposes a new ranking procedure based on the eigenvector in multicriteria outranking relations. The properties of the eigenvector method in ordinary outranking relations are investigated. Then, the eigenvector method is compared to that of qualification by several examples. Finally, we compare the eigenvector method with the distillation method in ELECTRE III in fuzzy outranking relations. The results of the two methods did not exhibit significant differences. The eigenvector method turns out useful, because it can promote a complementary viewpoint.

DEA Approach to the Allocation of Various TV Commercials to Dayparts

This paper presents an application of DEA to ex ante planning based on an empirical data, while many applications of DEA are directed to the ex post evaluations of accomplishments of competing DMUs.

Pseudo-Criterion Approaches to Evaluating Alternatives in Mangrove Forests Management

The concept of the pseudo-criterion plays an important role in complex decision problems involving imprecise, uncertain and indeterminate data such as mangrove forests management. The outranking relation methods such as ELECTRE are well known to deal with the pseudo-criterion.

On Decision of Optimum Index Fund

This paper is concerned with a traditional asset allocation of the Markowitz type and develops an efficient algorithm to design an index fund which is a compromise solution to the bicriteria optimization problem. A numerical example is provided to illustrate our algorithm.