Weighted Influence Non-linear Gauge System (WINGS) – An analysis method for the systems of interrelated components

The WINGS method has been derived from DEMATEL and can be widely used as a structural model for analysis of intertwined factors and causal relations between them. Its novelty comes from an idea of including in one mathematical mechanism both strength (importance) and influence of the system components. In particular, WINGS can be applied as the MCDA method for evaluating alternatives when interrelations between criteria cannot be neglected. For the problem with independent criteria, WINGS reproduces the additive aggregation of preferences, a classical method in MCDA.     

A general decomposition approach for multi-criteria decision trees

In this paper, we address the dynamic and multi-criteria decision-making problems under uncertainty, generally represented by multi-criteria decision trees. Decision-making consists of choosing, at each period, a decision that maximizes the decision-maker outcomes. These outcomes should often be measured against a set of heterogeneous and conflicting criteria. Generating the set of non-dominated solutions is a common approach considered in the literature to solve the multi-criteria decision trees, but it becomes very challenging for large problems. We propose a new approach to solve multi-criteria decision trees without generating the set of all non-dominated solutions, which should reduce the computation time and the cardinality of the solution set. In particular, the proposed approach combines the advantages of decomposition with the application of multi-criteria decision aid (MCDA) methods at each decision node. A generalization of the Bellman’s principle of decomposition to the multi-criteria context is put forward. A decomposition theorem is therefore proposed. Under the sufficient conditions stated by the theorem, the principle of decomposition will generate the set of best compromise strategies. Seven MCDA methods are then characterized (lexicographic, weighted sum, multi-attribute value theory, TOPSIS, ELECTRE III, and PROMETHEE II) against the conditions of the theorem of decomposition and against other properties (neutrality, anonymous, fidelity, dominance, independency), in order to confirm or infirm their applicability with the proposed decomposition principle. Moreover, the relationship between independency and temporal consistence is discussed as well as the effects of incomparableness, rank reversals, and use of thresholds. Two conjectures resulted from this characterization.     

New Pythagorean Entropy Measure with Application in Multi-Criteria Decision Analysis

The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The performance of the introduced method is illustrated in a real-life case study, including a multi-criteria company selection problem. In this example, we provide a numerical illustration to distinguish the entropy measure proposed from some existing entropies used for Pythagorean fuzzy sets and intuitionistic fuzzy sets. Statistical illustrations show that the proposed entropy measures are reliable for demonstrating the degree of fuzziness of both Pythagorean fuzzy set (PFS) and intuitionistic fuzzy sets (IFS). In addition, a multi-criteria decision-making method complex proportional assessment (COPRAS) was also proposed with weights calculated based on the proposed new entropy measure. Finally, to validate the reliability of the results obtained using the proposed entropy, a comparative analysis was performed with a set of carefully selected reference methods containing other generally used entropy measurement methods. The illustrated numerical example proves that the calculation results of the proposed new method are similar to those of several other up-to-date methods.     

The SMAA-PROMETHEE method

PROMETHEE methods are widely used in Multiple Criteria Decision Aiding (MCDA) to deal with real world decision making problems. In this paper, we propose to apply the Stochastic Multicriteria Acceptability Analysis (SMAA) to the family of PROMETHEE methods in order to explore the whole set of parameters compatible with some preference information provided by the Decision Maker (DM). The application of the presented methodology is described in a didactic example.     

The performance of the series III 200kv high current industrial ion implanter

Two years of operation of the Series III Implanter have revealed the full potential of this machine.

The arsenic and phosphorus performance of this machine has greatly exceeded the initial 4 mA design criterion and 8 mA beams of these elements are readily obtainable. The boron beam currents are very dependent upon source history, but 1.2 mA is always available and 3 mA can be obtained from a well conditioned source.

The single gap post-acceleration system has proved very successful, a particular advantage over multi-gap tubes being the 100% beam transmission for any post-acceleration voltage and milliampere beams.

The processor system consists of a large capacity (54–3″. 27–4″, 18–5″ or 9–6″ silicon wafers) racetrack carousel which gives a mechanical scan free of geometric errors for wafers up to 61/2″ diameter. The wafers are mounted on plates with a clamping technique designed for use with an automatic loading system. The large implantation area (approximately 4,000 cm²) minimizes the temperature rise during implantation. The large beam area (approximately 25 cm² at the carousel) minimizes the pulse heating effect as the wafers sweep through the beam.     

A characterization of the 2-additive Choquet integral through cardinal information

In the context of multiple criteria decision analysis, we present the necessary and sufficient conditions to represent a cardinal preferential information by the Choquet integral w.r.t. a 2-additive capacity. These conditions are based on some complex cycles called cyclones.     

PROMETHEE: A comprehensive literature review on methodologies and applications

In recent decades, several Multi-Criteria Decision Aid (MCDA) methods have been proposed to help in selecting the best compromise alternatives. In the meantime, the PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations) family of outranking methods and their applications has attracted much attention from academics and practitioners. In this paper, a classification scheme and a comprehensive literature review are presented in order to uncover, classify, and interpret the current research on PROMETHEE methodologies and applications. Based on the scheme, 217 scholarly papers from 100 journals are categorized into application areas and non-application papers. The application areas include the papers on the topics of Environment Management, Hydrology and Water Management, Business and Financial Management, Chemistry, Logistics and Transportation, Manufacturing and Assembly, Energy Management, Social, and Other Topics. The last area covers the papers published in several fields: Medicine, Agriculture, Education, Design, Government and Sports. The scholarly papers are also classified by (1) year of publication, (2) journal of publication, (3) authors’ nationality, (4) PROMETHEE as applied with other MCDA methods, and (5) PROMETHEE as applied with GAIA (Geometrical Analysis for Interactive Aid) plane. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of PROMETHEE methodologies and applications, and hence promote the future of PROMETHEE research.     

An MCDA approach for the selection of bike projects based on structuring and appraising activities

This paper presents an MCDA approach for the structuring and appraising activities of a large and complex decision problem. More specifically, the paper makes use of the three-step structuring process for decision analysis proposed by von Winterfeldt and Edwards: (1) identifying the problem; (2) selecting an appropriate analytic approach; and (3) developing a detailed analytic structure. For illustration of the approach a case study dealing with the assessment task of prioritising and selecting initiatives and projects from a public pool with limited funds is examined throughout the paper. The process is embedded in a Decision Support System (DSS) making use of the REMBRANDT technique for pair wise comparisons to determine project rankings. A procedure for limiting the number of pair wise comparisons to be made in the process is in this connection presented. Finally, strengths and weaknesses in the approach are discussed and conclusions are made.     

Stochastic multiobjective acceptability analysis for the Choquet integral preference model and the scale construction problem

The Choquet integral preference model is adopted in Multiple Criteria Decision Aiding (MCDA) to deal with interactions between criteria, while the Stochastic Multiobjective Acceptability Analysis (SMAA) is an MCDA methodology considered to take into account uncertainty or imprecision on the considered data and preference parameters. In this paper, we propose to combine the Choquet integral preference model with the SMAA methodology in order to get robust recommendations taking into account all parameters compatible with the preference information provided by the Decision Maker (DM). In case the criteria are on a common scale, one has to elicit only a set of non-additive weights, technically a capacity, compatible with the DM’s preference information. Instead, if the criteria are on different scales, besides the capacity, one has to elicit also a common scale compatible with the preferences given by the DM. Our approach permits to explore the whole space of capacities and common scales compatible with the DM’s preference information.     

A stochastic method for robustness analysis in sorting problems

ELECTRE TRI is a multiple criteria decision aiding sorting method with a history of successful real-life applications. In ELECTRE TRI, values for certain parameters have to be provided. We propose a new method, SMAA-TRI, that is based on stochastic multicriteria acceptability analysis (SMAA), for analyzing the stability of such parameters. The stability analysis can be used for deriving robust conclusions. SMAA-TRI allows ELECTRE TRI to be used with uncertain, arbitrarily distributed values for weights, the lambda cutting level, and profiles. The method consists of analyzing finite spaces of arbitrarily distributed parameter values. Monte Carlo simulation is applied in this in order to describe for each alternative the share of parameter values that have it assigned to different categories. We show the real-life applicability by re-analyzing a case study in the field of risk assessment.