Scientific Data Ranking Methods (eBook)

Theory and Applications

Manuela Pavan, Roberto Todeschini (Herausgeber)

eBook Download: EPUB

2008 | 1. Auflage
224 Seiten
Elsevier Science (Verlag)
978-0-08-093193-7 (ISBN)

Infos

This volume presents the basic mathematics of ranking methods through a didactic approach and the integration of relevant applications. Ranking methods can be applied in several different fields, including decision support, toxicology, environmental problems, proteomics and genomics, analytical chemistry, food chemistry, and QSAR.
. Covers a wide range of applications, from the environment and toxicology to DNA sequencing
. Incorporates contributions from renowned experts in the field
. Meets the increasing demand for literature concerned with ranking methods and their applications

Inhalt

Front Cover 1
Data Handling in Science and Technology – Scientific Data Ranking Methods: Theory and Applications Volume 27 4
Copyright Page 5
Table of Contents 6
Contributors 8
Preface 10
Chapter 1. Introduction to Ranking Methods 12
1. Definition of Order Relations 12
2. Order in Statistics 14
3. Order in Graphs 53
4. Order in Optimization Problems 54
References 57
Appendix A 59
Chapter 2. Total-Order Ranking Methods 62
1. Introduction 62
2. Total-Order Ranking Methods 64
3. Conclusions 81
References 81
Chapter 3. Partial Ordering and Hasse Diagrams: Applications in Chemistry and Software 84
1. Introduction 84
2. Partial-Order Theory 85
3. Software for Hasse Diagram Technique 88
4. Ranking of Chemicals as An Example 89
5. Applications of Hasse Diagram Technique to the Data Availability of Chemicals 94
6. Summary, Outlook and Conclusion 101
References 102
Chapter 4. Partial Ordering and Prioritising Polluted Sites 108
1. Introduction 108
2. Methodology 109
3. Applications 112
4. Conclusions 119
Acknowledgments 119
References 119
Chapter 5. Similarity/Diversity Measure for Sequential Data Based on Hasse Matrices: Theory and Applications 122
1. Introduction 122
2. Theory 123
3. Application of the Hasse Distance Approach to Sequential Data 127
4. Conclusions 148
References 148
Chapter 6. The Interplay between Partial-Order Ranking and Quantitative Structure–Activity Relationships 150
1. Introduction 150
2. Methodology 151
3. Results and Discussion 155
4. Conclusions and Outlook 164
References 165
Abbreviations 168
Chapter 7. Semi-Subordination Sequences in Multi-Measure Prioritization Problems 170
1. Introduction 170
2. Theory 172
References 178
Chapter 8. Multi-Criteria Decision-Making Methods: A Tool for Assessing River Ecosystem Health Using Functional Macroinvertebrate Traits 180
1. Introduction 180
2. Biomonitoring Program 182
3. Applications of Total-Order Ranking Techniques 186
4. Environmental Description of Serio River 186
5. Ecology of Serio River 188
6. What we Obtained Using This Method? 194
References 196
Appendix 199
Chapter 9. The DART (Decision Analysis by Ranking Techniques) Software 204
1. Introduction 204
2. The Dart Software 205
3. Example of Application of the Dart Software 208
4. Conclusions 218
References 218
Index 220

Textauszug

Chapter 2 Total-Order Ranking Methods

M. Pavan, R. Todeschini

Publisher Summary

This chapter describes the theory of the mostly known total-order ranking techniques. Total-order ranking methods are multicriteria decision making (MCDM) techniques used for the ranking of various alternatives on the basis of more than one criterion. The chapter reviews a number of total-order ranking methods that have been widely used to facilitate the structuring and understanding of the perceived decision problem. The chapter presents the simplest approaches, like the Pareto optimality and the simple additive ranking (SAR) approach followed by the approaches belonging to the so-called multiattribute value theory—that is, utility, desirability, and dominance functions. In these models, numerical scores are constructed to represent the degree to which an alternative may be preferred to another. These scores are developed initially for each criterion and aggregated into a higher level of preference models.

1 Introduction

Total-order ranking methods belong to multicriteria decision making (MCDM), a discipline in its own right, which deals with decisions involving the choice of a best alternative from several potential candidates in a decision, subject to several criteria or attribute that may be concrete or vague.

Typically, a decision problem is a situation where an individual has alternative courses of action available and has to select one of them, without an a priori knowledge of which is the best one. A decision process can be organized in three phases. The first phase is problem identification and structuring, which consists in the identification of the purpose of the decision, in the recognition of the problem to be solved, in the diagnosis of the cause–effect relationships for the decision situation and in the identification of the judgment criteria. The second phase is the so-called model development and use, which consist in the development of formal models, decision maker preferences, values, trade-offs, goals to compare the alternatives or actions under consideration to each other in a systematic and transparent way. The third phase is the development of action plans since the analysis does not solve the decision. The decision process, which results in the selection of the best solution, i.e. the solution where the positive outcomes outweigh possible losses, is efficient if the procedure to reach the solution is optimal. The aims of a decision process are to effectively generate information on the decision problem from available data, to effectively generate solutions and to provide a good understanding of the structure of a decision problem.

Multicriteria decision-making techniques are used for helping people in making their decision according to their preferences, in cases where there is more than one conflicting criterion, finding the optimal choice among the alternatives. Making a decision is not just a question of selecting a best alternative. Often the need is to rank all the alternatives for resource allocation or to combine the strengths of preferences of individuals to form a collective preference.

Mathematics applied to decision making provides methods to quantify or prioritize personal or group judgments that are typically intangible and subjective. Decision making requires comparing different kinds of alternatives by decomposing the preferences into many properties that the alternatives have, determining their importance, comparing and obtaining the relative preference of alternatives with respect to each property and synthesizing the results to get the overall preference. Therefore, the strategy consists in breaking down a complex problem into its smaller components and establishing importance or priority to rank the alternatives in a comprehensive and general way to look at the problem mathematically.

The key starting point of MCDM lies in attempting to represent often intangible goals in terms of the number of individual criteria. A challenging feature of MCDM methods is the identification of the set of criteria by which alternatives are to be compared. The selection criteria is part of the modeling and problem formulation, a significant phase often under-emphasized. A useful general definition of a criterion is the one provided by Bouyssou (1990) as a tool allowing comparison of alternatives according to a particular axis or point of view. It is generally assumed that each criterion can be represented by a surrogate measure of performance, represented by some measurable attribute of the consequences arising from the achievement of any particular decision alternative.

Some thoughts are to be considered in identifying the criteria: their value relevance, i.e. their link with the decision maker concept of their goals; their understandability and their measurability, i.e. the performance of the alternative against the criteria should be measurable; their non-redundancy in order to avoid that the concept they represent is in attributed greater importance; their judgmental independence, i.e. the preferences with respect to a single criterion should be independent from the level of another; their balancing between completeness and conciseness.

Subjectivity is intrinsic in all decision making and in particular in the choice of the criteria on which the decision is based and in their relative weight. Multicriteria decision making does not dissolve subjectivity, but it makes the need for subjective judgments explicit and the whole process by which they are considered is made transparent.

Over the years, several MCDM methods have been proposed (Hobbs and Horn, 1997) in different areas, with different theoretical background and facing different kinds of questions and providing different kinds of results (Hobbs and Meier, 1994).

Some of these methods have been developed to fulfill the need of specific problems; other methods are more general and have been used in different areas. The different MCDM methods are distinguished from each other in the nature of the model, in the information needed and in how the model is used. They have in common the aim to create a more formalized and better-informed decision-making process, the need to define alternatives to be considered, the criteria to guide the evaluation and the relative importance of the different criteria.

In this chapter, the theory of the mostly known total-order ranking techniques is described.

2 Total-Order Ranking Methods

Once the decision problem identification phase has generated a set of alternatives, which can be a discrete list of alternatives as well as be defined implicitly by a set of constraints on a vector of decision variables, and once the set of criteria against which the alternatives have to be analyzed and compared are defined, then a decision model has to be built to support decision makers in searching the optimal or the set of satisfactory solutions to the multicriteria decision problem. The decision model is made of two main components as described by Belton and Stewart (2003):

• Preferences in terms of each individual criterion, i.e. models describing the relative importance or desirability of achieving different levels of performance for each identified criterion. In addition, for each criterion it is necessary to ascertain explicitly if the best condition is satisfied by a minimum or a maximum criterion value, and the trend from the minimum to the maximum must also be established. The criteria setting is a crucial point since it requires the mathematization of decision criteria, which are often not completely defined or explicit.

• An aggregation model, i.e. a model allowing inter-criteria comparisons (such as trade-offs), in order to combine preferences across criteria. Criteria are not always in agreement; they can be conflicting, motivating the need to find an overall optimum that can deviate from the optima of one or more of the single criteria. Multicriteria decision-making methods are often based on an aggregation function Γ of the criteria fj, where j = 1,…, p:

     (1)

Thus, if an alternative is characterized by p criteria, then a comparison of different elements needs a scalar function, i.e. an order or ranking index, to sort them according to the numerical value of Γ. Several evaluation methods, which define a ranking parameter generating a total-order ranking, have been proposed in the literature.

The purpose of the decision model is to create a view of decision maker preferences based on a defined set of assumptions and to guide the decision maker in the optimum solution search.

Before reviewing some total-order ranking methods, some further terms and basic principles are introduced.

A p-dimensional system is generally considered, with an associated (n×p) data matrix X. To each of the n alternatives, a set of p criteria relevant to the decision-making procedure is associated. Each criterion can then be weighted to take account of the different importance of the criteria in the decision rule. The strategies to reach the optimal choice require the development of a ranking of the different options. Within a set of alternatives A (a, b, c, d), a ranking (order) on A is a relation with the following...

Produkt-Details

• Erscheint lt. Verlag: 17.11.2008
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Medizin / Pharmazie ► Gesundheitsfachberufe
• Themenwelt: Studium ► 2. Studienabschnitt (Klinik) ► Pharmakologie / Toxikologie
• Themenwelt: Naturwissenschaften ► Chemie ► Analytische Chemie
• Themenwelt: Technik ► Umwelttechnik / Biotechnologie
• ISBN-10: 0-08-093193-6 / 0080931936
• ISBN-13: 978-0-08-093193-7 / 9780080931937