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2015 | Buch

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Probabilistic Composition of Preferences, Theory and Applications

verfasst von: Annibal Parracho Sant'Anna

Verlag: Springer International Publishing

Buchreihe : Decision Engineering

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Putting forward a unified presentation of the features and possible applications of probabilistic preferences composition, and serving as a methodology for decisions employing multiple criteria, this book maximizes reader insights into the evaluation in probabilistic terms and the development of composition approaches that do not depend on assigning weights to the criteria.

With key applications in important areas of management such as failure modes, effects analysis and productivity analysis – together with explanations about the application of the concepts involved –this book makes available numerical examples of probabilistic transformation development and probabilistic composition.

Useful not only as a reference source for researchers, but also in teaching classes of graduate courses in Production Engineering and Management Science, the key themes of the book will be of especial interest to researchers in the field of Operational Research.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Multiple Criteria Decision Analysis

Abstract

A probabilistic approach to multicriteria decision problems can take in due account the uncertainty that is inevitably present in preference evaluations. Translating the preference measurements according to different criteria into probabilities of being chosen as the best alternative has two advantages. First, it makes comparable preference evaluations that come in entirely different scales. Besides, it opens probabilistic ways to automatically combine the evaluations according to the multiple criteria.

Annibal Parracho Sant’Anna

Chapter 2. Approaches to Criteria Combination

Abstract

Two main approaches to consider the importance of the criteria in a multicriteria decision may be employed. The preferences according to each of them may be combined into a global preference by a weighted average where the importance of the criteria enters separately as weights. Otherwise the interaction between the evaluations by the multiple criteria must be taken into account when combining them and the importance of sets of criteria taken together must be computed. A simple procedure to determine the importance in the first case can be based on pairwise comparison of the criteria. A procedure to compute the importance of the sets of criteria to apply the Choquet integral in the second case may be based on pairwise comparison of preferences between distributions of probability on the space of criteria.

Annibal Parracho Sant’Anna

Chapter 3. The Probabilistic Approach to Preferences Measurement

Abstract

As the value of an attribute only signals the position of a probability distribution of the preference, the preference for an alternative according to any criterion can be given in terms of probability of it being chosen. Composition of these probabilities to obtain a global preference combining the multiple criteria can then be performed in probabilistic terms.

Annibal Parracho Sant’Anna

Chapter 4. Computation of Probabilities of Preference

Abstract

The starting point to the computation of preferences by multiple criteria are vectors of objective measurements of attributes of the alternatives or evaluations in a Likert scale, or even approximate rankings. These initial values are treated as location parameters of probability distributions, for instance as modes of triangular distributions or means of normal distributions. For each criterion, the probability of a realization of the distribution representing each alternative being the best in a sample can then be computed. The final score of an alternative is obtained combining its multiple probabilities of being the best.

Annibal Parracho Sant’Anna

Chapter 5. Composition by Joint Probabilities

Abstract

The difficulty involved in the composition of the criteria by weighted average, due to the difficulty of assigning weights to criteria and to sets of criteria, was already signaled in the preceding chapters. The probabilistic approach allows forgo the weighting of the criteria and get overall scores of preference by calculating joint probabilities.

Annibal Parracho Sant’Anna

Chapter 6. Composition by DEA Distance to the Frontier

Abstract

In the preceding chapter the composition of the preferences according to the different criteria was made by rules that do not weight the criteria. These rules were based on different points of view formulated in terms of joint probabilities. A different approach to avoid a previous determination of weights, based on multivariate distances to the frontiers, is considered in this chapter.

Annibal Parracho Sant’Anna

Chapter 7. Dynamic Probabilistic Indices

Abstract

A DEA approach to access the evolution of productivity along time exploring the idea of the Malmquist index involves calculating the ratio between the distances to the production frontier of 2 years of evaluation of the alternative being evaluated: one representing the observed production during the year to which the frontier is built and the other representing the observed production of the next or the previous year. The same type of substitution is here applied with a probabilistic composition algorithm to generate probabilistic Malmquist indices.

Annibal Parracho Sant’Anna

Chapter 8. Probabilities in the Problem of Classification

Abstract

Evaluation of alternatives may be derived from probabilistic comparisons made with different sets of profiles which represent ordered classes. This may be used to solve the problem of, instead of choosing the best or worst alternative, identifying alternatives that correspond to each of a set of different levels of performance.

Annibal Parracho Sant’Anna

Chapter 9. Capacities Determination

Abstract

A capacity may be derived from the observed evaluations by following the principle of maximizing posterior probabilities. By this choice, of the posterior probability as paradigm, will be assigned highest capacity to those sets of criteria for which is highest the probability of some alternative maximizing the preference. Thus more importance is assured to those criteria with highest power of isolated discriminating a best option and if criteria repeat each other their importance is not magnified by such repetition.

Annibal Parracho Sant’Anna

Chapter 10. Rough Sets Modeling

Abstract

The transformation in probabilities of being the best can reduce the number of possible values of the attributes. By this property, it may be used to amplify the roughness of decision attributes in Rough Sets Theory applications. This can be explored to increase the index of quality of approximation and simplify the classification rules.

Annibal Parracho Sant’Anna

Chapter 11. Application to FMEA Priority Assessments

Abstract

A risk priority probability, obtained by multiplying the probabilities of being the mode of failure of higher risk simultaneously with respect to severity, occurrence and detectability, is here employed instead of the classical priority risk number of FMEA. A probabilistic classification of risks with respect to classes previously determined is also discussed.

Annibal Parracho Sant’Anna

Backmatter

Titel: Probabilistic Composition of Preferences, Theory and Applications
verfasst von: Annibal Parracho Sant'Anna
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-11277-0
Print ISBN: 978-3-319-11276-3
DOI: https://doi.org/10.1007/978-3-319-11277-0

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