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1992 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Fuzzy Multiple Attribute Decision Making

Methods and Applications

verfasst von: Shu-Jen Chen, Ching-Lai Hwang

Verlag: Springer Berlin Heidelberg

Buchreihe : Lecture Notes in Economics and Mathematical Systems

Enthalten in: Professional Book Archive

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Über dieses Buch

This monograph is intended for an advanced undergraduate or graduate course as well as for researchers, who want a compilation of developments in this rapidly growing field of operations research. This is a sequel to our previous works: "Multiple Objective Decision Making--Methods and Applications: A state-of-the-Art Survey" (No.164 of the Lecture Notes); "Multiple Attribute Decision Making--Methods and Applications: A State-of-the-Art Survey" (No.186 of the Lecture Notes); and "Group Decision Making under Multiple Criteria--Methods and Applications" (No.281 of the Lecture Notes). In this monograph, the literature on methods of fuzzy Multiple Attribute Decision Making (MADM) has been reviewed thoroughly and critically, and classified systematically. This study provides readers with a capsule look into the existing methods, their characteristics, and applicability to the analysis of fuzzy MADM problems. The basic concepts and algorithms from the classical MADM methods have been used in the development of the fuzzy MADM methods. We give an overview of the classical MADM in Chapter II. Chapter III presents the basic concepts and mathematical operations of fuzzy set theory with simple numerical examples in a easy-to-read and easy-to-follow manner. Fuzzy MADM methods basically consist of two phases: (1) the aggregation of the performance scores with respect to all the attributes for each alternative, and (2) the rank ordering of the alternatives according to the aggregated scores.

Inhaltsverzeichnis

Frontmatter
I. Introduction
Abstract
Making decisions is a part of our daily lives. The major concern is that almost all decision problems have multiple, usually conflicting, criteria. Research on how to solve such problems has been enormous. Methodologies, as well as their applications, appear in professional journals of different disciplines. Diversified as such problems may be, they are broadly classified into two categories: (1) Multiple Attribute Decision Making (MADM) and (2) Multiple Objective Decision Making (MODM). From a practical viewpoint, MADM is associated with problems whose number of alternatives has been predetermined. The Decision Maker (DM) is to select/prioritize/rank a finite number of courses of action. On the other hand, MODM is not associated with problems in which the alternatives have been predetermined. The DM’s primary concern is to design a “most” promising alternative with respect to limited resources.
Shu-Jen Chen, Ching-Lai Hwang
II. Multiple Attribute Decision Making — An Overview
Abstract
Multiple Attribute Decision Making (MADM) refers to making decisions in the presence of multiple, usually conflicting, attributes. Problems for multiple attributes decision making are common occurrences in every aspect of life.
Shu-Jen Chen, Ching-Lai Hwang
III. Fuzzy Sets and Their Operations
Abstract
Fuzzy set theory is developed for solving problems in which descriptions of activities and observations are imprecise, vague, and uncertain. The term “fuzzy” refers to the situation in which there are no well-defined boundaries of the set of activities or observations to which the descriptions apply. For example, one can easily assign a person seven feet tall to the “class of tall men”. But it would be difficult to justify the inclusion or exclusion of a six-foot tall person to that class, because the term “tall” does not constitute a well-defined boundary. This notion of fuzziness exists almost everywhere in our daily life, such as the “class of red flowers,” the “class of good kickers,” the “class of expensive cars,” or “numbers close to 10,” etc. These classes of objects cannot be well represented by classical set theory. In classical set theory, an object is either in a set or not in a set. An object cannot partially belong to a set.
Shu-Jen Chen, Ching-Lai Hwang
IV. Fuzzy Ranking Methods
Abstract
Recall that in Chapter 2 we define the Multiple Attribute Decision Making (MADM) problem as:
$$\text{D=}\begin{matrix} {{\text{A}}_{1}}\\ {{\text{A}}_{2}}\\ \vdots\\ {{\text{A}}_{\text{m}}}\\ \end{matrix}\text{ }\left[\begin{matrix} {{\text{X}}_{1}}\text{ }{{\text{X}}_{2}}\text{ }\cdots \text{ }{{\text{X}}_{\text{n}}}\\ {{\text{X}}_{11}}\text{ }{{\text{X}}_{12}}\text{ }\cdots \text{ }{{\text{X}}_{1\text{n}}}\\ {{\text{X}}_{21}}\text{ }{{\text{X}}_{22}}\text{ }\cdots \text{ }{{\text{X}}_{\text{2n}}}\\ \vdots \text{ }\\ {{\text{X}}_{\text{m1}}}\text{ }{{\text{X}}_{\text{m2}}}\text{ }\cdots \text{ }{{\text{X}}_{\text{mn}}}\\ \end{matrix}\right]$$
$$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{W} = ({\text{W}}_1 {\text{,W}}_2 {\text{,}} \ldots {\text{,W}}_{\text{n}} {\text{)}} $$
where Ai, i = 1, ..., m are possible courses of action (or alterna-tives); Xj, j = 1, ..., n are attributes with which alternative performances are measured; xij is the performance (or rating) of alternative Ai with respect to attribute Xj; wj, j = 1,...,n are the relative importance of attributes.
Shu-Jen Chen, Ching-Lai Hwang
V. Fuzzy Multiple Attribute Decision Making Methods
Abstract
A MADM problem is given as:
$$\text{D=}\begin{matrix} {{\text{A}}_{1}}\\ {{\text{A}}_{2}}\\ \vdots\\ {{\text{A}}_{\text{m}}}\\ \end{matrix}\text{ }\left[\begin{matrix} {{\text{X}}_{1}}\text{ }{{\text{X}}_{2}}\text{ }\cdots \text{ }{{\text{X}}_{\text{n}}}\\ {{\text{X}}_{11}}\text{ }{{\text{X}}_{12}}\text{ }\cdots \text{ }{{\text{X}}_{1\text{n}}}\\ {{\text{X}}_{21}}\text{ }{{\text{X}}_{22}}\text{ }\cdots \text{ }{{\text{X}}_{\text{2n}}}\\ \vdots \text{ }\\ {{\text{X}}_{\text{m1}}}\text{ }{{\text{X}}_{\text{m2}}}\text{ }\cdots \text{ }{{\text{X}}_{\text{mn}}}\\ \end{matrix}\right]$$
$${\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{w}} = ({{w}_{1}},{{w}_{2}}, \ldots ,{{w}_{n}})$$
where Ai, i = 1, ..., m, are possible courses of action (candidates, alternatives); Xj, j = 1,...,n, are attributes with which alternative performances are measured; xij is the performance score (or rating) of alternative Ai with respect to attribute Xj; wj, j = 1,...,n are the relative importance of attributes.
Shu-Jen Chen, Ching-Lai Hwang
VI. Concluding Remarks
Abstract
This study is a sequel to our previous works on “Multiple Objective Decision Making--Methods and Applications” [H12], “Multiple Attribute Decision Making--Methods and Applications” [H13], and “Group Decision Making Under Multiple Criteria--Methods and Applications” [H14]. It gives a state-of-the-art survey of the existing methods which solve fuzzy MADM problems and their applications. It also provides readers with a capsule look into the existing methods, their characteristics, and their applicability to the analysis of fuzzy MADM problems. Many diversified methods are reviewed thoroughly and critically, and classified systematically. We also present a new and practical fuzzy MADM approach.
Shu-Jen Chen, Ching-Lai Hwang
VII. Bibliography
Shu-Jen Chen, Ching-Lai Hwang
Backmatter
Metadaten
Titel
Fuzzy Multiple Attribute Decision Making
verfasst von
Shu-Jen Chen
Ching-Lai Hwang
Copyright-Jahr
1992
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-46768-4
Print ISBN
978-3-540-54998-7
DOI
https://doi.org/10.1007/978-3-642-46768-4