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DEX (Decision EXpert): A Qualitative Hierarchical Multi-criteria Method

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Part of the Studies in Systems, Decision and Control book series (SSDC,volume 407)

Abstract

DEX (Decision EXpert) is a hierarchical, qualitative, rule-based, multi-criteria decision modeling method. It combines multi criteria decision analysis with artificial intelligence and is particularly suited for sorting/classification decision problems. DEX puts special attention on the transparency, comprehensibility, consistency, and completeness of decision models, as well as on methods for the analysis, justification, and explanation of decisions. The approach relies on using software tools that actively support the decision maker in both the creation and utilization stages of the process. Since its inception in the 1980s, DEX has been successfully applied in hundreds of real-world decision projects in various areas, including economy, ecology, agronomy, medicine, and health care. In the last decade, there is an increasing trend of including DEX models in decision support systems. In this chapter, DEX is described from the theoretical and practical viewpoint and further explained in terms of motivation, history, software, applications, and method extensions. The presentation is supported by three examples: a didactic example of employee selection and two real-world industrial applications of choosing a raw-material location and assessing electric energy production technologies, respectively.

Keywords

  • Decision Expert (DEX)
  • Multi-criteria modeling
  • Qualitative decision model
  • Decision rules
  • Decision support system
  • DEXi

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Notes

  1. 1.

    Actually, DEX implementations distinguish between increasing, decreasing and unordered scales. Here, we simplify the definition without loss of generality.

Abbreviations

\(\mathcal{A}=\{{A}_{1},{A}_{2},\dots ,{A}_{q}\}\) :

Alternatives

\({A}_{i}\in \mathcal{A}, {A}_{i}=\{{a}_{x,i }\in {E}_{x}, \forall x\in X\}\) :

An alternative

\({a}_{x,i}\in {A}_{i}\) :

Value of \({A}_{i}\) assigned to attribute \(x\)

\({B}_{x}\subset {D}_{x}\) :

Subset of bad values of attribute \(x\)

\({C}_{y}={\prod }_{x\in S(y)}{D}_{x}\) :

Domain of \({f}_{y}\)

\({D}_{x}\) :

Value scale of attribute \(x\)

\({E}_{x}\) :

Range of values that can be assigned to attribute \(x\)

\({E}_{y}\) :

Range of \({f}_{y}\)

\(e=(\mathbf{x},y)\in {T}_{y}\) :

Elementary decision rule, an entry in \({T}_{y}\)

\(F\) :

Set of aggregation functions of a DEX model

\({\mathcal{F}}_{y}\) :

Fuzzy distributions over \({D}_{y}\)

\({f}_{y}: {C}_{y}\to {E}_{y}\) :

Aggregation function associated with attribute \(y\)

\({g}_{y}\) :

An approximation of \({f}_{y}\)

\({G}_{x}\subset {D}_{x}\) :

Subset of good values of attribute \(x\)

\({I}_{i}\subset {A}_{i}\) :

Subset of values of \({A}_{i}\), assigned to input attributes

\({I}_{y}\) :

Set of intervals over \({D}_{y}\)

\({m}_{x}=|{D}_{x}|\) :

Number of categories of scale \({D}_{x}\)

\(M=(X,D,S,F)\) :

A DEX model

\({N}_{x}\subset {D}_{x}\) :

Subset of neutral values of attribute \(x\)

\({O}_{i}\subset {A}_{i}\) :

Subset of values of \({A}_{i}\), assigned to output (aggregate) attributes

\({\mathrm{ord}(v}_{x,i})=i\) :

Ordinal value of \({v}_{x,i}\)

\(P(x)\) :

Set of parents of attribute \(x\)

\({\mathcal{P}}_{y}\) :

Probability distributions over \({D}_{y}\)

\({r}_{y}=|{C}_{y}|\) :

Size of \({C}_{y}\) and the corresponding \({T}_{y}\)

\(S:X\to {2}^{x}\) :

Descendant function

\(S(x)\) :

Set of descendants of attribute \(x\)

\({\mathcal{S}}_{y}\) :

The power set of \({D}_{y}\)

\({T}_{y}=\{(\mathbf{x},y), \mathbf{x}\in {C}_{y},y\in {E}_{y}\}\) :

Decision table associated with attribute \(y\)

\({v}_{x,i}\in {D}_{x}\) :

\(i\)-th qualitative value (category) of attribute \(x\)

\({v}_{x,i}{\preccurlyeq v}_{x,j}\) :

Weak preference relation

\(w, {w}_{i}\in \mathcal{R}\) :

Relative weight (importance) of an attribute

\(x, {x}_{i},y\in X\) :

An attribute

\(X=\left\{{x}_{1},{x}_{2},\dots ,{x}_{n}\right\}\) :

Set of attributes

\(\omega \in [-0.5, +0.5]\) :

An offset to qualitative value \(v\)

3D:

Three-dimensional

AHP:

Analytic Hierarchy Process, an MCDM method

AQ:

Algorithm Quasi-optimal, a machine rule learning algorithm

CDPC:

Consistency-Driven Pairwise Comparisons, an MCDM method

DECMAK:

DECision MAKing, an early predecessor of DEX

DEX:

Decision EXpert, a qualitative MCDM method

DEXi:

Software implementing the DEX method

DRSA:

Dominance-based Rough Set Analysis, an MCDM approach

DSS:

Decision Support System

ELECTRE:

ELimination Et Choix Traduisant la REalité (ELimination Et Choice Translating REality), a family of MCDM methods

HINT:

Hierarchical INduction Tool, a machine-learning method for developing DEX models from data

MACBETH:

Measuring Attractiveness by a Categorical Based Evaluation Technique, an MCDM method

MCDM:

Multi-Criteria Decision Modeling

MCHP:

Multi-Criteria Hierarchy Process, a hierarchical MCDM approach

QQ:

Qualitative-Quantitative, an approach to ranking of alternatives using a DEX model

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The author acknowledges the financial support from the Slovenian Research Agency, research core funding P2-0103.

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Bohanec, M. (2022). DEX (Decision EXpert): A Qualitative Hierarchical Multi-criteria Method. In: Kulkarni, A.J. (eds) Multiple Criteria Decision Making. Studies in Systems, Decision and Control, vol 407. Springer, Singapore. https://doi.org/10.1007/978-981-16-7414-3_3

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