Two kinds of explicit preference information oriented capacity identification methods in the context of multicriteria decision analysis

• Date: 01 May 2018
• Author: Endre Pap,Aniko Szakal,Jian‐Zhang Wu
• DOI: http://doi.org/10.1111/itor.12472
• Published date: 01 May 2018

Intl. Trans. in Op. Res. 25 (2018) 807–830

DOI: 10.1111/itor.12472

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Two kinds of explicit preference information oriented capacity

identification methods in the context of multicriteria

decision analysis

Jian-Zhang Wua, Endre Papb,c and Aniko Szakalc

aSchool of Business, Ningbo University, No. 818 Fenghua Road, Jiangbei District, Ningbo City, China 315211

bSingidunum University, Belgrade, Serbia

cObuda University, Budapest, Hungary

E-mail: sjzwjz@gmail.com [Wu]; pap@dmi.uns.ac.rs[Pap]; szakal@uni-obuda.hu [Szakal]

Received 14 September 2016; receivedin revised form 11 September 2017; accepted 14 September 2017

Abstract

The decision maker’s preference information on the importance and interaction of decision criteria can be

explicitly described bythe probabilistic interaction indices in the framework of the capacity based multicriteria

decision analysis. In this paper, we first investigate some properties of the probabilistic interaction indices

of the empty set, and propose the maximum and minimum empty set interaction principles based capacity

identificationmethods, which can be considered as the comprehensive interaction trend preferenceinformation

oriented capacity identification methods. Then, by introducing the deviation variables, the goal constraints,

as well as the goal objective function, we give a new and more flexible approach to representing the decision

maker’s explicit preference information on the kind and degree of the interaction of any given combination

of decision criteria as well as on the degree of the importance of any decision criterion, and construct

the nonempty set interaction indices based capacity identification method, which can be considered as the

detailed explicit preference information oriented identification method. Finally, two illustrative examples are

respectively given to show the feasibility and applicability of the two kinds of methods. In addition, the

comparison analysis between these two kinds of methods and some existing capacity identification methods

are also mentioned.

Keywords: multicriteria decision analysis; capacity identification method; Choquet integral; Shapley importance and

interaction index; explicit preference information; goal programming

1. Introduction

In the framework of the capacity based multicriteria decision analysis, the capacity identification

method is one of the research focuses and its major aim is to deal with the exponential complexity

inherent in the construction process (Grabisch, 1996). The capacity identification methods usually

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International Transactionsin Operational Research C

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808 J.-Z. Wuet al. / Intl. Trans. in Op. Res. 25 (2018) 807–830

begin with the decision maker’s explicit preference information about the multiple decision criteria

(Angilella et al., 2004, 2010; Grabisch et al., 2008; Grabisch and Labreuche, 2008; Kojadinovic,

2007; Marichal and Roubens, 2000; Roubens, 2002; Wu et al., 2014), which is provided from the

comparison perspective, e.g., criterion iis more important than criterion j, the interaction between

criteria iand jis greater than that between criteria kand l, and so on. Generally, these explicit

preference information aboutdecision criteria can only constitute a region of the feasible capacities

and some additional selection principle should be applied to identify the most satisfactory one(s)

(Wu et al., 2014).

Most of the additional selection principles are depended on a learning set (Grabisch et al.,

2008), which consists of some typical or known alternatives as well as the decision maker’s pref-

erence on them. The preference can be given in terms of the desired overall evaluations of all the

alternatives or by a weak partial order on them. Undoubtedly, these preferences on the typical

or known alternatives also reflect the decision maker’s judgments on the corresponding decision

criteria in some extent and can be regarded as an implicit form of the decision maker’s preference

about the decision criteria. This learning set depended, or called the implicit preference informa-

tion depended, capacity identification methods mainly include the least-squares based approaches

(Grabisch et al., 2000b, 2008; Grabisch and Labreuche, 2008), the maximum split approaches

(Marichal and Roubens, 2000), the TOMASO (Tool for Ordinal Multi-Attribute Sorting and Or-

dering) approaches (Meyer and Roubens, 2005; Roubens, 2002), the least absolute deviation crite-

rion based linear programming model (Beliakov, 2009), the nonadditive robust ordinal regression

model (Angilella et al., 2014, 2010; Corrente et al., 2015; Greco et al., 2008, 2014), the maximum

log-likelihood principle based optimization model (Fallah Tehrani et al., 2012; H¨

ullermeier and

Tehrani, 2013), and the maximum margin principle based optimization model (Fallah Tehrani

et al., 2012). The major obstacle of this type of identification method in practical application is that

the construction of learning set is indeed a very time-consuming process (Grabisch et al., 2008).

On the other hand, there are a few explicit preference information depended selection principles,

such as the maximum entropyprinciple (Kojadinovic, 2007; Kojadinovic et al., 2005; Marichal, 2002;

Wu and Zhang, 2010), the compromiseprinciple (Wu et al., 2014), and the least square and absolute

deviation principles (Wu et al., 2015). The compromise principle based identification methods also

need the partial evaluations of all decision alternatives (Wu et al., 2014). The least square and

absolute deviation principles are based on a type of refined explicit preference information called

the multicriteria correlation preference information (MCCPI) (Wu et al., 2015). The above three

types of selection principles can be employed without involving the implicit preference information

or the learning set.

In summary, we can develop the following two basic directions to further enrich the capacity

identification theory and methods: (1) to propose more identification principles that depend only

on the explicit preference information about the decision criteria and (2) to give more approaches,

besides the comparison representation form, flexibly representing decision maker’s explicit prefer-

ence information on higher order interactions between, even among decision criteria. In this paper,

we discuss the capacity identification issue from a perspective of the probabilistic interaction index

and make some contributions to the above two basic directions. For the first direction, we propose

the maximum and minimum empty set interaction (Min-ESI) index principles and the nonempty

set interaction indices oriented (NSIIO) identification principle, which all belong to the explicit

preference information depended capacity identification principle. For the second direction, in the

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2017 The Authors.

International Transactionsin Operational Research C

2017 International Federation of OperationalResearch Societies