Stochastic multiple‐criteria decision making with 2‐tuple aspirations: a method based on disappointment stochastic dominance

• Published date: 01 May 2018
• Date: 01 May 2018
• Author: Peide Liu,Xia Liang,Yanping Jiang
• DOI: http://doi.org/10.1111/itor.12430

Intl. Trans. in Op. Res. 25 (2018) 913–940

DOI: 10.1111/itor.12430

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RESEARCH

Stochastic multiple-criteria decision making with 2-tuple

aspirations: a method based on disappointment stochastic

dominance

Xia Lianga,b, Yanping Jianga,∗and Peide Liub

aSchool of Business Administration, Northeastern University,Shenyang 110169, China

bSchool of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, China

E-mail: susanliangxia@163.com [Liang]; ypjiang@mail.ned.edu.cn [Jiang]; peide.liu@gmail.com [Liu]

Received 10 May2016; received in revised form 29 April 2017; accepted 3 May 2017

Abstract

Considering the disappointment aversion behavior of decision makers, we define three types of disappoint-

ment stochastic dominance rules and disappointment stochastic dominance degree between two stochastic

variables. Then we prove some important properties of disappointment stochastic dominance. With respect

to the stochastic multiple-criteria decision-making (SMCDM) problem with criterion 2-tuple aspirations,

a novel method based on disappointment stochastic dominance is proposed. To begin with, based on the

2-tuple aspirationon each criterion, for the situations of discrete and continuous stochastic criterion values,the

aspiration alternative and its cumulative distribution functions of stochastic criterion values are constructed.

Next, the disappointment stochastic dominance relation between each alternative and aspiration alternative

is determined based on the definition of disappointment stochastic dominance. Further, the corresponding

disappointment stochastic dominance degree is calculated. And the overall disappointment stochastic dom-

inance degree of each alternative over the aspiration alternative is calculated to obtain the ranking result.

Finally,an example of selecting desirable computer development project(s) is given to illustrate the feasibility

and validity of the proposed method.

Keywords: multiple-criteria decision analysis; SMCDM; 2-tuple aspiration; aspiration alternative; disappointment

stochastic dominance

1. Introduction

In the actual process of decision making, decision makers usually give imprecise information to

represent their evaluations of alternatives, such as stochastic variables instead of round numbers

(Lahdelma and Salminen, 2001; Zaras, 2001, 2004; Mousavi et al., 2013; Jiang et al., 2015). There

∗Corresponding author.

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914 X. Liang et al. / Intl. Trans. in Op. Res. 25 (2018) 913–940

are many examples of stochastic variables in real life, such as choosing the most desirable computer

development project (Zaras and Martel, 1994; Nowak, 2004; Fan et al., 2010), investing the most

potential industry (Zhang et al., 2010; Fanet al., 2013), formatting a management strategy fora forest

ecosystem (Lahdelma and Salminen, 2009), and selecting the most desirablestrategy for an electricity

retailer (Lahdelma et al., 2006; Liu et al., 2011). Thus, the stochastic multiple-criteria decision-

making (SMCDM) problem has attracted many scholars’ attention because of its broad application

backgrounds. At present, there are some effective methods to solve the SMCDM problem, such

as stochastic dominance (SD) method (Zaras, 2001, 2004), stochastic multicriteria acceptability

analysis method (Lahdelma and Salminen, 2001, 2009; Lahdelma et al., 2006), set pair analysis

(SPA) method (Hu and Yang, 2011), and so on.

In the process of SMCDM, criterion aspirations are usually considered by a decision maker. In

view of the present research, two types of criterion aspirations are considered: (a) only the expected

value met by the criterion values is given (Huynh et al., 2007; Nowak, 2007; Hu and Yang, 2011;

Yanet al., 2011; Bi and Zhang, 2012; Tan et al., 2014). The expected value is denoted as target value.

Taking the venture capital problem, for example, the decision maker expects that the investment

incomes are more than $2 million. (b) 2-Tuple aspiration, that is, both target value and probability

level are given (Klubeck, 2011). Here, probability level refers to the probability achieved by the

criterion values meeting the target value. Taking a service-quality evaluation of service department,

for example, the customer expects the probability in which the phone answered by a service staff

within 30 seconds is above 0.9 (Klubeck, 2011). Also taking a venturecapital problem, for example,

the investment decision makers expect the probability in which the investment income more than

$10 million is above 0.7. As the criterion aspirations could accurately express the real intention of

a decision maker so as to make the decision results closer to reality, the SMCDM with criterion

aspirations becomes a significant topic.

From different perspectives, some methods for solving SMCDM problems with criterion aspi-

rations have been proposed. Bordley and Kirkwood (2004) developed an approach based on the

performance targets to assess a preference function for a multiobjective decision under uncertainty,

and applied the method to new product development. Nowak (2007) studied discrete SMCDM

problem and proposed an interactive methodology for solving this problem. The new procedure is

based on three concepts: aspiration level, stochastic dominance and preference threshold. Huynh

et al. (2007) explored a fuzzy target based approach to decision making under uncertainty. Con-

sidering different attitudes of the decision maker, the target-based formulation for the problem of

decision making in the face of uncertainty about the state of nature and imprecision about payoffs

has been also provided. With respect to the dynamic multiple-criteria decision-making (MCDM)

problems with discrete random variables, considering the decision maker’s attitude toward risk,

Hu and Yang (2011) proposed a novel method based on the prospect theory and SPA. By estab-

lishing the optimizing model, the criterion weight vector was obtained. Then the ranking result of

alternatives was obtained based on the pair analysis method. Yan et al. (2011) presented a proba-

bilistic approach for linguistic multiple experts decision making, which is able to deal with semantic

overlapping in linguistic aggregation. They also proposed a ranking procedure based on the target-

oriented decision model, in which the decision makers’ preferences are considered. With respect

to the group decision problem in which the decision maker is target-oriented and the attribute

values of alternatives is random variable, Bi and Zhang (2012) analyzed different types of targets

provided by the decision makers and identified the corresponding utility functions. According to a

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2017 The Authors.

International Transactionsin Operational Research C

2017 International Federation of OperationalResearch Societies