An Interval Linguistic Distribution Model for Multiple Attribute Decision Making Problems with Incomplete Linguistic Information

An Interval Linguistic Distribution Model for Multiple Attribute Decision Making Problems with Incomplete Linguistic Information

Wen-Tao Guo (School of Knowledge Science, Japan Advanced Institute of Science and Technology (JAIST), Nomi, Japan), Van-Nam Huynh (School of Knowledge Science, Japan Advanced Institute of Science and Technology (JAIST), Nomi, Japan) and Yoshiteru Nakamori (School of Knowledge Science, Japan Advanced Institute of Science and Technology (JAIST), Nomi, Japan)
Copyright: © 2015 |Pages: 19
DOI: 10.4018/IJKSS.2015100102
OnDemand PDF Download:
$30.00
List Price: $37.50

Abstract

In this paper, the authors propose an interval linguistic distribution model for multiple attribute decision making (MADM) problems with incomplete linguistic information, in which they use intervals as evaluators' confidence levels indicating their belief degrees that a linguistic term fits an evaluation. By introducing the extent of ignoring information into this model, it can deal with incomplete linguistic assessments and then allow evaluators to avoid the dilemma that they have to supply complete assessments when not available. In addition, the uncertain subjective judgments on attributes of alternatives are represented as distributions on the linguistic term set used as an instrument for assessment in this model. This feature can be regarded as a measure for evaluators to handle uncertain information. The aggregation operators and expected utilities are also introduced for the purpose of aggregation and ranking problems of interval linguistic distributions. Finally, an example is used to illuminate the proposed model.
Article Preview

1. Introduction

In practice, most of the multiple attribute decision making (MADM) problems involve both kinds of qualitative and quantitative attributes. While quantitative attributes can be measured by means of numeric values, qualitative attributes which are often associated with uncertain information perhaps can only be assessed by linguistic information. The use of linguistic information implies the necessity of operating with the mechanism for computing with words (CW, for short) (Zadeh, 1996) so as to fusion linguistic information and then provide an evaluation for decision making.

So far, numerous models have been proposed for CW, especially some models have been widely applied to linguistic decision making applications, in which linguistic computational models based on fuzzy linguistic approach are common ones used to represent and aggregate linguistic information. Basically, these linguistic computational models can be classified into three categories, linguistic computational model based on membership functions (e.g., (Bonissone and Decker, 1986; Degani and Bortolan, 1988)), linguistic symbolic computational model based on ordinal scales (e.g., (Delgado et al., 1993; Xu, 2004; Yager, 1981)), and linguistic symbolic computational model based on 2-tuple representation and its extensions (e.g., (Dong et al., 2013; Herrera et al., 2000; Wang and Hao, 2006)). These linguistic computational models provide suitable and flexible space in a computation stage for CW. However, as far as we know, these models seldom touch upon the field that the uncertain subjective judgments are represented by not just one or two labels, but by interval distribution assessments with incomplete linguistic information over the whole linguistic term set, as studied in the evidential reasoning approach, such as (Wang et al., 2006; Wang et al., 2007; Xu et al., 2006).

In fact, interval uncertainty is very common in MADM problems. For example, evaluator may feel difficult to assess a basic attribute by a precise point estimation, i.e., “I think it might be 50% good”. However, it may largely increase the evaluator’s confidence if he/she assesses the same basic attribute by interval estimation, i.e., “I think it is 50%-70% good”. Apparently, it is more rational by making use of intervals to indicate evaluator’s inner thoughts in some situations. Moreover, experiences show that evaluator may not always be confident enough to provide subjective assessments to individual grades only, but at times wishes to be able to assess beliefs to subsets of adjacent grades. Such ignorance is referred to as local ignorance or interval uncertainty (Xu et al., 2006). Therefore, using interval linguistic distribution assessment might be a sensible option in such circumstances.

In addition, a pair of nonlinear optimization models was constructed to estimate the upper and lower bounds of intervals, which represented the combined belief degrees in evidential reasoning approach (Wang et al., 2006; Wang et al., 2007; Xu et al., 2006). Although the nonlinear optimization models overcome the limitations of irrationality or sub-optimality of previous models, as pointed by Wang et al. (Wang et al., 2007), it is quite computationally complicated, which leaves decision makers lots of inconvenience. Therefore, they mentioned using software package to solve practical problems (Wang et al., 2007).

Complete Article List

Search this Journal:
Reset
Open Access Articles: Forthcoming
Volume 8: 4 Issues (2017): 3 Released, 1 Forthcoming
Volume 7: 4 Issues (2016)
Volume 6: 4 Issues (2015)
Volume 5: 4 Issues (2014)
Volume 4: 4 Issues (2013)
Volume 3: 4 Issues (2012)
Volume 2: 4 Issues (2011)
Volume 1: 4 Issues (2010)
View Complete Journal Contents Listing