Advances in Decision Sciences

Volume 2015, Article ID 801308, 14 pages

http://dx.doi.org/10.1155/2015/801308

## A Hybrid Multiattribute Decision Making Model for Evaluating Students’ Satisfaction towards Hostels

^{1}Labuan Faculty of International Finance, Universiti Malaysia Sabah, 87000 Labuan, Sabah, Malaysia^{2}Department of Decision Science, School of Quantitative Sciences, Universiti Utara Malaysia, 06010 Sintok, Kedah, Malaysia

Received 18 October 2014; Accepted 13 April 2015

Academic Editor: Mahyar A. Amouzegar

Copyright © 2015 Anath Rau Krishnan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper proposes a new hybrid multiattribute decision making (MADM) model which deals with the interactions that usually exist between hostel attributes in the process of measuring the students’ satisfaction towards a set of hostels and identifying the optimal strategies for enhancing their satisfaction. The model uses systematic random stratified sampling approach for data collection purpose as students dwelling in hostels are “naturally” clustered by block and gender, factor analysis for extracting large set of hostel attributes into fewer independent factors, *λ*-measure for characterizing the interactions shared by the attributes within each factor, Choquet integral for aggregating the interactive performance scores within each factor, Mikhailov’s fuzzy analytical hierarchy process (MFAHP) for determining the weights of independent factors, and simple weighted average (SWA) operator to measure the overall satisfaction score of each hostel. A real evaluation involving fourteen Universiti Utara Malaysia (UUM) hostels was carried out in order to demonstrate the model’s feasibility. The same evaluation was performed using an additive aggregation model in order to illustrate the effects of ignoring the interactions shared by attributes in hostel satisfaction analysis.

#### 1. Introduction

These days, mushrooming number of universities forces each of them to try all the possible means to survive or win in the competitive marketplace. In the attempt to reflect themselves as the best place for pursuing tertiary education, certain universities are unceasingly putting effort in offering accommodations or hostels with satisfying quality as pleasing hostel condition always appears as one of the criteria for some students in choosing a university [1]. Apart as a strategy to attract large number of students, providing satisfying hostel life is also a key to encourage the students to be more engaged with the education environment [2] and thus could drive them for better academic performance [3, 4]. Besides, the students who are satisfied with their hostels express higher sense of attachment and tend to further their studies in the same intuition. In nutshell, it is essential for the universities to timely identify and implement appropriate strategies in fulfilling the students’ actual needs and enhance the students’ satisfaction towards their hostels.

Unfortunately, identifying the optimal strategies is not a simple task as the degree of students satisfaction towards the hostels is normally influenced by multiple attributes. Following are some of the hostel attributes highlighted in past studies: number of roommates [5]; floor level [6]; recreation area, drain condition, and distance to clinic [7]; thermal comfort, indoor air quality, and furniture quality [8]; hostel maintenance, laundry [9]; internet facilities [10]; fees, room safety, and room size [11]; study room, ATM machine [12].

Besides, the review on past literature discloses that there is only minimal number of quantitative approaches that have been presented to this date in determining the optimal strategies for boosting the satisfaction towards a hostel. Most of the past studies (e.g., [11]) only employed factor analysis to discover the factors that influence the students’ satisfaction but the tool alone failed to offer other types of essential information for the hostel administration (e.g., type of interactions between attributes and weights of the factors) in deciding efficient strategies. In addition, in several studies, the overall satisfaction score of each hostel under evaluation was simply computed by using the common arithmetic aggregator which presumes independency among attributes. However, in reality most of the attributes used for an assessment are interacted to each other [13]. The hostel attributes hold the same characteristic as well.

Hence, it is can be concluded that there is a need for a quantitative model which mainly deals with or considers the interactions between attributes in the process of evaluating the performance of a set of hostels based on students’ satisfaction, in order to implement more practical strategies in enhancing their satisfaction.

This paper is organized as follows. Firstly, the needs for enhancing students’ satisfaction towards a hostel and the existing problems relating to hostel evaluation are elucidated. Secondly, a review on past literature focusing on the usage of Choquet integral and its associated *λ*-measure is presented. Thirdly, the proposed hybrid MADM model is introduced. Fourthly, the workability of the proposed model is demonstrated by conducting a real analysis involving fourteen University Utara Malaysia (UUM) hostels. The contributions of the paper and the potential future research are summarized in the final section.

#### 2. Aggregation Phase in MADM

MADM refers to a process of selecting, ranking, or classifying a set of alternatives based on varied, usually conflicting, attributes [14]. Applying multiple attribute utility theory (MAUT) techniques appears as a well-accepted standard, quantitative means for modeling MADM problems [15]. There are only three basic phases in implementing any of the MAUT techniques [16]. In the first phase, all the pertinent attributes for evaluating the alternatives under consideration are identified. The core components of a typical MAUT model are comprised of a set of alternatives denoted by and a set of attributes represented by . In the following phase, the weights of attributes and performance score of each alternative with respect to each attribute are derived where some judgments or preference values from the experts or respondents are usually required for this purpose [17]. In the final phase, a specific function, namely, aggregation operator, is used to compose the set of weights and performance scores of each alternative into a single global score [18]. Based on these global scores, the alternatives can be then ranked up, classified, or selected where an alternative with highest global score signifies the most preferred alternative for the evaluation problem.

##### 2.1. Aggregation Based on Choquet Integral

Normally, additive operators such as SWA which assume independency between attributes [19] are simply employed for the aggregation purpose. Unfortunately, this assumption is completely irrelevant to real scenario where in many cases, the attributes hold interactive characteristics [13, 20]. Therefore, aggregation should not be always performed via additive aggregators as they failed to model the interactions between attributes [21, 22]. However, with the aid of Choquet integral operator [23], the interactions between attributes can be captured during aggregation [24, 25]. The usage of Choquet integral requires a prior identification of monotone measure weights, . These weights represent not only the importance of each attribute but also the importance of all possible combinations or subsets of attributes [26–28]. As a result, for a MADM problem comprising number of attributes, number of weights needs to be identified prior to employing Choquet integral [29, 30].

-measure which was introduced by Sugeno [31] appears as one of the broadly used monotone measures due to its ease of usage, mathematical soundness, and modest degree of freedom characteristics [32]. Let be a finite set. A set function defined on the set of the subsets of , , is called a *λ*-measure if it meets the following conditions:(a), and , (boundary condition);(b), if , then implies (monotonic condition);(c), for all where and .According to [33, 34], consider the following.(a)If then it implies that the attributes are sharing subadditive (redundancy) effects. This means a significant increase in the performance of the target can be achieved by only enhancing some attributes in which have higher individual weights.(b)If then it interprets that the attributes are sharing superadditive (synergy support) effects. This means a significant increase in the performance of the target can be achieved by simultaneously enhancing all the attributes in regardless of their individual weights.(c)If then it indicates that the attributes are noninteractive.As is finite, the entire *λ*-measure weights can be identified usingwhere , denotes the individual weights of attributes. If , whereas if , the value of can be identified by solving

The identified *λ*-measure weights and the available performance scores can be then swapped into Choquet integral model to compute the global score of each alternative. Let be a monotone measure on and let be the performance score of an alternative with respect to each attribute in . Suppose . Then, and the aggregated score using Choquet integral can be determined using the following equation [35]:where relies on the performance score with respect to each attribute. For better understanding, assume that the scores of a student, in three subjects (attributes), Mathematics (), Physics (), Literature (), are 75, 80, and 50 respectively. Since , and the aggregated score of the student using Choquet integral, .

#### 3. Methodology

The steps for executing the proposed hybrid model can be summarized as follows.

##### 3.1. Identification of Attributes

In the first stage, a set of relevant attributes to assess the hostels under consideration are identified. Omitting any important attributes could lead to misleading decision.

##### 3.2. Data Collection Using Systematic Random Stratified Sampling Approach

In the second stage, a questionnaire is designed based on the predetermined attributes as an instrument to collect the required data for the evaluation. Through the questionnaire, the selected students (respondents) are requested to express their satisfaction on each attribute with respect to their hostels and also to state their general views on the importance each attribute in determining a student’s satisfaction, based on a preset Likert scale. Systematic random stratified sampling approach can be utilized in selecting the respondents for the survey purpose. According to [12], this sampling approach has been applied in many hostel evaluation studies as the students are usually or “naturally” grouped into groups, that is, by block and gender.

##### 3.3. Deriving Decision Matrix (Hostels versus Attributes)

In the third stage, the decision matrix of the evaluation problem which shows the performance score of each hostel with respect to each attribute is derived. The performance score of a hostel with respect to an attribute can be identified by averaging the satisfaction scores given by the students from hostel .

##### 3.4. Factor Analyzing the Data on the Importance of Attributes

In the fourth stage, the large dataset on the importance of attributes is used to perform factor analysis in order to extract the large set of attributes into fewer independent factors.

##### 3.5. Constructing Simpler Hierarchal Evaluation System

By adhering to the result of factor analysis, the complex hostel evaluation problem is decomposed into a simpler hierarchical structure which depicts the goal of the evaluation, the factors which independently contributes to the actualization of the goal, and the interacted attributes within each factor together with the hostels’ performance scores extracted from the derived decision matrix, in order to conduct the analysis in an organized means with better understanding.

##### 3.6. Identification of Monotone Measure Weights

Since the attributes within each factor are being interactive, Choquet integral can be then employed in order to aggregate the performance scores within each factor. However, before applying Choquet integral, the -measure weights need to be identified. The identification process can be simplified as follows.

Firstly, the experts are required to express the individual importance or contribution of each attribute towards its corresponding factor in linguistic terms. Based on these terms, one of the eight fuzzy conversion scales as suggested by Chen and Hwang [36] is selected in order to quantify the linguistic terms into their respective fuzzy numbers. Further details on the principle of selecting the best scale can be found in [36]. Then, the corresponding crisp values for each of these fuzzy values are identified using a fuzzy scoring method as suggested in [36]. Subsequently, the final individual importance of an attribute corresponding to factor can be determined using Suppose represents the experts involved in the analysis; then, based on (4), denotes the crisp importance of attribute with respect to factor that is derived from expert and implies the total number of experts involved. These final values actually represent the individual weights of attributes, , . Equations (2) and (1) can be then applied in order to find the interaction parameter, *λ* and *λ*-measure weights of each factor.

##### 3.7. Choquet Integral for Aggregating Interactive Scores

With the available -measure weights, Choquet integral model (3) can be then used to aggregate the interactive performance scores within each factor. As a result, by end of this step, each hostel will have an aggregated score with respect to each factor (in other words, each hostel will have a set of factor scores) and thus a new decision matrix (hostels versus factors) can be developed for further analysis.

##### 3.8. Using MFAHP for Allocating Weights on Independent Factors

MFAHP [37] is used to identify the weights of independent factors due to its ability to capture the uncertainty that usually embedded in human’s judgments and to derive the weights of the factors and consistency value of pairwise comparison matrix simultaneously by simply solving the nonlinear optimization model suggested in [37]. With respect to the proposed model, MFAHP can be executed as follows.

Firstly, after achieving consensus via Delphi method, the experts are required to linguistically express the mutually agreed judgments on the relative importance of the factors through a single pairwise matrix (for sake of simplicity) based on Saaty’s fuzzy AHP scale as shown in Table 1. It has to be mentioned here that in order to avoid using reciprocal judgment (values between and ) which could lead to rank reversal problem, MFAHP only requires the experts to offer assessment whenever factor is equally or more important than . If they consider that is less important than then the assessment should be done oppositely where is compared to . It can be noticed that the reciprocal judgments are not offered in Table 1 as they are not required for using MFAHP.