Applied Computational Intelligence and Soft Computing

Volume 2018, Article ID 9346945, 14 pages

https://doi.org/10.1155/2018/9346945

## Development of Decision Support Model for Selecting a Maintenance Plan Using a Fuzzy MCDM Approach: A Theoretical Framework

^{1}Atılım University, 06836, İncek, Ankara, Turkey^{2}Department of Industrial Engineering, Ankara Yıldırım Beyazıt University, 06010 Ankara, Turkey

Correspondence should be addressed to Babak Daneshvar Rouyendegh (B. Erdebilli); moc.liamg@5102illibedre.kebab

Received 10 May 2018; Revised 5 September 2018; Accepted 27 September 2018; Published 1 November 2018

Academic Editor: Samuel Huang

Copyright © 2018 Fathia Sghayer Abdulgader 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

In complex decision making, using multicriteria decision-making (MCDM) methodologies is the most scientific way to ensure an informed and justified decision between several alternatives. MCDMs have been used in different ways and with several applications that proved their efficiency in achieving this goal. In this research, the advantages and disadvantages of the different MCDM methodologies are studied, along with the different techniques implemented to increase their accuracy and precision. The main aim of the study is to develop a hybrid MCDM process that combines the strengths of several MCDM methods and apply it to choose the best fit maintenance policy/strategy for industrial application. Moreover, fuzzy linguistic terms are utilized in all of the used MCDM techniques in order to eliminate the uncertainty and ambiguity of the results. Through an extensive literature review performed on studies that have used MCDM methods in a hybrid context and using fuzzy linguistic terms, a model is developed to use fuzzy DEMATEL-AHP-TOPSIS hybrid technique. The model with its application is the first of its kind, which combines the strengths of fuzzy DEMATEL in establishing interrelationships between several criteria, as well as performing a pairwise comparison between the criteria for prioritization using the fuzzy AHP method. Thereafter, the alternatives are compared using fuzzy TOPSIS method by establishing negative and positive solutions and calculating the relative closeness for each of the alternatives. Furthermore, six main criteria, twenty criteria, and five alternatives are selected from the literature for the model application.

#### 1. Introduction

Multiple criteria decision making (MCDM) is a procedure that permits to settle on choices within the sight of various, typically clashing, criteria. The issues of MCDM can be comprehensively grouped into two classes [1]:(1)Multiple Attribute Decision Making (MADM) includes the choice of the “best” option from preindicated options described in terms of multiple attributes.(2)Multiple Objective Decision Making (MODM) includes the plan of choices which advance the numerous goals of the Decision Maker.(3)The ordinary MCDM issue manages the assessment of an arrangement of options regarding an arrangement of choice criteria.

Multicriteria Decision Making is a valuable tool in numerous practical, producing, material determination, military, and constructional issues particularly assuming an essential part in fields of project choice, extended assessment, monetary advantage assessment, staff evaluation, et cetera. So far numerous methods have been proposed to solve multiple attribute decision-making problems. Multiattribute Decision Making is the investigation of recognizing and picking choices in light of the qualities and inclinations of the decision maker. Settling on a choice suggests that there are elective decisions to be considered and in such a case we will not just distinguish whatever number of these options as could be allowed; however, we will choose the one that best fits with our objectives, targets, qualities, etc. [1].

There are numerous ways to classify MCDM strategies. One approach is to group them as per the kind of information they utilize, according to deterministic, stochastic, or fuzzy MADM methods. However, there may be situations which involve combinations of all the above data types (such as stochastic and fuzzy data). Another way of classifying MCDM is according to the number of decision makers included in the decision process [2].

##### 1.1. AHP

A standout among the most well-known procedures for complex decision-making issues is the analytic hierarchy process (AHP) created by Saaty (1980), which breaks down a decision-making problem into an arrangement of progressions of goals, attributes (or criteria), and options. AHP can have the same number of levels as expected to completely describe a specific decision situation. Various practical attributes make AHP a helpful system. These incorporate the capacity to deal with decision situations including subjective judgements, various decision makers, and the capacity to give measures of consistency of inclination. Intended to reflect the way individuals really think, AHP keeps on being the most exceedingly respected and broadly utilized decision-making strategy. AHP can effectively manage substantial (i.e., objective) and nontangible (i.e., subjective) characteristics, particularly where the subjective judgements of various people constitute an essential part of the decision process [3].

The application of the AHP to the complex problem usually involves four major steps [3]:(1)Separate the complex issue into various little constituent components and after that structure the components in a hierarchical frame.(2)Make a series of pairwise comparisons among the elements according to a ratio scale.(3)Use the eigenvalue method to estimate the relative weights of the elements.(4)Aggregate these relative weights and synthesize them for the final measurement of given decision alternatives.

The AHP technique has the following identified advantages [2]:(1)Flexibility, instinctive interest to the decision makers, and its capacity to check irregularities: for the most part, users discover pairwise comparison type of information, direct and helpful.(2)The AHP method supports group decision-making through consensus by calculating the geometric mean of the individual pairwise comparisons.

Nevertheless, the following disadvantages about using the AHP method can also be identified [2]:(1)With AHP the decision issue is deteriorated into various subsystems, inside which and between which a considerable number of pairwise comparisons should be finished. This approach has the burden that the quantity of pairwise comparisons to be made may turn out to be extensive (n (n−1)/2) and in this way turn into a protracted assignment.(2)There is the artificial limitation of the use of the 9-point scale. Sometimes, the decision- maker might find it difficult to differentiate between them and tell for example whether one alternative is 6 or 7 times more important than another.

##### 1.2. TOPSIS

This technique depends on the idea that the chosen alternative ought to have the most limited Euclidean separation from the perfect arrangement, and the most distant from the negative ideal solution. The ideal solution is a speculative answer for which all ascribed esteems relate to the maximum attribute values in the database including the satisfying solutions; the negative ideal solution is the theoretical answer for which all attribute values correspond to the minimum attribute values in the database. TOPSIS along with these lines gives an answer that is not just nearest to the theoretically best, but likewise is the most distant from the hypothetically worst [1].

*The TOPSIS method is expressed in a succession of six steps as follows.*

*Step **1*. Calculate the normalized decision matrix and the normalized value.

*Step **2*. Calculate the weighted normalized decision matrix.

*Step **3*. Determine the ideal and negative ideal solutions.

*Step **4*. Calculate the separation measures using the m-dimensional Euclidean distance, the separation measures of each alternative from the positive ideal solution, and the negative ideal solution.

*Step **5*. Calculate the relative closeness to the ideal solution.

*Step **6*. Rank the preference order.

Similar to the AHP technique, TOPSIS has its advantages, which are as follows [4]:(1)It takes contribution as any number of criteria and attributes.(2)It has genuinely instinctive physical importance in light of the thought of separation from perfect arrangements.

Moreover, the following disadvantages are identified for TOPSIS.(1)It is easy and can give unreliable results.(2)TOPSIS in its standard form is deterministic and does not consider uncertainty in weightings [4].

##### 1.3. DEMATEL

DEMATEL is based on the premise of diagram hypothesis, enabling investigations and solutions of issues by visualization technique. This structural modeling method embraces the type of a coordinated chart, a causal impact outline, to introduce the association connections and the values of influential impact between variables. Through examination of visual relationship of levels among framework factors, all components are isolated into causal gathering and affected gathering. And this can provide researchers with a better understanding of the structural relationship between system elements and find ways to solve complicated system problems [5, 6].

The relationships between cause and effect factors are converted into the DEMATEL. Suppose that a system composes a set of elements , and particular pairwise relations are decided for modeling with respect to a mathematical relation. The major steps are [5] as follows:(1)Generating the direct relation matrix. Measuring the relationship between criteria requires that the comparison scale be designed into four levels: 0 (no influence) 1 (very low influence) 2 (low influence) 3 (high influence) 4 (very high influence)An initial direct relation matrix A is a n _ n matrix obtained by pairwise comparisons, in which is denoted as the degree to which the criterion i affects the criterion j.(2)Normalizing the direct relation matrix. It is based on the direct relation matrix A.(3)Attaining the total relation matrix. Once the normalized direct relation matrix S is obtained, the total relation matrix I is denoted as the identity matrix.(4)Producing a causal diagram. The sum of rows and the sum of columns are separately denoted as vectors D and R within the total relation matrix M. A cause and effect graph can be acquired by mapping the dataset of (D R, D _ R). The horizontal axis vector (D R) named “Prominence” is made by adding D to R, which reveals how much importance the criterion has. Similarly, the vertical axis (D _ R) named “Relation” is made by subtracting D from R, which may group criteria into a cause group. Or, if the (D _ R) is negative, the criterion is grouped into the effect group.(5)Obtaining the inner dependence matrix. In this step, the sum of each column in total relation matrix is equal to 1 by the normalization method, and then the inner dependence matrix can be acquired [7].

#### 2. MCDM Equipment Maintenance Application

There are several applications, where MCDM methods were used in the literature for equipment maintenance strategy selection, empowerment, or optimization. Muinde et al. (2014) identified five main types of maintenance strategies, which are passive, reactive, preventive, predictive, and proactive. In this study, the authors used the AHP method to select the most suitable strategy for the case study of a cement factory in Kenya by preforming twenty interviews with the maintenance staff, who provided their evaluation on the pairwise comparison questionnaire between the different criteria. Moreover, the study used factor analysis in order to group the different factors into criteria based on their interdependency [8].

Subsequently, the authors highlight that more than one decision maker has been sought in order to ensure consensus among the maintenance department members. In the results of the study, the criteria of the study were evaluated and assigned to scores against the alternative, where the highest score was found for proactive maintenance (54.58%), followed by preventive (22.94%), predictive (22.65%), and reactive (10.23%). Figure 1 shows the AHP model along with the scores of the criteria and alternatives [8].