1. Introduction
Pipe materials are prone to chemical corrosion or scaling during waste-water collection and transportation, due to complex and harmful compounds contained. If the corrosion intensifies, it may cause failure of piping system, resulting in leakage and possible environmental damage [
1]. Selection of appropriate materials is a premise to help with the careful design of a piping system, ultimately to ensure its operation in a safe and reliable way.
Material selection is crucial for engineering design [
2]. It is a complex issue, in which a decision maker may encounter a number of conflicting or competing attributes, e.g., that the economic and functional performance of materials to some extent may not match each other [
3]. Basically, the selection of materials is to meet the design requirements [
4]. Mercer [
5] presented that reliability and longevity was critical to selection of pipe materials, in which internal pressure and external loads were the primary criteria to assess their performances. Anojkumar et al. [
6] further incorporated the mechanical properties with corrosion resistance into the selection criteria of pipe materials. Zhang et al. [
7] took the compatibility of materials with the working fluid into the selection criteria of heating pipes. In addition to materials’ functional performances, economic attributes are also important factors in influencing material selection to decrease the manufacturing cost [
8,
9]. Kayfeci [
10] made a selection from five insulation materials based on their market price. Mendrinos et al. [
11] evaluated the performance of pipe materials for a borehole heat exchanger (BHE) in terms of their installation costs. Zhao et al. [
12] designed economic evaluation criteria for the selection of plastic pipes, including procurement cost, processing cost and market share. With the concept of environmentally conscious design emerging in lean manufacturing, material selection pays more attention to mitigation of the product’s lifecycle environmental impact [
13]. Du et al. [
14] investigated the possible lifecycle impacts on different pipe materials to lead optimal selection. Akhtar et al. [
15] selected the optimal pipe among four common sewage pipes based on their lifecycle environmental impacts.
The above-mentioned studies inform us of the key criteria that should be considered in pipe-materials selection, including functional, economic, and environmental aspects. However, they seldom surveyed the impact of correlation among different criteria that may give rise to information overlapping. Our study filled such a gap by using the correlation test to eliminate the most interrelated criteria, through which Mahalanobis distance is further coupled with the multicriteria decision-making (MCDM) method to reduce the uncertainty of the selection results.
Multicriteria decision making (MCDM) is classified into multiple-objective decision making (MODM) and multiple-attribute decision making (MADM) [
16]. The former mainly focuses on applying optimization to satisfy predefined objective functions, whilst the latter ranks a finite number of alternatives according to their performances on a set of predetermined attributes [
12,
17]. Since multiple factors are being taken into decision analysis, MADM methods, including the Analytic Hierarchy Process (AHP), Elimination Choice Translating Reality (ELECTRE), the Preference-ranking Organization Method for Enrichment Evaluations (PROMETHEE), the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Vise Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR), Complex Proportional Assessment (COPRAS), etc., are widely employed to help decision makers carry out trade-offs among various alternatives. AHP has evolved into weighting the assignment of different criteria in a hierarchical indicator system [
18], dealing with the inconsistency of group decision making [
19], and examining the performance of Pareto-optimality on a set of feasible solutions [
20]. ELECTREmay couple with AHP to rank alternatives depending upon their outranking relationships [
21]. However, the methods fail to explain the information that lies in the differences of ranking scores [
22]. PROMETHEE fills such gap by using different scores to indicate the degree of preference among alternatives [
23]. AHP, ELECTRE and PROMETHEE are based upon pairwise comparison among attributes to rank alternatives, which is time consuming in computation, especially when the number of alternatives or attributes enlarges in the decision-making process [
24,
25]. TOPSIS, VIKOR and COPRAS are comparatively simple, systematic, and logical for decision makers to obtain the optimal option when facing a number of competing criteria [
26]. TOPSIS and VIKOR are similar but different from their normalizations in selected indicators [
27]. The latter focuses on a compromise solution between individual utility and group utility, by which the alternatives ranking may be deviated due to the differences in subjective weightings [
28,
29]. Similarly, COPRAS is identified by using the utility degree to rank alternatives, which may cause results sensitive to the process of normalization [
30]. TOPSIS is more adaptive to qualitative and quantitative information, by discriminating alternatives in terms of their Euclidean distances from the ideal solution [
31,
32]. It has been identified as reliable and efficient in a number of studies on materials selection, for its easy computation and clear trade-offs among various criteria [
33]. In addition, TOPSIS is inherently effective to couple with fuzzy set to tackle the uncertainty involved in decision making on materials selection [
34,
35].
Engineering designers usually express their preference or judgment in a linguistic environment, which may result in vagueness [
36]. The TOPSIS is unable to deal with such vagueness, which calls for improvement [
37]. Fuzzy set provides the insight into TOPSIS development, by transforming the linguistic information into fuzzy numbers, to indicate decision maker’s preference and judgment [
38,
39]. However, linguistic variables in an ordinary fuzzy set are not clear enough to express the decision maker’s preference by using an exact numerical value of either 0 or 1 [
40,
41]. In such a case, this study applies intervalued trapezoidal intuitionistic fuzzy number (IVTIFN) to handling ambiguity in linguistic information, by which its predetermined numerical interval may better specify the fuzzification in a fixed bounded limit [
42].
This study provides a MCDM-based computational approach, which couples IVTIFN with the TOPSISto aid engineers in the selection of commercially available materials. Mahalanobis distance is incorporated into IVTIFN–TOPSIS, to discriminate similarities of alternative materials by eliminating the highly correlated decision criteria. An illustrative case example is given to demonstrate its actual application. The study is expected to provide insight into sustainable design of waste-water piping system, ultimately to improve its sustainability.
3. An Illustrative Case Example
The case example is to conduct materials selection for waste-water piping in a newly constructed municipal sewage treatment plant in Chengdu City, China. According to the design requirements, the nominal diameter of the pipeline is 200 mm, which has to tolerate the pressure of 1.6 MPa. Currently, there is a wide variety of commercial pipe materials on the market, including carbon steels, copper, ductile iron, polyethylene (PE), polyvinyl chloride (PVC), pentatricopeptide repeats (PPR), etc. Given their applications to sewage treatment, this study chooses four common pipe materials, i.e., carbon steel (M1), galvanized steel (M2), PVC (M3) and high-density PE (HDPE) (M4) for further precise selection.
A group comprised of five experienced engineers has been involved in the consultation on pipe materials selection, including two project managers from the treatment plant and three engineers who are engaged in the design of sewage collection and transportation system. Their subjective judgments on the performances of the four alternative materials in respect to each criterion are given in
Table 2.
Table 3 shows the subjective judgments of the five involved engineers on the importance of the proposed criteria.
5. Conclusions
This study employs IVTIFN−TOPSIS to select materials for waste-water piping, in which IVTIFN is used to deal with subjective and linguistic information. To overcome information overlapping and overestimation of evaluation criteria, Mahalanobis distance is introduced to improve the computational approach by elimination of highly correlated criteria.
A case example is to verify the model application, to conduct materials selection for waste-water piping in a municipal treatment plant. Except for general attention given to the materials’ functionalities, i.e., anticorrosion and anticlogging, the economic and environmental attributes have been taken into consideration, to increase the sustainability of material selection. Four commonly-available commercial materials, including PVC, HDPE, carbon steel, and galvanized steel are taken as the available alternatives. Both of the results from the IVTIFN−TOPSIS (E) and the IVTIFN−TOPSIS (M) model show that plastic pipes are better than the metal material alternatives. In particular, HDPE is the optimal material, whilst PVC is near optimal for the piping system design.
The study is expected to provide insight into sustainable design of waste-water piping system. However, there are limitations remaining in the proposed method. The materials’ performances in respect of each criterion are mainly evaluated by the five invited engineers, whose judgments are fully dependent upon their empirical experiences. This further may result in deliberate preferences in the selection process. Future study will center on the quantification of the materials’ performances regarding functional, economic and environmental attributes, thus to reinforce the objectivity of the decision making.