An interval-valued intuitionistic fuzzy MABAC approach for material selection with incomplete weight information

doi:10.1016/j.asoc.2015.10.010

Applied Soft Computing

Volume 38, January 2016, Pages 703-713

https://doi.org/10.1016/j.asoc.2015.10.010 Get rights and content

Highlights

•
A hybrid group decision making approach is proposed for material selection.
•
Uncertain and vague information is handled by interval-valued intuitionistic fuzzy sets.
•
A maximizing optimization model is established for determining criteria weights.
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An extended group decision making method is used to rank alternative materials.
•
The applicability and effectiveness are illustrated with two application examples.

Abstract

In engineering design, selecting the most suitable material for a particular product is a typical multiple criteria decision making (MCDM) problem, which generally involves several feasible alternatives and conflicting criteria. In this paper, we aim to propose a novel approach based on interval-valued intuitionistic fuzzy sets (IVIFSs) and multi-attributive border approximation area comparison (MABAC) for handling material selection problems with incomplete weight information. First, individual evaluations of experts concerning each alternative are aggregated to construct the group interval-valued intuitionistic fuzzy (IVIF) decision matrix. Consider the situation where the criteria weight information is partially known, a linear programming model is established for determining the criteria weights. Then, an extended MABAC method within the IVIF environment is developed to rank and select the best material. Finally, two application examples are provided to demonstrate the applicability and effectiveness of the proposed IVIF-MABAC approach. The results suggest that for the automotive instrument panel, polypropylene is the best, for the hip prosthesis, Co–Cr alloys-wrought alloy is the optimal option. Finally, based on the results, comparisons between the IVIF-MABAC and other relevant representative methods are presented. It is observed that the obtained rankings of the alternative materials are good agreement with those derived by the past researchers.

Graphical abstract

Introduction

The selection of the optimum material for a particular product is critical for an enterprise to survive from today's fierce competitive environment. In most current practices, engineers and designers are forced to select the right material to meet the product's functional requirements, such as higher product performance, weight saving, and cost reduction [1]. Being the main activity of engineering design process, appropriate selection of materials can significantly reduce manufacturing cost and increase organization competitiveness, customer satisfaction, and profitability [2], [3]. But in view of the large number of possible materials and the wide range of manufacturing processes available in the market, material selection for engineering applications has become one of the most challenging issues faced by design engineers. Moreover, material selection is the prerequisite for a chain of other engineering selection problems, which include manufacturing process selection, machine selection, tool selection, material handling equipment selection, supplier selection, and so on [4]. Therefore, material selection problem has gathered more and more attention from both academics and practitioners in the past decades [4], [5], [6].

Material selection method under uncertain environment can be introduced as a new research area for solving complex material selection problems. Although the existing approaches have had contributions to material selection under uncertainty, most of the related literature described the individual performance of alterative materials with classical fuzzy sets. Because of the complex and unconstructed nature and context of many real world material selection problems, performance information of alternatives usually has to be expressed by the use of more advanced uncertain modelling tools. Recently, several researches have started to propose new methods for material selection of high uncertainty based on, for example, interval 2-tuple linguistic model [7] and uncertain membership linguistic variables [8], which can depict uncertain material performance information more precisely and completely. However, there is few or no researches can be found in the literature concerning material selection by utilizing interval-valued intuitionistic fuzzy sets (IVIFSs). The IVIFS theory was introduced by Atanassov and Gargov [9] for dealing with ambiguity in the information and fuzziness in decision makers’ judgments in practical decision making problems. Its basic feature is that both membership and nonmembership functions of an element to a given set are considered and taken on interval values rather than exact numbers. Thus, there is a significantly important need to investigate more effective and suitable mathematical methods by utilizing the IVIFSs in order to better handle material selection problems of high ambiguity and uncertainty.

On the other hand, material selection for a specific engineering application can be recognized as a kind of multiple criteria decision making (MCDM) problem [4], [10]. It is necessary to take into account several criteria comprehensively when making a decision of material selection, such as performance, price, usability, machinability, recycling, environment, and maintainability [4], [6]. Actually, many material selection problems in product design can be taken within the frame of MCDM, and, as reviewed in the literature review section, a lot of MCDM methods have been employed for identifying the most suitable material [11], [12], [13]. The multi-attributive border approximation area comparison (MABAC) method is a new MCDM method recently proposed by the research center at the University of Defence in Belgrade [14]. It has a simple computation process, systematic procedure, and a sound logic that represents the rationale of human decision making. Hence, it is an interesting research topic to apply MABAC in the material selection process to rank and determine the best material under the interval-valued intuitionistic fuzzy (IVIF) context.

Based on the aforementioned discussions, this paper aims to develop an extended version of the MABAC method for handling material selection problems within the decision environment of IVIFSs. The proposed material selection approach has the ability to reflect both subjective judgments and objective information in realistic applications under the IVIF environment. For some situations where the information about criteria weights is partially known, a linear programming model based on maximum distance measure is further integrated into the proposed approach to determine the weight vector of criteria. Finally, two application examples are examined for the material selection to demonstrate the implementation process of the IVIF-MABAC approach. The results show that the proposed approach can assist engineers and designers to make their efficient decisions for solving intricate material selection problems under uncertainty.

The remainder of this paper is organized as follows. Section 2 presents the literature reviews of material selection methods and applications of IVIFSs, and Section 3 introduces some basic concepts, definitions, and operations related to IVIFSs. In Section 4, a new material selection model is proposed by combing IVIFSs and the MABAC method. Furthermore, this section establishes a mathematical programming model for obtaining the criteria weights under limited weight information. In Section 5, two illustrative examples are provided to demonstrate the effectiveness and practicality of the proposed IVIF-MABAC. Finally, concluding remarks and suggestions for future research are given in Section 6.

Section snippets

Material selection methods

In the literature, a diversity of material selection methods has been developed to assist designers to select the apt material for a given engineering application and to increase the efficiency in product design and development process. For example, Jahan and Edwards [15] proposed an extended VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje) method for addressing material selection problems with simultaneous availability of interval data and target based-criteria. Jeya Girubha and

Preliminaries

The concept of intuitionistic fuzzy sets (IFSs) was first introduced by Atanassov [28] to generalize fuzzy sets [29]. Its definition can be given as follows:

Definition 1

[28]. Let a set $X = \{x_{1}, x_{2}, ..., x_{n}\}$ be a universe of discourse, an IFS A in X is defined as:

A = \{〈x, μ_{A} (x), v_{A} (x)〉 |x \in X\},

where

μ_{A} : X \to [0,1]

represents the membership degree and

v_{A} : X \to [0,1]

represents the nonmembership degree of the element x ∈ X to A, respectively, with the condition that for all x ∈ X,

0 \leq μ_{A} (x) + v_{A} (x) \leq 1 .

For any IFS A and x ∈ X, $π_{A} (x) = 1 - μ_{A} (x) - v_{A} (x)$ is called the

The IVIF-MABAC approach for material selection

To select the optimal material for a given application, we put forward a novel framework based on IVIFSs and the MABAC method for solving material selection problems with incomplete weight information. In short, the proposed approach for material evaluation and selection consists of three main stages: determining the performance of materials, calculating the weights of criteria, and obtaining the ranking orders of alternatives. In the first stage, the performance ratings of alternatives on each

Illustrative examples

In this section, two real material selection examples are cited to demonstrate the implementation process and effectiveness of the proposed IVIF-MABAC approach. The first example is an automotive instrument panel material selection problem that includes subjective data and incomplete weight information. The second example describes a typical biomedical problem, selecting hip prosthesis materials with objective data, target criteria, and unknown weight information.

Conclusions

In this paper, we proposed a novel approach based on an extended MABAC method within the IVIF environment to solve material selection problems with incomplete weight information. The performance or rating of each alternative on every of the criteria is estimated based on IVIFSs, and a new MCDM method, the MABAC, is used to rank and select the most desirable candidate material. Additionally, incomplete weight information is more realistic in many practical engineering design problems, especially

Acknowledgments

The authors are very grateful to the respected editor and the anonymous referees for their constructive comments and suggestions, which helped to improve the overall quality of the paper. This work was partially supported by the National Natural Science Foundation of China (No. 71402090), the Project funded by China Postdoctoral Science Foundation (Nos. 2014M560356, 2015T80456), the Program for Young of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning (No.

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An interval-valued intuitionistic fuzzy MABAC approach for material selection with incomplete weight information

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Material selection methods

Preliminaries

The IVIF-MABAC approach for material selection

Illustrative examples

Conclusions

Acknowledgments

Mater. Design

Mater. Design

Mater. Design

Mater. Design

Mater. Design

Mater. Design

Mater. Design

Mater. Design

Fuzzy Sets Syst.

Mater. Design

Expert Syst. Appl.

Mater. Design

Appl. Math. Model.

Expert Syst. Appl.

Mater. Design

Mater. Design

Mater. Design

Mater. Design

Mater. Design

Inf. Sci.