Research Article | Open Access

Hui Zhang, Hui Gao, Peide Liu, "Interval Type-2 Fuzzy Multiattribute Group Decision-Making for Logistics Services Providers Selection by Combining QFD with Partitioned Heronian Mean Operator", *Complexity*, vol. 2019, Article ID 6727259, 25 pages, 2019. https://doi.org/10.1155/2019/6727259

# Interval Type-2 Fuzzy Multiattribute Group Decision-Making for Logistics Services Providers Selection by Combining QFD with Partitioned Heronian Mean Operator

**Academic Editor:**Mojtaba Ahmadieh Khanesar

#### Abstract

Logistics service (LS) has key impacts on customersâ€™ satisfaction. Quality function deployment (QFD) can guarantee that logistic services providerâ€™s (LSP) attributes are in accordance with the customerâ€™s preferences for the LS. The partitioned Heronian mean (PHM) operator assumes that all attributes are partitioned into several clusters. Herein, the attributes in the same clusters are interrelated, while the attributes in different clusters are independent, and the operator can be utilized to solve LSP selection (LSPS) problems in which all attributes are partitioned into several clusters. Interval type-2 fuzzy sets (IT2FSs) can more competently express the ambiguity and vagueness and have more powerful processing abilities. In this paper, we propose a novel LSPS method from the customersâ€™ perspective by combining QFD with the PHM operator in IT2FSs environments. First, we develop the interval type-2 fuzzy PHM (IT2FPHM) operator and the interval type-2 fuzzy weighted PHM (IT2FWPHM) operator and discuss some properties of them. Then, based on the relationships between the customer requirements (CRs) and the technical attributes (TAs), QFD is utilized in order to convert the CRs for LS concerns into multiple attributes for LSPâ€™s TAs. Finally, a case of a fresh E-business LSPS is used in order to demonstrate the validity and rationality of the proposed method, and some comparisons are used in order to show the superiority of the proposed method.

#### 1. Introduction

As global competition becomes increasingly keen; many businesses are trying to decrease costs, increase efficiency, and improve service by means of logistics [1, 2]. The demand for the number and type of logistics services providers (LSP) is increasing [2]. In addition, LSP selection (LSPS) has become a decision for businesses that attempt to highlight their core competence and entrust their other noncore activities to some technical and specialized companies [3]. Therefore, selecting the most suitable LSP is a significant and critical decision that is complex because of the existence of various ambiguity and uncertainly based attributes. Hu et al. [4] developed a multiobjective mixed-integer nonlinear programming model to determine the optimal selection strategy of function LSP. Martikainen et al. [5] developed a process of building potential business models for an LSP operating in a local food supply chain. Chen et al. [6] introduced an evaluation system of LSP for omnichannel environment by identifying the probability of the logistics provider fulfilling a criterion.

In this regard, multiattributes decision-making (MADM) or multiattributes group decision-making (MAGDM) techniques can make it easy for businesses to solve this decision problem [7]. This is because the LSP can be evaluated based on the conflicting attributes. The MADM or MAGDM method can choose the most suitable LSP among the candidate LSPs. Li et al. [8] presented a hybrid information MADM method based on integrated cumulative prospect theory to solve LSP problems. Pamucar et al. [9] proposed a novel integrated interval rough number MADM method based on the multiattribute border approximation area comparison. Wang et al. [10] introduced a hybrid MADM method by combining Decision-Making Trial and Evaluation Laboratory (DEMATEL), analytic network process (ANP), and fuzzy analytic hierarchy process (FAHP) to deal with reverse logistics enterprises selection problems.

However, in the real LSPS process, due to indeterminacy and inaccuracy, the evaluated values (EVs) of most of attributes, such as green competencies, pollution control, social responsibility, respect for freshness, reliability, empathy, quality stability, flexible time of receipt, and so on, cannot be adequately stated using type-1 fuzzy sets (T1FSs). Under the circumstances, type-2 fuzzy sets (T2FSs) can be utilized as a suitable technique for dealing with these indeterminacies and inaccuracies.

T2FSs, which were first developed by Zadeh [11], are known as an extension of T1FSs. The transparent diversity between them is that the memberships of T1FSs are crisp values but the memberships of T2FSs are T1FSs; therefore, T2FSs can more sufficiently reflect ambiguity and vagueness than T1FSs, and the research on T2FSs has attracted increasingly more attention. Considering the computational complexity, interval T2FSs (IT2FSs) [12] are the most vigorously applied T2FSs, and have been extended widely to control [13], identification and prediction [14], order allocation [15], data clustering [16], transportation mode selection [17], global supplier selection [18], etc.

The interval type-2 fuzzy aggregation operators can aggregate some IT2FSs into an overall one, and they are commonly utilized to deal with MADM or MAGDM problems in the context of IT2FSs. Zhang [19] presented the MAGDM approach based on some trapezoidal interval type-2 fuzzy (TIT2F) aggregation operators, such as the TIT2F weighted average (TIT2FWA) operator, the generalized TIT2FWA (GTIT2FWA) operator, the TIT2F order weighted average (TIT2FOWA) operator, the generalized TIT2FOWA (GTIT2FOWA) operator, the TIT2F hybrid averaging (TIT2FHA) operator, and the generalized TIT2FHA (GTIT2FHA) operator. However, these aggregation operators suppose that all the IT2FSs are independent. Obviously, this is unreasonable in the real MADM or MAGDM problems. In innumerable situations, we should consider the objective interrelationships between attributes, and then Heronian mean (HM) operator can complete this function. The HM operator [20], which has some advantages over the Bonferroni mean operator [21], considers the correlation between an attribute and itself and can avoid redundant calculations. Wang et al. [22] introduced a novel MAGDM method based on the TIT2F generalized HM (TIT2FGHM) operator and weighted TIT2FGHM (WTIT2FGHM) operator to deal with provider selection problems.

Nevertheless, in many real MADM or MCGDM problems, the interrelationships between attributes may not always exist [23â€“26]. For instance, when solving fresh E-business LSPS problems, we take into account these attributes as follows: distribution speed (), quality stability (), encasement (), professional cold storage and transport equipment (), flexible time of receipt (), service-oriented attitude (), and feedback speed (). Obviously, the higher the technical level of professional cold storage and transport equipment, the stronger the quality stability. Similarly, the greater the service consciousness of a service-oriented business, the faster the feedback speed. Therefore, based on the interrelationships between different attributes, we can divide these seven attributes into the following three partitions: , , and , where is related with and is not related with ,,,, and . With this being the case, the aggregation results are likely to be unreasonable when applying the HM operator. Then, some researchers developed the partitioned HM (PHM) operator, which can break away from the above limitations. Liu et al. [27] presented two MAGDM methods based on the linguistic intuitionistic fuzzy partitioned geometric HM (LIFPGHM) operator and the weighted LIFPGHM operator. However, the literatures on the MADM or MAGDM method based on the PHM operator with IT2FSs information are very few.

In addition, as market competition intensifies, enterprises should conform their managements and operations to meet the customersâ€™ requirements and survive in the market competitive environments. Quality function deployment (QFD) is a very powerful tool when the LSPS needs to ensure customersâ€™ satisfaction [28]. As a general rule, the QFD transformations are represented by a framework matrix, which is known as the house of quality (HOQ), and customer needs (CRs) can be translated into technical attributes (TAs) according to the relations between the CRs and TAs. In the last few years, the QFD has attracted increasingly more attention, especially for the LSPS. Liao and Kao [29] developed an approach by integrating QFD, the fuzzy extended analytic hierarchy process and multiple segment goal programming to improve logistics services. Yazadani et al. [30] integrated QFD with gray relation analysis in order to assess the importance of the LS indicators in the supply chain. Li et al. [31] proposed a technique using QFD to construct a benchmarked recovery process for the third party reverse LSP.

The LSPS process is analyzed as a combination of CRs and TAs (LSP attributes). That is, the relationship between a customerâ€™s satisfaction evaluation attributes (CRs) and LSP attributes (TAs) can be expressed using HOQ. These two kinds of attributes are taken from the customerâ€™s perspective and the expertâ€™s perspective, respectively. Customers provide EVs about the importance of the customerâ€™s satisfaction evaluation attributes and the rating of alternatives. Experts provide EVs about the relation between the customerâ€™s satisfaction evaluation attributes and the LSP attributes. After aggregation, the customerâ€™s preferences are converted into the rating of the weights of the LSP attributes and the rating of the alternatives regarding the LSP attributes through the QFD [32].

From the literature survey, it can be seen that researchers have already applied many approaches and all kinds of combined approaches to choose the most suitable LSP. However, no attempt from customersâ€™ perspective has been made so far to develop a sound mathematical model for dealing with LSPS problems that take into account the interaction between LSP attributes. Furthermore, it also supposes all LSP attributes are partitioned into several clusters where the attributes in the same clusters are interrelated while the attributes in different clusters are independent. That is, there are no studies that address with LSPS problems using the PHM operator and QFD, especially, with respect to the information of IT2FSs. Therefore, it is meaningful and valuable to develop a LSPS method based on the PHM operator and QFD in environments with IT2FSs.

Based on the above analysis, the main contributions of this paper are summarized as follows.(1)We convert the EVs of the importance degrees of CRs into the ones of TAs using the relationships between CRs and TAs based on QFD. Here, the customers provide the EVs of the importance degree of CRs, and the experts assess the relationship between CRs and TAs.(2)We develop the IT2FPHM operator and IT2FWPHM operator and discuss some properties of them.(3)We propose an LSPS method based on QFD and the PHM operator using IT2FSs. It can assure that LSP attributes are in accordance with the customerâ€™s satisfaction evaluation attributes and can ensure customersâ€™ satisfaction by integrating the classical QFD.(4)We verify the validity and rationality of the presented method using a case study about the fresh E-business LSPS and its superiority is illustrated using some comparisons.

The rest of this paper is organized as follows. Section 2 reviews the classical QFD and some basic concepts and operational laws of IT2FSs. Section 3 develops the novel LSPS method under the IT2FSs based on QFD and the PHM operator. Section 4 addresses the case of a fresh E-business LSPS. Section 5 gives some conclusions.

#### 2. Preliminaries

##### 2.1. The QFD Method

QFD [33] was initially developed by Yoji Akao in Japan in 1972. It is a desirable strategic design tool to support enterprises in improving their products and services that takes customersâ€™ satisfaction as the directional and significant driving factors in product or service design. The main favorable characteristic of this tool is the ability to select the preferred technical designs that meet customersâ€™ demands by bridging the gap between the customers and the product or service design teams. However, in reality, it is hard to evaluate technical designsâ€™ overall performance values using CRs, but they can be obtained using TAs. Therefore, converting CR (such as product, service, and so on) assessments into TA (such as product, production, process, management design, and so on) assessments is the crucial work of this tool.

As a rule, the QFD transformations are represented using a framework matrix, which is known as the house of quality (HOQ). The HOQ is the fundamental planning technique of QFD and contains the following six items, as displayed in Figure 1: the CR matrix, the TA matrix, the relationship matrix between CRs and TAs, the relative importance of CRs, the inner interrelationships between TAs, and the relative importance of TAs.

The detailed QFD method contains the following steps.

*Step 1 (identify the CRs). *The CRs for a specified product or service are first identified. Then, the attributes of the CRs are defined.

*Step 2 (determine the weights of the CRs). *The customers provide their EVs for each attribute of CRs by applying crisp numbers or fuzzy numbers. The global EVs of the attributes of CRs are obtained using some average operators (such as the weighted average (WA) operator, the power average (PA) operator, and so on).

*Step 3 (identify the TAs). *The technical attributes are identified based on the attributes of CRs.

*Step 4. *Determine the relationships between the CRs and TAs and build the corresponding relationship matrix, which states to what degree the attributes of TAs influence the attributes of CRs.

*Step 5 (determine the interdependencies among TAs). *The correlations between TAs play an important role in QFD applications and are essential in product or service design. Since the PHM operator can effectively deal with these correlations between TAs, in this step, it is unnecessary for us to take them into account.

*Step 6. *Calculate the weights of TAs based on the weights of CRs and the relationships between the CRs and TAs.

##### 2.2. IT2FS

*Definition 1 ([34]). *Let be the universe of discourse. A T2FS can be expressed using a type-2 membership function as follows:where represents an interval in . Meanwhile, the T2FS can also be expressed as follows:where is the primary membership (PM) at and denotes the second membership (SM) at . For discrete spaces, is replaced by .

*Definition 2 ([34]). *Let be a T2FS in . If all , then is called an IT2FS. This is expressed as follows:Clearly, IT2FS in is totally determined by the PM, which is known as the footprint of uncertainty (FOU). The FOU may be expressed as follows:

Because the operations on IT2FSs are complicated, IT2FSs are universally handled by certain simplified forms. In this paper, we apply the trapezoid IT2FS (TIT2FS) to solve MCGDM problems.

*Definition 3 ([35]). *Let and be two generalized trapezoidal fuzzy numbers where the height of a generalized fuzzy number is positioned in . Let and be the heights of and , respectively. An IT2FS (as shown in Figure 2) in the universe of discourse can be defined as follows:where and are the T1FSs, , , , , and . The lower membership function (MF) and the upper MF are defined as follows:

*Definition 4 ([36]). *Let and be two IT2FSs. Then, the operational laws between and are defined as follows:

*Definition 5 ([35]). *Let be an IT2FS for any . Then, the of is defined as follows:where is a given coefficient, and .

*Definition 6 ([35]). *Let be an IT2FS for any . Then, can be defined as follows:

*Definition 7 ([35, 37]). *Let be an IT2FS. Then, the rank-based distance measure function (RDMF) between and can be defined as follows:where .

Generally, the value of parameter can denote the decision-makerâ€™s (DMâ€™s) preference in real MCDM problems. If the DMâ€™s attitude is negative, can be 1; if the DMâ€™s attitude is positive, can be 0; and if the DMâ€™s attitude is indifferent, can be 0.5. In this paper, in order to reduce computational complexity, we assume that DMâ€™s attitude is indifferent in the practical decision-making (DM) environment, i.e., is 0.5.

*Definition 8 ([35, 37]). *Let and be two IT2Ss. Then, the ranking of and based on RDMF can be defined as follows:(1)If , then .(2)If , then .

##### 2.3. PHM Operator

*Definition 9 ([20]). *Let be a set of positive numbers, and . Then, the HM operator of can be defined as follows:

*Definition 10 ([21, 22]). *Let be a set of positive numbers, which is divided into clusters as , where , , , and represents the cardinality of . For any , the partitioned HM (PHM) operator of can be defined as follows:

#### 3. IT2FPHM Operator and IT2FWPHM Operator

*Definition 11. *Let be a collection of IT2FSs, which is divided into clusters , where , , , and represents the cardinality of . For any , the IT2FPHM operator of , and can be defined as follows:

Theorem 12. *Let be a collection of IT2FSs, and . The aggregated value of the IT2FPBM operator is still an IT2FS, and *

*Proof. *Based on (11) and (13), we getandThen,Finally, we can obtain

Theorem 13 (idempotency). *Let be a collection of IT2FSs. If all are equal, that is, , then*

*Proof. *Similarity, we can obtainIn addition, .

Therefore, we can obtain .

Theorem 14 (commutativity). *Let and be two collections of IT2FSs. If is any permutation of then *

*Proof. *Based on (35), we can get