Supplier Selection Group Decision Making in Logistics Service Value Cocreation Based on Intuitionistic Fuzzy Sets

Intuitionistic fuzzy information aggregation plays an important role in intuitionistic fuzzy set theory and is widely used in group decision making. In this paper, an induced intuitionistic fuzzy Einstein hybrid aggregation operator (I-IFEHA) is investigated for supplier selection group decision making in logistics service value cocreation based on fuzzy measures. We first introduce some aggregation operators and Einstein operations on intuitionistic fuzzy sets and develop a new induced intuitionistic fuzzy Einstein hybrid aggregation operator to accommodate the environment in which the given arguments are intuitionistic fuzzy values. Then, we study the supplier selection group decision model in logistics service value cocreation based on intuitionistic fuzzy sets with the I-IFEHA operator. Finally, an example of 3PL supplier selection in logistics service value cocreation environment is given to verify the developed approach and to demonstrate the effectiveness of the developed approach.


Introduction
In today's business world, more and more companies rely on outsourcing their logistics services to 3PL to reduce costs, improve business performance, and focus on their core business.Supplier selection has received considerable attention for its significant effect towards successful logistics and supply chain management [1].The 3PL supplier selection issue is a typical multiple attribute decision making problem in complex business environment.The study of 3PL supplier selection mainly includes the following two main issues; one is the selection criteria of 3PL supplier [2][3][4][5][6][7] and the other is the selection models and approaches of 3PL supplier [8][9][10][11][12][13][14][15][16].In many decision making scenarios, most decision information provided by the decision maker is often imprecise or uncertain due to the complex decision making environment, lack of data, or the decision maker's limited knowledge.The accuracy of 3PL supplier selection decision making process is based on the correct information from fuzzy data.To calculate the fuzzy data, Atanassov introduced the concept of intuitionistic fuzzy set (IFS) characterized by a membership function and nonmembership function, which is more suitable for dealing with fuzziness and uncertainty than the ordinary fuzzy set developed by Atanassov et al. [17][18][19][20].Since its appearance, IFS has received more and more attention in the field of multiple attribute decision making [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].Xu [36] developed the intuitionistic fuzzy weighted averaging (IFWA) operator, the intuitionistic fuzzy ordered weighted averaging (IFOWA) operator, and the intuitionistic fuzzy hybrid aggregation (IFHA) operator.Xu and Yager [37] proposed some intuitionistic fuzzy geometric aggregation operators and applied them to multiattribute decision making problems.Merigó [38] presented a new operator that unifies the OWA operator with the WA when we assess the information with induced aggregation operators called the induced ordered weighted averaging-weighted average (IOWAWA) operator.Wei [39] proposed the dynamic intuitionistic fuzzy weighted geometric (DIFWG) and induced intuitionistic fuzzy ordered weighted geometric (I-IFOWG) operator [40].Xu and Wang [41] developed the induced generalized intuitionistic fuzzy ordered weighted averaging (I-GIFOWA) operator.
It is clear that the above operators are based on the algebraic operational laws of IFSs for carrying the combination process and are not consistent with the limiting case of ordinary fuzzy sets [20].For an intersection, a good alternative to the algebraic operational laws is Einstein operation laws for fuzzy sets.Wang and Liu [42,43] developed intuitionistic fuzzy aggregation operators based on Einstein operators.Zhao and Wei [20] developed the intuitionistic fuzzy Einstein hybrid averaging (IFEHA) operator and intuitionistic fuzzy Einstein hybrid geometric (IFEHG) operator and applied the intuitionistic fuzzy Einstein hybrid averaging (IFEHA) operator and intuitionistic fuzzy Einstein hybrid geometric (IFEHG) operator to deal with multiple attribute decision making under intuitionistic fuzzy environments.Xu et al. [44] developed an I-IFOWA  operator which generalizes some of the intuitionistic fuzzy Einstein aggregation operators and apply the I-IFOWA  operator and the IFWA  operator to multiple attribute group decision making with intuitionistic fuzzy information.Yet it is worthy of pointing out that there is little investigation on aggregation technologies using the Einstein operations on IFS and the induced intuitionistic fuzzy aggregation operator is more suitable for aggregation individual intuitionistic fuzzy values into collective intuitionistic fuzzy value.Therefore, this paper focuses on developing an induced intuitionistic fuzzy aggregation operator based on Einstein operators considering both the weights of positions and attributes.
In order to do so, the remainder of the paper is organized as follows.Section 2 briefly introduces some basic concepts related to intuitionistic fuzzy sets and some existing intuitionistic fuzzy aggregating operators.In Section 3, based on the induction of Einstein operation laws, we develop an induced intuitionistic fuzzy Einstein hybrid aggregation operator (I-IFEHA) and study some desired properties of the operator.In Section 4, we study the supplier selection group decision model in logistics service value cocreation and apply I-IFEHA operator to deal with supplier selection group decision making problems.In Section 5, an illustrative example for 3PL supplier selection in logistics service value cocreation environment is given to illustrate the concrete application of the approach.Section 6 concludes the paper and gives some remarks.

Preliminaries
In the following, we will first briefly introduce some basic concepts, aggregation operators related to intuitionistic fuzzy sets (IFSs) to facilitate future discussions.[17] is an extension of the classical fuzzy set, which is a suitable way to deal with vagueness.It can be defined as follows.
Definition 4. Let  = (  , ]  ) be an IFV; an accuracy function  of an intuitionistic fuzzy value can be represented as follows [22]: The function  is used to evaluate the accuracy of an IFV.The larger the value of (), the higher the degree of accuracy of the IFV .

The Intuitionistic Fuzzy Aggregation
Operator.Intuitionistic fuzzy information aggregation plays an important role in intuitionistic fuzzy set theory.Xu [36] proposed some intuitionistic fuzzy aggregation operators to aggregate the intuitionistic fuzzy information.

The Induced Intuitionistic Fuzzy Einstein Hybrid Aggregation Operator
Besides the algebra operations for IFVs, there are various -norms and -conorms can satisfy the requirements of the conjunction and disjunction operators.Einstein operations include the Einstein product which is a -norm and Einstein sum which is -conorms can be used to perform the corresponding intersections and unions of IFVs.Wang and Liu [42] extended the Einstein operations to the IFVs.Let  and  be two IFSs; then the Einstein operators are as follows: (1) (2) (3) (4) Based upon the definition of Einstein operations for IFVs and intuitionistic fuzzy aggregation operator proposed by Xu [36], Wang and Liu [42] proposed the intuitionistic fuzzy Einstein weighted averaging operator (IFEWA) and intuitionistic fuzzy Einstein ordered weighted averaging operator (IFEOWA).
Definition 11 (see [42]).Let   = (  , ]  ) ( = 1, 2, . . ., ) be a collection of IFVs and an intuitionistic fuzzy Einstein ordered weighted averaging operator of dimension  is a mapping IFEOWA: where  () is th largest of   ( = 1, 2, . . ., ) and  = ( 1 ,  2 , . . .,   )  is the aggregation-associated weighting vector with From Definitions 10 and 11, we know that the IFEWA operator weights only represent the intuitionistic fuzzy values, while the IFWOWA operator weights only represent the ordered positions of the intuitionistic fuzzy values.To solve this drawback and reflect the importance degrees of both given arguments and their ordered positions, Zhao and Wei [20] proposed an intuitionistic fuzzy Einstein hybrid aggregation operator (IFEHA), which is defined as follows.
Theorem 17 (boundedness).Let   = (   , ]   ) ( = 1, 2, . . ., ) be a collection of IFVs and let  − = min    ,  + = max    ; then Theorem 18 (monotonicity).Let   = (   , ]   ) ( = 1, 2, . . ., ) and   = (   , ]   ) ( = 1, 2, . . ., ) be two collections of IFVs; if   ≤   for all j, then  [9].With the review of 67 3PL selection articles published within 1994-2013 period, Aicha revealed 11 key 3PL selection criteria, and each one is defined by a set of attributes; the study revealed cost was the widely adopted criteria, followed by relationship, service, and quality [7].Although the abovementioned selection criteria are widely used in 3PL selection, the selection criteria are operational-oriented, while supply chain strategic and service value creation factors were seldom considered in logistics supplier selection in previous studies.It is necessary to reconsider the selection criteria in logistics service value cocreation scenario.

Supplier Selection Group Decision Model in Logistics Service Value Cocreation Based on Intuitionistic Fuzzy Sets
The creation of value is the core premise of establishing and maintaining the customer relationship and is the core purpose and central process of economic exchange [46].In supply chain management environment, more and more companies realize the importance of logistics service value cocreation with partners.Logistics service value cocreation has become the new way for the 3PL to find an innovative mode to achieve competitive advantage and for the customers to achieve more customized product and service offerings [47].The supplier selection is one of the most important issues for logistics service value cocreation in SCM environment.The emerging trend in 3PL supplier selection is the integration of traditional selection attributes, such as cost, response time, quality, and location, with the new factors in service value cocreation, such as new value creation, knowledge management, and service innovation.We integrate the traditional operational-oriented selection attributes and value cocreation oriented SCM strategic selection attributes to establish a comprehensive selection attributes for supplier selection in logistics service value cocreation scenario.The attributes of supplier selection in logistics service value cocreation are shown in Table 1.

An Approach to Supplier Selection Group Decision Making in Logistics Service Value Cocreation with Intuitionistic Fuzzy
Information.In this section, we apply I-IFEHA operator and IFEWA operator to multiple attribute group decision making for supplier selection in logistics service value cocreation based on intuitionistic fuzzy information.
Step 1. Choose the attributes for logistics supplier selection based on the logistics service value cocreation decision making model.

Illustrative Example and Discussion
In this section, we discuss a group of decision making problems in the logistics supply chain environment, which are concerned with a 4PL solution provider searching the best 3PL supplier for service value cocreation with its customer (an international manufacturing company group).Now suppose that there are five global 3PL suppliers   ( = 1, 2, 3, 4, 5) and three decision makers (whose weighting vector  = (0.4,0.25, 0.35)  ) from different professional fields are involved in the decision making.In the following, we utilize the procedure to find the decision result.
Step 3. Give the associated vector  = (0.3, 0.45, 0.25)  of the I-IFEHA , operator.Then we utilize the I-IFEHA , operator to aggregate all the intuitionistic fuzzy decision matrices into a collective decision matrix  = (  ) × (as listed in Table 5).

Table 1 :
The attributes of supplier selection in logistics service value cocreation.
1. Determine the attributes for 3PL supplier selection in service value cocreation environment.The attributes which are considered here in selection for the best 3PL supplier are as follows; (1)  1 is value collaboration ability with each other; (2)  2 is knowledge matching ability; (3)  3 is service innovation ability; (4)  4 is quality of service; (5)  5 is resource interaction ability.