In this Chapter, we imagine a decision maker (or a group of experts) trying to establish or examine fair procedures to combine opinions about alternatives related to different points of view.

Multiple criteria decision making

Despite the importance of decision-making (DM) techniques for construction of effective decision models for supplier selection, there is a lack of a systematic literature review for it. This paper provides a systematic literature review on articles published from 2008 to 2012 on the application of DM techniques for supplier selection. By using a methodological decision analysis in four aspects including decision problems, decision makers, decision environments, and decision approaches, we finally selected and reviewed 123 journal articles. To examine the research trend on uncertain supplier selection, these articles are roughly classified into seven categories according to different uncertainties. Under such classification framework, 26 DM techniques are identified from three perspectives: (1) Multicriteria decision making (MCDM) techniques, (2) Mathematical programming (MP) techniques, and (3) Artificial intelligence (AI) techniques. We reviewed each of the 26 techniques and analyzed the means of integrating these techniques for supplier selection. Our survey provides the recommendation for future research and facilitates knowledge accumulation and creation concerning the application of DM techniques in supplier selection.

Application of decision-making techniques in supplier selection: A systematic review of literature

Technological and Economic Development of Economy

Pythagorean fuzzy sets PFSs, originally proposed by Yager Yager, Abbasov. Int J Intell Syst 2013;28:436-452, are a new tool to deal with vagueness considering the membership grades are pairs µ,i¾? satisfying the condition µ2+i¾?2i¾?1. As a generalized set, PFSs have close relationship with intuitionistic fuzzy sets IFSs. PFSs can be reduced to IFSs satisfying the condition µ+i¾?i¾?1. However, the related operations of PFSs do not take different conditions into consideration. To better understand PFSs, we propose two operations: division and subtraction, and discuss their properties in detail. Then, based on Pythagorean fuzzy aggregation operators, their properties such as boundedness, idempotency, and monotonicity are investigated. Later, we develop a Pythagorean fuzzy superiority and inferiority ranking method to solve uncertainty multiple attribute group decision making problem. Finally, an illustrative example for evaluating the Internet stocks performance is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Some Results for Pythagorean Fuzzy Sets

With respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of intuitionistic fuzzy numbers or interval-valued intuitionistic fuzzy numbers, some new group decision making analysis methods are developed. Firstly, some operational laws, score function and accuracy function of intuitionistic fuzzy numbers or interval-valued intuitionistic fuzzy numbers are introduced. Then two new aggregation operators: induced intuitionistic fuzzy ordered weighted geometric (I-IFOWG) operator and induced interval-valued intuitionistic fuzzy ordered weighted geometric (I-IIFOWG) operator are proposed, and some desirable properties of the I-IFOWG and I-IIFOWG operators are studied, such as commutativity, idempotency and monotonicity. An I-IFOWG and IFWG (intuitionistic fuzzy weighted geometric) operators-based approach is developed to solve the MAGDM problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of intuitionistic fuzzy numbers. Further, we extend the developed models and procedures based on I-IIFOWG and IIFWG (interval-valued intuitionistic fuzzy weighted geometric) operators to solve the MAGDM problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of interval-valued intuitionistic fuzzy numbers. Finally, some illustrative examples are given to verify the developed approach and to demonstrate its practicality and effectiveness.

Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making

In this paper, we investigate the hesitant fuzzy multiple attribute decision making (MADM) problems in which the attributes are in different priority level. Motivated by the ideal of prioritized aggregation operators [R.R. Yager, Prioritized aggregation operators, International Journal of Approximate Reasoning 48 (2008) 263-274], we develop some prioritized aggregation operators for aggregating hesitant fuzzy information, and then apply them to develop some models for hesitant fuzzy multiple attribute decision making (MADM) problems in which the attributes are in different priority level. Finally, a practical example about talent introduction is given to verify the developed approaches and to demonstrate its practicality and effectiveness.

Hesitant fuzzy prioritized operators and their application to multiple attribute decision making

The aim of this paper is to investigate the multiple attribute decision-making problems with intuitionistic fuzzy information, in which the information about attribute weights is incompletely known, and the attribute values take the form of intuitionistic fuzzy numbers. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional grey relational analysis (GRA) method, by which the attribute weights can be determined. Then, based on the traditional GRA method, calculation steps for solving intuitionistic fuzzy multiple attribute decision-making problems with incompletely known weight information are given. The degree of grey relation between every alternative and positive-ideal solution and negative-ideal solution are calculated. Then, a relative relational degree is defined to determine the ranking order of all alternatives by calculating the degree of grey relation to both the positive-ideal solution (PIS) and negative-ideal solution (NIS) simultaneously. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting

The generalized Heronian mean and geometric Heronian mean operators provide two aggregation operators that consider the interdependent phenomena among the aggregated arguments. In this paper, the generalized Heronian mean operator and geometric Heronian mean operator under the q‐rung orthopair fuzzy sets is studied. First, the q‐rung orthopair fuzzy generalized Heronian mean (q‐ROFGHM) operator, q‐rung orthopair fuzzy geometric Heronian mean (q‐ROFGHM) operator, q‐rung orthopair fuzzy generalized weighted Heronian mean (q‐ROFGWHM) operator, and q‐rung orthopair fuzzy weighted geometric Heronian mean (q‐ROFWGHM) operator are proposed, and some of their desirable properties are investigated in detail. Furthermore, we extend these operators to q‐rung orthopair 2‐tuple linguistic sets (q‐RO2TLSs). Then, an approach to multiple attribute decision making based on q‐ROFGWHM (q‐ROFWGHM) operator is proposed. Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Some q‐rung orthopair fuzzy Heronian mean operators in multiple attribute decision making

The aim of this paper is to investigate the multiple attribute decision making problems with intuitionistic fuzzy information, in which the information about attribute weights is incompletely known, and the attribute values take the form of intuitionistic fuzzy numbers. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional gray relational analysis (GRA) method, by which the attribute weights can be determined. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. Then, based on the traditional GRA method, calculation steps for solving intuitionistic fuzzy multiple attribute decision-making problems with incompletely known weight information are given. Furthermore, we have extended the above results to an interval-valued intuitionistic fuzzy environment and developed modified GRA method for interval-valued intuitionistic fuzzy multiple attribute decision-making with incompletely known attribute weight information. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Guiwu Wei

Papers

Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making

Hesitant fuzzy prioritized operators and their application to multiple attribute decision making

GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting

Some q‐rung orthopair fuzzy Heronian mean operators in multiple attribute decision making

Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making