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Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. Besides, it is a universal operator since it can contain other general operators by assigning some special parameter values. However, the MM can only process the crisp numbers. Inspired by the MM' advantages, the aim of this paper is to extend MM to process the intuitionistic fuzzy numbers (IFNs) and then to solve the multi-attribute group decision making (MAGDM) problems. Firstly, we develop some intuitionistic fuzzy Muirhead mean (IFMM) operators by extending MM to intuitionistic fuzzy information. Then, we prove some properties and discuss some special cases with respect to the parameter vector. Moreover, we present two new methods to deal with MAGDM problems with the intuitionistic fuzzy information based on the proposed MM operators. Finally, we verify the validity and reliability of our methods by using an application example, and analyze the advantages of our methods by comparing with other existing methods.

In this paper, we proposed a single-valued neutrosophic normalized weighted Bonferroni mean (SVNNWBM) operator on the basis of Bonferroni mean, the weighted Bonferroni mean (WBM), and the normalized WBM. Firstly, the definition, operational laws, characteristics, and comparing method of single-valued neutrosophic numbers (SVNNs) are introduced. Then, the SVNNWBM operator is developed, and some properties and special cases of this operator are analyzed. Furthermore, an approach is developed to solve the multiple attribute decision-making problems with SVNNs based on the SVNNWBM operator. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Linguistic neutrosophic numbers (LNNs) can easily describe the incomplete and indeterminate information by the truth, indeterminacy, and falsity linguistic variables (LVs), and the Hamy mean (HM) operator is a good tool to deal with multiple attribute group decision making (MAGDM) problems because it can capture the interrelationship among the multi-input arguments. Motivated by these ideas, we develop linguistic neutrosophic HM (LNHM) operator and weighted linguistic neutrosophic HM (WLNHM) operator. Some desirable properties and special cases of two operators are discussed in detail. Furthermore, considering the situation in which the decision makers (DMs) can't give the suitable weight of each attribute directly from various reasons, we propose the concept of entropy for linguistic neutrosophic set (LNS) to obtain the attribute weight vector objectively, and then the method for MAGDM problems with LNNs is proposed, and some examples are used to illustrate the effectiveness and superiority of the proposed method by comparing with the existing methods.

The notions of complex q-rung orthopair fuzzy sets (Cq-ROFSs) and linguistic sets (LSs) are two different concepts to deal with uncertain information in multi-attribute group decision-making (MAGDM) problems. The Heronain mean (HM) and geometric Heronain mean (GHM) operators are an effective tool used to aggregate some q-rung orthopair linguistic fuzzy numbers (q-ROLFNs) into a single element. The purpose of this manuscript is to propose a new concept called complex q-rung orthopair linguistic sets (Cq-ROLSs) to cope with complex uncertain information in real decision-making problems. Then the fundamental laws and their examples of the Cq-ROLSs are also given. Furthermore, the notions of complex q-rung orthopair linguistic Heronian mean (Cq-ROLHM) operator, complex q-rung orthopair linguistic weighted Heronian mean (Cq-ROLWHM) operator, complex q-rung orthopair linguistic geometric Heronian mean (Cq-ROLGHM) operator, complex q-rung orthopair linguistic weighted geometric Heronian mean (Cq-ROLWGHM) operator are proposed and their basic properties are also discussed. Moreover, we develop a novel approach to MAGDM using proposed operators and a numerical example is used to describe the flexibility and explicitly of the initiated operators. In last, the comparison between proposed method and existing work is also discussed in detail.

q -rung picture fuzzy sets can handle complex fuzzy and impression information by changing a parameter q based on the different hesitation degree, and Yager operator is a useful aggregation technology that can control the uncertainty of valuating data from some experts and thus get intensive information in the process of decision-making. Thus, in this paper, we develop specific types of operators, namely, q -rung picture fuzzy Yager weighted average, q -rung picture fuzzy Yager ordered weighted average, q -rung picture fuzzy Yager hybrid weighted average, q -rung picture fuzzy Yager weighted geometric, q -rung picture fuzzy Yager ordered weighted geometric and q -rung picture fuzzy Yager hybrid weighted geometric operators. We propose q -rung picture fuzzy Yager aggregation operators to handle multiple attribute decision-making problems in a modernize way. Moreover, we discuss the effect of parameter on the decision-making results. To demonstrate the superiority and advantage of our proposed method, a comparison with existing methods is presented.

The 2-dimensional uncertain linguistic variable (2DULV) can depict decision-makers’ subjective assessments on the reliability of given evaluation results, which is a valid and practical tool to express decision information. In this study, we develop an improved MABAC method with 2DULVs to handle multiattribute group decision-making (MAGDM) problems where the weight information of attributes is unknown. First, some related theories of 2DULVs and the basic procedure of the MABAC method are briefly reviewed. Then, the maximum comprehensive evaluation value method is extended to 2DULVs to obtain combination weights of attributes, in which the subjective weights are determined according to the best–worst method (BWM) and the objective weights are calculated by the maximum deviation method. Besides, the generalized weighted average operator for 2DULVs (2DULGWA) is utilized to aggregate the evaluation information given by all experts. Finally, an improved MABAC for 2DULVs (2DUL-MABAC) is proposed, and an example is carried out to explain the validity of the proposed approach.

This paper focuses on the multiattribute group decision making problems with linguistic intuitionistic fuzzy information. Firstly the concept of linguistic intuitionistic fuzzy numbers (LIFNs) is introduced, and then based on the LIFNs, some new aggregation operators based on Bonferroni mean and power operator are proposed, such as linguistic intuitionistic fuzzy power Bonferroni mean (LIFPBM) operator, linguistic intuitionistic fuzzy weighted power Bonferroni mean (LIFWPBM) operator, linguistic intuitionistic fuzzy geometric power Bonferroni mean (LIFGPBM) operator, and linguistic intuitionistic fuzzy weighted geometric power Bonferroni mean (LIFWGPBM) operator. Then, some properties are proved such as idempotency, permutation, and boundedness. Besides, some special situations of the operators are explored. After that, an approach based of the LIFWGPBM and LIFWGPBM operators is proposed. Finally an example is used to illustrate the validity of the developed method.

With the considerable development of tourism market, as well as the expansion of the e-commerce platform scale, increasing tourists often prefer to select tourism products such as services or hotels online. Thus, it needs to provide an efficient decision support model for tourists to select tourism products. Online reviews based on the user experience would help tourists improve decision efficiency on tourism products. Therefore, in this study, a quantitative method for hotel selection with online reviews is proposed. First, with respect this problem with online reviews, by analyzing sentiment words in online reviews, tourists’ sentiment preferences are transformed into the format of distribution linguistic with respect to sentiment levels. Second, from a theoretical perspective, we proposed a method to determine the ideal solution and nadir solution for distribution linguistic evaluations. Next, based on the frequency of words for evaluating hotel and the distribution linguistic evaluations, the weight vector of the evaluation features is determined. Further, a novel DL-VIKOR method is developed to rank and then to select hotels. Finally, a realistic case from TripAdvisor.com for selecting hotel is used to demonstrate practically and feasibility of the proposed model. First published online 19 July 2019

Supply and distribution management of blood products is a challenging task due to their short lifespan. The problem is even more sophisticated considering uncertain demand for these products. This paper addresses integrated inventory-routing of blood in a supply chain network consisting of a single supplier and a group of blood centers. Transshipment among blood centers is allowed to decrease the cost of excess inventory and shortage of goods. A mathematical model is developed that decides on the optimal quantity of supplied blood, delivery plan, inventory level, and quantity of products transshipped between blood centers with the objective of minimizing total costs. In addition, a robust optimization approach is adopted to deal with uncertainty in demand. Since the proposed model is NP-hard, a heuristic solution algorithm is developed that improves solution quality by determining the most efficient change in vehicle routes in each search stage. The efficiency of the proposed algorithm is examined in a set of numerical experiments and using data from a real case of supply and distribution management of blood platelets. The results indicated that allowing transshipment reduces the need for supply capacity at the supplier, product shortage, inventory level, and the total cost.

Linguistic neutrosophic number (LNN) can describe evaluation information by three linguistic variables indicating truth-membership, indeterminacy-membership and falsity-membership respectively, which is an effective tool to represent uncertainty, the partitioned Maclaurin symmetric mean (PMSM) operator can reflect the interrelationships among criteria where there are interrelationships among criteria in the same partition, but the criteria in different partitions are irrelevant, so, in this paper, we extend the PMSM operator to LNNs, define linguistic neutrosophic partitioned Maclaurin symmetric mean operator and linguistic neutrosophic weighted partitioned Maclaurin symmetric mean (LNWPMSM) operator, and discuss the properties and theorems of the proposed operators. Then we propose a clustering algorithm for linguistic neutrosophic sets based on the similarity measure to give some objective and reasonable partitions among criteria, and based on the LNWPMSM operator and the objective partition structure of the criteria, a novel multi-criteria group decision-making method is developed for linguistic neutrosophic environment. Finally, one practical example is presented to illustrate the applicability of the proposed method, and a comparison analysis is to show the advantages of the proposed method compared with the existing methods.