Jian-qiang Wang

An extended TODIM approach with intuitionistic linguistic numbers

In many practical problems, multiple alternatives are ranked with respect to related criteria, and the criterias weights are usually unknown. In order to solve this kind of multicriteria decision making (MCDM) problem, this paper proposes an interactive MCDM approach based on an acronym in Portuguese of interactive and multicriteria decision-making (TODIM) method and nonlinear programming (NLP) with intuitionistic linguistic numbers (ILNs). First, by comparing the existing operations and comparison methods for ILNs, new operations and a new comparison method are defined based on linguistic scale functions to obtain rational results. Second, considering their linguistic terms, membership degrees, and nonmembership degrees as a whole, the generalized distance between ILNs is defined with an adjustable parameter. Third, the total ranking of alternatives is obtained using the proposed NLP-based TODIM approach based on the generalized ILN distance. Finally, an example of selecting hotels from a tourism website is presented to verify the validity and feasibility of the proposed approach. A comparison with existing methods is also conducted and analyzed.

A Projection-Based Todim Method Under Multi-Valued Neutrosophic Environments and Its Application in Personnel Selection

The personnel selection is a vital activity for companies, and multi-valued neutrosophic sets (MVNSs) can denote the fuzziness and hesitancy in the processes of the personnel selection. The extant fuzzy TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) methods take advantage of distance to denote the difference between two fuzzy sets (FSs). Nevertheless, the distance measurement, which ignores the included angle between two FSs, cannot comprehensively reflect the difference between two FSs. To cover this defect, a projection-based TODIM method with MVNSs for personnel selection is established to consider the risk preference of decision-makers and overcome the defect of the extant fuzzy TODIM methods. The proposed TODIM method makes use of an improved comparison method which overcomes the deficiency of extant comparison method. Furthermore, a projection-based difference measurement is defined and utilized in the projection-based TODIM method. We conduct a numerical example of the personnel selection to explain the application of the projection-based TODIM method and discuss the influence of the parameter. Finally, the proposed method is compared with several extant methods to verify its feasibility.

An interval neutrosophic linguistic multi-criteria group decision-making method and its application in selecting medical treatment options

Selecting medical treatments is a critical activity in medical decision-making. Usually, medical treatments are selected by doctors, patients, and their families based on various criteria. Due to the subjectivity of decision-making and the large volume of information available, accurately and comprehensively evaluating information with traditional fuzzy sets is impractical. Interval neutrosophic linguistic numbers (INLNs) can be effectively used to evaluate information during the medical treatment selection process. In this study, a medical treatment selection method based on prioritized harmonic mean operators in an interval neutrosophic linguistic environment, in which criteria and decision-makers are assigned different levels of priority, is developed. First, the rectified linguistic scale functions of linguistic variables, new INLN operations, and an INLN comparison method are developed in order to prevent data loss and distortion during the aggregation process. Next, a generalized interval neutrosophic linguistic prioritized weighted harmonic mean operator and a generalized interval neutrosophic linguistic prioritized hybrid harmonic mean operator are developed in order to aggregate the interval neutrosophic linguistic information. Then, these operators are used to develop an interval neutrosophic linguistic multi-criteria group decision-making method. In addition, the proposed method is applied to a practical treatment selection method. Furthermore, the ranking results are compared to those obtained using a traditional approach in order to confirm the practicality and accuracy of the proposed method.

An Interval Type-2 Fuzzy Likelihood-Based MABAC Approach and Its Application in Selecting Hotels on a Tourism Website

As an extension of type-1 fuzzy sets (T1FSs), interval type-2 fuzzy sets (IT2FSs) can be used to model both extrinsic and intrinsic uncertainties. Based on the likelihood of interval type-2 fuzzy numbers (IT2FNs), this paper proposes a new multi-attributive border approximation area comparison (MABAC) approach to solve multi-criteria decision-making (MCDM) problems. First, an algorithm to decompose IT2FNs into the embedded type-1 fuzzy numbers (T1FNs) is proposed. Second, based on the closeness degree of T1FNs, the likelihood of IT2FNs is defined using the decomposition algorithm, and related properties are discussed. Third, the total ranking of alternatives is obtained using the MABAC approach based on the likelihood of IT2FNs. Finally, a practical example of selecting hotels from a tourism website is presented to verify the validity and feasibility of the proposed approach. A comparative analysis with existing methods is also described.

Probability multi-valued neutrosophic sets and its application in multi-criteria group decision-making problems

This paper introduces probability multi-valued neutrosophic sets (PMVNSs) based on multi-valued neutrosophic sets and probability distribution. PMVNS can serve as a reliable tool to depict uncertain, incomplete, inconsistent and hesitant decision-making information and reflect the distribution characteristics of all provided evaluation values. This paper focuses on developing an innovative method to address multi-criteria group decision-making (MCGDM) problems in which the weight information is completely unknown and the evaluation values taking the form of probability multi-valued neutrosophic numbers (PMVNNs). First, the definition of PMVNSs is described. Second, an extended convex combination operation of PMVNNs is defined, and the probability multi-valued neutrosophic number weighted average operator is proposed. Moreover, two cross-entropy measures for PMVNNs are presented, and a novel qualitative flexible multiple criteria method (QUALIFLEX) is developed. Subsequently, an innovative MCGDM approach is established by incorporating the proposed aggregation operator and the developed QUALIFLEX method. Finally, an illustrative example concerning logistics outsourcing is provided to demonstrate the proposed method, and its feasibility and validity are further verified by comparison with other existing methods.

Multi-criteria decision-making method based on single-valued neutrosophic linguistic Maclaurin symmetric mean operators

This paper investigates a wide range of generalized Maclaurin symmetric mean (MSM) aggregation operators, such as the generalized arithmetic MSM and the generalized geometric MSM, whose predominant characteristic is capturing the interrelationships among multi-input arguments. The single-valued neutrosophic linguistic set plays an essential role in decision making, which can serve as an extension of either a linguistic term set or a single-valued neutrosophic set. This study centers on multi-criteria decision-making (MCDM) issues in which criteria are weighed differently and criteria values are expressed as single-valued neutrosophic linguistic numbers. Based on this foundation, we extend a series of MSM aggregation techniques under single-valued neutrosophic linguistic environments and propose procedures for solving MCDM problems. We also explore the influence of parameters on aggregation results. Finally, we provide a practical example and conduct a comparison analysis between the proposed approach and other existing methods in order to verify the proposed approach and demonstrate its validity.

A multihesitant fuzzy linguistic multicriteria decision‐making approach for logistics outsourcing with incomplete weight information

In selecting logistics service providers, the evaluation criteria can be easily prioritized and possibly interrelated with each other, and the assessment of alternatives under qualitative criteria is usually accomplished by more than one decision maker. A novel multicriteria decision-making approach with multihesitant fuzzy linguistic term elements (MHFLTEs) based on the Heronian mean (HM) and prioritized average operators can effectively deal with the problems inherent in such a scenario. Multihesitant fuzzy linguistic term sets (MHFLTSs) were proposed on the basis of multihesitant fuzzy sets (MHFSs) and hesitant fuzzy linguistic sets (HFLSs), where each MHFLTE can contain nonconsecutive and repeated linguistic terms. Using MHFLTEs, one decision maker can provide one or several consecutive linguistic terms in evaluating an alternative under one specific criterion, different decision makers’ evaluation values can be collected, and the frequency of a linguistic term in the evaluation information can accord with reality. This paper revises the basic operations and comparison method for MHFLTEs on the basis of the originals and defines some multihesitant fuzzy linguistic HM operators for MHFLTEs to deal with problems in which weight information cannot be accurately established for criteria, but their priorities can be provided in groups or without groups. Finally, the validity and effectiveness of the proposed approach are demonstrated through an illustration of a logistics outsourcing problem and a comparison analysis.

Multi-criteria decision-making based on generalized prioritized aggregation operators under simplified neutrosophic uncertain linguistic environment

A simplified neutrosophic uncertain linguistic set that integrates quantitative and qualitative evaluation can serve as an extension of both an uncertain linguistic variable and a simplified neutrosophic set. It can describe the real preferences of decision-makers and reflect their uncertainty, incompleteness and inconsistency. This paper focuses on multi-criteria decision-making (MCDM) problems in which the criteria occupy different priority levels and the criteria values take the form of simplified neutrosophic uncertain linguistic elements. Having reviewed the relevant literatures, this paper develops some generalized simplified neutrosophic uncertain linguistic prioritized weighted aggregation operators and applies them to solve MCDM problems. Finally, an illustrative example is given, and two cases of comparison analysis are conducted with other representative methods to demonstrate the effectiveness and feasibility of the developed approach.

An improved MULTIMOORA approach for multi-criteria decision-making based on interdependent inputs of simplified neutrosophic linguistic information

Multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) is a useful method to apply in multi-criteria decision-making due to the flexibility and robustness it introduces into the decision process. This paper defines several simplified neutrosophic linguistic distance measures and employs a distance-based method to determine criterion weights. Then, an improved MULTIMOORA approach is presented by integrating the simplified neutrosophic linguistic normalized weighted Bonferroni mean and simplified neutrosophic linguistic normalized geometric weighted Bonferroni mean operators as well as a simplified neutrosophic linguistic distance measure. This approach ranks alternatives according to three ordering methods, and then, uses dominance theory to combine the three rankings into a single ranking. Finally, this paper presents a practical case example and conducts a comparative analysis between the proposed approach and existing methods in order to verify the feasibility and effectiveness of the developed methodology.

An extension of the ELECTRE approach with multi-valued neutrosophic information

In this paper, an extension Elimination and Choice Translating Reality (ELECTRE) method is introduced to handle multi-valued neutrosophic multi-criteria decision-making (MCDM) problems. First of all, some outranking relations for multi-valued neutrosophic numbers (MVNNs), which are based on traditional ELECTRE methods, are defined, and several properties are analyzed. In the next place, an outranking method to deal with MCDM problems similar to ELECTRE III, where weights and data are in the form of MVNNs, is developed. At last, an example is provided to demonstrate the proposed approach and testify its validity and feasibility. This study is supported by the comparison analysis with other existing methods.