Hong-yu Zhang

An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets

The novel operations of simplified neutrophic numbers (SNNs) and relational properties are developed.Some outranking relations for SNNs are defined based on ELECTRE, and properties among the outranking relations are further discussed in detail.Based on the outranking relations of SNNs, the ranking approach is developed to handle MCDM problems. In this paper, a new outranking approach for multi-criteria decision-making (MCDM) problems is developed in the context of a simplified neutrosophic environment, where the truth-membership degree, indeterminacy-membership degree and falsity-membership degree for each element are singleton subsets in 0,1. Firstly, the novel operations of simplified neutrosophic sets (SNSs) and relational properties are developed. Then some outranking relations for simplified neutrosophic number (SNNs) are defined, based on ELECTRE, and the properties within the outranking relations are further discussed in detail. Additionally, based on the outranking relations of SNNs, a ranking approach is developed in order to solve MCDM problems. Finally, two practical examples are provided to illustrate the practicality and effectiveness of the proposed approach. Moreover, a comparison analysis based on the same example is also conducted.

Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems

An interval-valued hesitant fuzzy linguistic set (IVHFLS) can serve as an extension of both a linguistic term set and an interval-valued hesitant fuzzy set. This new set combines quantitative evaluation with qualitative evaluation; these can describe the real preferences of decision-makers and reflect their uncertainty, hesitancy, and inconsistency. This work focuses on multi-criteria decision-making (MCDM) problems in which the criteria are in different priority levels and the criteria values take the form of interval-valued hesitant fuzzy linguistic numbers (IVHFLNs). The new approach to solving these problems is based on the prioritized aggregation operators of IVHFLNs. Having reviewed the relevant literature, we provide interval-valued hesitant fuzzy linguistic operations and apply some linguistic scale functions, which have been improved on the basis of psychological theory and prospect theory. Ultimately, two kinds of prioritized aggregation operators of IVHFLNs are developed, which extend to a grouping prioritized situation and are applied to MCDM problems. Finally, an example is provided to illustrate and verify the proposed approach in two separate situations, which are then compared to other representative methods.

Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems

As a variation of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete and inconsistent information that exists in the real world. Simplified neutrosophic sets (SNSs) have been proposed for the main purpose of addressing issues with a set of specific numbers. However, there are certain problems regarding the existing operations of SNSs, as well as their aggregation operators and the comparison methods. Therefore, this paper defines the novel operations of simplified neutrosophic numbers (SNNs) and develops a comparison method based on the related research of intuitionistic fuzzy numbers. On the basis of these operations and the comparison method, some SNN aggregation operators are proposed. Additionally, an approach for multi-criteria group decision-making (MCGDM) problems is explored by applying these aggregation operators. Finally, an example to illustrate the applicability of the proposed method is provided and a comparison with some other methods is made.

An outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets

Abstract The main purpose of this paper is to suggest an approach of multi-criteria decision-making that combines a hesitant fuzzy linguistic term set (HFLTS) with an outranking method involving systematic comparisons of the assessment values of alternatives for each criterion. A HFLTS is more suitable than the traditional fuzzy linguistic set for describing decision-makers’ preferences when they prefer to use several linguistic terms in expressions. After reviewing existing studies of HFLTSs, a novel outranking relational system of HFLTSs is developed and dominance relations for HFLTSs are introduced using outranking degrees of HFLTSs. In order to verify the efficacy of the developed method, an illustrative example is given and comparisons are made between the proposed method and other existing ones.

Interval neutrosophic sets and their application in multicriteria decision making problems.

As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. And interval neutrosophic sets (INSs) have been proposed exactly to address issues with a set of numbers in the real unit interval, not just a specific number. However, there are fewer reliable operations for INSs, as well as the INS aggregation operators and decision making method. For this purpose, the operations for INSs are defined and a comparison approach is put forward based on the related research of interval valued intuitionistic fuzzy sets (IVIFSs) in this paper. On the basis of the operations and comparison approach, two interval neutrosophic number aggregation operators are developed. Then, a method for multicriteria decision making problems is explored applying the aggregation operators. In addition, an example is provided to illustrate the application of the proposed method.

Method of multi-criteria group decision-making based on cloud aggregation operators with linguistic information

Abstract The cloud model, which can synthetically describe the randomness and fuzziness of qualitative concepts and implement uncertain transformations between a qualitative concept and its quantitative instantiations, has attracted considerable attention from researchers studying multi-criteria group decision-making problems involving linguistic information. In this paper, some operations of clouds and several new aggregation operators are proposed. These include the cloud weighted arithmetic averaging (CWAA) operator, cloud-ordered weighted arithmetic averaging (COWA) operator, and cloud hybrid arithmetic (CHA) operator. The conversion between linguistic variables and clouds is introduced. Based on this conversion, a linguistic multi-criteria group decision-making method is developed. In this method, linguistic variables are first converted into clouds and then aggregated using cloud aggregation operators. The proposed method is then compared to the existing methods to confirm its feasibility and rationality.

Interval-valued intuitionistic fuzzy multi-criteria decision-making approach based on prospect score function

This paper analyzes the limitations of existing score functions of intuitionistic fuzzy set. A new score function is defined based on the prospect value function, and examples are given to demonstrate the validity of this score function. As for the interval-valued intuitionistic fuzzy multi-criteria decision-making problems in which criteria weights are fixed, and the criteria values of alternatives are in the form of interval intuitionistic fuzzy numbers, an interval-valued intuitionistic fuzzy multi-criteria decision-making approach is proposed based on the prospect score function. This approach gives a matrix of score function values and a comprehensive evaluation value of each alternative. And the order of alternatives is listed by comparing the projection values of each alternative to the positive ideal solution. Finally, an example shows the feasibility and validity of this approach.

An outranking approach for multi-criteria decision-making problems with interval-valued neutrosophic sets

In this paper, a novel outranking approach for multi-criteria decision-making (MCDM) problems is proposed to address situations where there is a set of numbers in the real unit interval and not just a specific number with a neutrosophic set. Firstly, the operations of interval neutrosophic sets and their related properties are introduced. Then some outranking relations for interval neutrosophic numbers (INNs) are defined based on ELECTRE IV, and the properties of the outranking relations are further discussed in detail. Additionally, based on the outranking relations of INNs, a ranking approach is developed in order to solve MCDM problems. Finally, two practical examples are provided to illustrate the practicality and effectiveness of the proposed approach. Moreover, a comparison analysis based on the same examples is also conducted.

Multi-criteria decision-making methods based on the Hausdorff distance of hesitant fuzzy linguistic numbers

A hesitant fuzzy linguistic set is an extension of both a linguistic term set and a hesitant fuzzy set. It combines a quantitative evaluation with a qualitative evaluation, which can describe the real preferences of decision makers and reflect their uncertainty, hesitancy and inconsistency. The focus of this paper is those multi-criteria decision-making (MCDM) problems in which the criteria values take the form of hesitant fuzzy linguistic numbers (HFLNs). Having reviewed the relevant literature, the Hausdorff distance for HFLNs is provided and some linguistic scale functions are applied. Subsequently, two hesitant fuzzy linguistic MCDM methods are proposed, which are based on the proposed distance measure and the TOPSIS and TODIM methods. The first of these MCDM methods is based on complete rationality, whilst the second is based on bounded rationality. Finally, an illustrative example is provided to verify the proposed methods, which are then compared to the existing approaches.

Multi-criteria decision-making based on hesitant fuzzy linguistic term sets: An outranking approach

Abstract Hesitant fuzzy linguistic term sets (HFLTSs) are introduced to express the hesitance existing in linguistic evaluation as clearly as possible. However, most existing methods using HFLTSs simply rely on the labels or intervals of linguistic terms, which may lead to information distortion and/or loss. To avoid this problem, linguistic scale functions are employed in this paper to conduct the transformation between qualitative information and quantitative data. Moreover, the directional Hausdorff distance, which uses HFLTSs, is also proposed and the dominance relations are subsequently defined using this distance. An outranking approach, similar to the ELECTRE method, is constructed for ranking alternatives in multi-criteria decision-making (MCDM) problems, and the approach is demonstrated using a numerical example related to supply chain management. Because of the inherent features of the directional Hausdorff distance and the defined dominance relations, this approach can effectively and efficiently overcome the hidden drawbacks that may hamper the use of HFLTSs. Finally, the accuracy and effectiveness of the proposed approach is further tested through sensitivity and comparative analyses.