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Multi-criteria decision-making (MCDM) entails a heterogeneous decision-making problem, which poses challenges for decision-makers (DMs) in generating an optimal solution. To address this, we have proposed a heterogeneous evaluation framework. First, a novel picture fuzzy cross-entropy measure was defined with the simultaneous consideration of uncertainty and hesitancy of picture fuzzy information, overcoming the shortcomings of the existing cross-entropy measure in relation to its validity and properties. Next, an optimisation-model for determining the objective weights of criteria was constructed based on the proposed closeness measurement and the step-wise weight assessment ratio analysis (SWARA) method. This model was constituted from both objective and subjective perspectives under the circumstance of completely unknown criterion information. Additionally, the conventional Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) method was extended to the picture fuzzy environment, and a normalisation method was developed to transform heterogeneous judgments, including linguistic terms, interval numbers, and picture fuzzy numbers, into a unified representation form. A heterogeneous picture fuzzy SWARA-MARCOS evaluation framework was then established and used to solve a military equipment supplier selection problem. The results demonstrated the validity and feasibility of the proposed evaluation framework, while sensitivity, comparative, and complexity analyses demonstrated the robustness and superiority of it. [ABSTRACT FROM AUTHOR]

Single-valued neutrosophic hesitant fuzzy sets (SVNHFSs) have recently become a subject of great interest for researchers, and have been applied widely to multi-criteria decision-making (MCDM) problems. In this paper, the single-valued neutrosophic hesitant fuzzy geometric weighted Choquet integral Heronian mean operator, which is based on the Heronian mean and Choquet integral, is proposed, and some special cases and the corresponding properties of the operator are discussed. Moreover, based on the proposed operator, an MCDM approach for handling single-valued neutrosophic hesitant fuzzy information where the weights are unknown is investigated. Furthermore, an illustrative example to demonstrate the applicability of the proposed decision-making approach is provided, together with a sensitivity analysis and comparison analysis, which proves that its results are feasible and credible. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, multi-criteria decision-making (MCDM) problems based on the qualitative flexible multiple criteria method (QUALIFLEX), in which the criteria values are expressed by multi-valued neutrosophic information, are investigated. First, multi-valued neutrosophic sets (MVNSs), which allow the truth-membership function, indeterminacy-membership function and falsity-membership function to have a set of crisp values between zero and one, are introduced. Then the likelihood of multi-valued neutrosophic number (MVNN) preference relations is defined and the corresponding properties are also discussed. Finally, an extended QUALIFLEX approach based on likelihood is explored to solve MCDM problems where the assessments of alternatives are in the form of MVNNs; furthermore an example is provided to illustrate the application of the proposed method, together with a comparison analysis. [ABSTRACT FROM AUTHOR]

In this paper, the cross-entropy of intuitionistic hesitant fuzzy sets (IHFSs) is developed by integrating the cross-entropy of intuitionistic fuzzy sets (IFSs) and hesitant fuzzy sets (HFSs). First, several measurement formulae are discussed and their properties are studied. Then, two approaches, which are based on the developed intuitionistic hesitant fuzzy cross-entropy, are proposed for solving multi-criteria decision-making (MCDM) problems within an intuitionistic hesitant fuzzy environment. For both methods, an optimisation model is established in order to determine the weight vector for MCDM problems with incomplete information on criteria weights. Finally, an example is provided in order to illustrate the practicality and effectiveness of the proposed approaches. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

Single-valued neutrosophic sets (SVNSs), which involve in truth-membership, indeterminacy-membership and falsity-membership, play a significant role in describing the decision-makers' preference information. In this study, a single-valued neutrosophic multi-criteria decision-making (MCDM) approach is developed based on Shapley fuzzy measures and power aggregation operator that takes a correlative relationship among criteria into account and also simultaneously reduces the effects of abnormal preference information. Firstly, two aggregation operators, namely, generalized weighted single-valued neutrosophic power Shapley Choquet average (GWSVNPSCA) operator and generalized weighted single-valued neutrosophic power Shapley Choquet geometric (GWSVNPSCG) operator, are accordingly defined, and the corresponding properties are discussed as well. Secondly, based on the proposed aggregation operators, an integrated MCDM approach is proposed to effectively solve single-valued neutrosophic problems where the weight information is incompletely known. A programming model is constructed to obtain the optimal Shapley fuzzy measure. Next, the proposed operators are utilized to aggregate the decision-makers' preference information. Finally, a theoretical example with tourism attraction selection is provided to examine the efficacy of the developed approach, in which the results is found reasonable and credible. [ABSTRACT FROM AUTHOR]

With respect to multi-criteria decision-making (MCDM) problems in which the criteria denote the form of single-valued neutrosophic sets (SVNSs), and the weight information is also fully unknown, a novel MCDM method based on qualitative flexible multiple criteria (QUALIFLEX) is developed. Firstly, the improved cosine measure of the included angle between two SVNSs is defined. Then, the improved single-valued neutrosophic projection is developed, and the corresponding improved single-valued neutrosophic bidirectional projection and single-valued neutrosophic bidirectional projection difference are investigated. Moreover, the partial ordering relation of SVNSs is developed. Secondly, an extended QUALIFLEX method based on an improved single-valued neutrosophic projection measure is proposed to handle MCDM problems in which the weights of criteria are completely unknown. Finally, an example for selection of a green supplier, as well as a performance comparison analysis, are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Multi-valued neutrosophic sets (MVNSs) consider the truth-membership, indeterminacy-membership, and falsity-membership simultaneously, which can more accurately express the preference information of decision-makers. In this paper, the normalized multi-valued neutrosophic distance measure is developed firstly and the corresponding properties are investigated as well. Secondly, the normalized multi-valued neutrosophic distance difference is defined and the corresponding partial ordering relation is discussed. Thirdly, based on the developed distances and comparison method, an extended multi-valued neutrosophic QUALItative FLEXible multiple criteria (QUALIFLEX) method is proposed to handle MCDM problems where the weights of criteria are completely unknown. Finally, an example for selection of medical diagnostic plan is provided to demonstrate the proposed method, together with sensitivity analysis and comparison analysis. [ABSTRACT FROM AUTHOR]