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In this paper, an improved technique for order preference by similarity to an ideal solution (TOPSIS) method was proposed based on completely unknown attribute weight information, as well as taking multiple criteria decision making of interval-valued intuitionistic fuzzy number as the evaluation information. First of all, a cumulative interval score function considering the influence of hesitation as well as a cumulative score function containing the risk preference of the decision maker were constructed. Then, a new information entropy function was constructed by using the newly defined score function, which presents a new method that directly utilizes evaluation information to obtain criterion weight. Next, all schemes were sequenced by virtue of relative closeness and the criterion weight of each alternative and ideal scheme. Finally, the effectiveness of the proposed method was illustrated by comparison with examples.

Score functions play an important role in ranking hesitant fuzzy elements (HFEs) and hesitant fuzzy sets (HFSs). Currently, various kinds of HFE and HFS score functions have been investigated in the literature. However, the essential characteristic and generation mechanism of these score functions have not been systematically studied. To address these issues, this paper introduces an axiomatic definition of deviation degree measure and proposes a general form of dual HFE and HFS deviation score functions, from which a family of existing HFE and HFS score functions can be derived. Besides, we develop two ranking methods based on a pair of dual deviation score functions for distinguishing HFEs and HFSs that are indiscernible by a single score function. Moreover, the mathematical and behavioral properties of HFS deviation score functions are analyzed for applying them in practice. Finally, the proposed ranking method for HFSs is applied to the multi-criteria decision-making problems with hesitant fuzzy information.

We consider the problem of uncertainty assessment for low dimensional components in high dimensional models. Specifically, we propose a novel decorrelated score function to handle the impact of high dimensional nuisance parameters. We consider both hypothesis tests and confidence regions for generic penalized M-estimators. Unlike most existing inferential methods which are tailored for individual models, our method provides a general framework for high dimensional inference and is applicable to a wide variety of applications. In particular, we apply this general framework to study five illustrative examples: linear regression, logistic regression, Poisson regression, Gaussian graphical model and additive hazards model. For hypothesis testing, we develop general theorems to characterize the limiting distributions of the decorrelated score test statistic under both null hypothesis and local alternatives. These results provide asymptotic guarantees on the type I errors and local powers. For confidence region construction, we show that the decorrelated score function can be used to construct point estimators that are asymptotically normal and semiparametrically efficient. We further generalize this framework to handle the settings of misspecified models. Thorough numerical results are provided to back up the developed theory.

The financial risk evaluation is critically vital for enterprises to identify the potential financial risks, provide decision basis for financial risk management, and prevent and reduce risk losses. In the case of considering financial risk assessment, the basic problems that arise are related to strong fuzziness, ambiguity and inaccuracy. q-rung orthopair fuzzy set (q-ROFS), portrayed by the degrees of membership and non-membership, is a more resultful tool to seize fuzziness. In this article, the novel q-rung orthopair fuzzy score function is given for dealing the comparison problem. Later, the and operations are explored and their interesting properties are discussed. Then, the objective weights are calculated by CRITIC (Criteria Importance Through Inter-criteria Correlation). Moreover, we present combined weights that reflects both subjective preference and objective preference. In addition, the q-rung orthopair fuzzy MCDM (multi-criteria decision making) algorithm based on CoCoSo (Combined Compromise Solution) is presented. Finally, the feasibility of algorithm is stated by a financial risk evaluation example with corresponding sensitivity analysis. The salient features of the proposed algorithm are that they have no counter-intuitive case and have a stronger capacity in differentiating the best alternative. First published online 03 March 2020

The 5G industry is of great concern to countries to formulate a major national strategy for 5G planning, promote industrial upgrading, and accelerate their economic and technological modernization. When considering the 5G industry evaluation, the basic issues involve strong uncertainty. Pythagorean fuzzy sets, depicted by membership degree and non-membership degree, are a more resultful means for capturing uncertainty. In this paper, the comparison issue in Pythagorean fuzzy environment is disposed by proposing novel score function. Next, the ⊖ and ⊘ operations are defined and their properties are proved. Later, the objective weight is calculated by Criteria Importance Through Inter-criteria Correlation method. Meanwhile, the combined weight is determined by reflecting both subjective weight and the objective weight. Then, the Pythagorean fuzzy decision making algorithm based Combined Compromise Solution is developed. Lastly, the validity of algorithm is expounded by the 5G evaluation issue, along with their sensitivity analysis. The main advantages of proposed algorithm are: (1) have no counterintuitive phenomena; (2) without division or antilogarithm by zero problem; (3) own stronger ability to distinguish alternatives.

The MULTIMOORA method is better than some of the existing decision making methods. However, it has not been improved to process Pythagorean fuzzy sets (PFSs). The decision results of the MULTIMOORA method greatly depend on the distance measure and score function. Although there are many studies focusing on proposing distance measures and score functions for PFSs, they still show some defects. In this paper, we propose two novel distance measures and a novel score function for PFSs for proposing a novel Pythagorean fuzzy MULTIMOORA method. To this end, two distance measures, Dice distance and Jaccard distance, are proposed for computing the deviation degree between two PFSs, and their general forms are also discussed. Afterward, a novel score function based on determinacy degree and indeterminacy degree is put forward for approximately representing PFSs. Then, the original MULTIMOORA method is extended by using the Dice distance and score function and it is used to solve the multicriteria decision making problems under the PFS information context. Finally, a real case for evaluating solid-state disk productions is handled using the proposed Pythagorean fuzzy MULTIMOORA method and another case for evaluating energy projects is given to verify the advantages of our studies by comparing them with the existing Pythagorean fuzzy distance measures, score functions, and decision making methods.

Bayesian robustness under model misspecification is a current area of active research. Among recent ideas is that of raising the likelihood function to a power. In this paper we discuss the choice of appropriate power and provide examples.

In today’s world, the demand for sustainable third-party reverse logistics providers (S3PRLPs) becomes an increasingly considerable issue for industries seeking improved customer service, cost reduction and sustainability perspectives. However, the assessment and selection of right S3PRLP is a complex uncertain decision-making problem due to involvement of numerous conflicting attributes, imprecise human mind and lack of information. Recently, Fermatean fuzzy set (FFS) has been recognized as one of the suitable tools to tackle the uncertain and inaccurate information. In this paper, we introduce a hybrid methodology based on CRITIC and EDAS methods with Fermatean fuzzy sets (FFSs) to solve the S3PRLP selection problem in which the attributes and decision makers’ weights are completely unknown. In this framework, CRITIC approach is applied to calculate the attribute weight and EDAS method is used to evaluate the priority order of S3PRLP options. To do this, a new improved generalized score function (IGSF) is developed with its elegant properties. Also, a formula is discussed to calculate the decision makers’ weights based on the developed IGSF. Next, developed framework is applied to assess a case study of S3PRLP selection problem with Fermatean fuzzy information, which elucidates the usefulness and practicality of the proposed method. Finally, comparative study is implemented to show the strength of introduced framework with extant approaches. The outcomes of the work confirm that the introduced approach is more feasible and well-consistent with the other extant approaches.

The main purpose of the current study is to explore a novel q-rung orthopair fuzzy score function and extend the measurement of alternatives and ranking according to the compromise solution (MARCOS) method with unknown weight information to the context of q-rung orthopair fuzzy numbers (q-ROFNs). For this, first, the drawbacks of the existing score functions are highlighted via several solid examples. Then, to fill the gaps of the existing ones, a novel score function and its relevant characteristics are delineated. To determine the objective weights of criteria, q-rung orthopair fuzzy criteria importance through intercriteria correlation (CRITIC) method is modeled based on the derived weights of decision-makers (DMs), standard deviation, and correlation coefficient. Following that, the q-rung orthopair fuzzy MARCOS approach is established to cope with multi-criteria group decision-making (MCGDM) problems. Later, a case study of solid waste management is addressed to show the practicality of the presented method. Lastly, the derived results are validated through three phases: two sensitivity analyses, rank reversal phenomena, and comparative analysis.

In this paper, we initiate a new axiomatic definition of single-valued neutrosophic distance measure and similarity measure, which is expressed by single-valued neutrosophic number that will reduce the information loss and remain more original information. Meanwhile, a novel score function is proposed. Then, the objective weights of various attributes are determined via gray system theory. Moreover, we present the combined weights, which can show both the subjective information and the objective information. Later, we present three algorithms to deal with multi-attribute decision-making problem based on revised Technique for Order Preference by Similarity to an Ideal Solution, Multi-Attributive Border Approximation area Comparison and similarity measure. Finally, the effectiveness and feasibility of approaches are demonstrated by two numerical examples.