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In the face of increasingly complex data forms and decision-making problems, the uncertainty of information poses a major challenge to multi-attribute decision-making methods. How to effectively organize information and serve realistic decision-making problems has attracted extensive attention in the academic circles. In view of this, based on the distribution law of random variables, we put forward the basic concept of probability numbers and construct a general framework, including the concepts of type, order, item, isomorphism and isomerism, same domain and same distribution of probability numbers. On this basis, we further define the expectation and variance formula of probability numbers, and its operation rules are defined for the same type of probability numbers. To compare the dominance and inferiority of probability numbers further accurately, we put forward the concepts of dominance degree and comparability degree of probability numbers, so that decision makers can realize the ranking of probability numbers by calculating the comprehensive dominance degree. In view of the related concepts of probability numbers, we summarize the properties and theorems of probability numbers and prove them. In addition, a probability numbers-based multi-attribute decision-making framework model is proposed to solve the multi-attribute decision-making problem. Decision makers can select appropriate sub-models to construct personalized multi-attribute decision-making methods according to actual needs. At the end of the paper, we apply the method to the multi-attribute decision case of campus express stations evaluation and verify the scientificity and rationality of the evaluation method. The concept of probability numbers and its decision model proposed in this paper extend the concept category of numbers, enrich the multi-attribute decision-making method based on probability numbers, and have certain reference significance for further research of uncertain decision theory and method. [ABSTRACT FROM AUTHOR]

Multi-attribute group decision-making (MAGDM) is one of the research hotspots in human cognitive and decision-making theory. However, there are still challenges to the existing MAGDM methods in modeling uncertain linguistics of decision-makers' (DMs') cognitive information and objectively obtaining weights. Therefore, this paper aims to develop a new MAGDM method considering incomplete known weight information under spherical uncertain linguistic sets (SULSs) to model uncertain information in MAGDM problems. The method mainly includes the following aspects. Firstly, a new concept, which enables an intuitive evaluation of neutral membership and hesitancy degrees at the linguistic evaluation, has been is first developed for capturing the more uncertain information. Secondly, the cosine similarity measure (CSM) and cross-entropy measure (CEM) are widely used to measure ambiguous information because of their robustness of measurement results. The CSM and CEM are extended to SULSs to calculate the DMs' and attributes weights quantitively, respectively. Thirdly, in terms of effective integration of fuzzy information to obtain more accurate decision results, the Hamy mean (HM) and dual Hamy mean (DHM) operators are valued due to their consideration of the interrelationships between inputs. Two extension operators, named spherical fuzzy uncertain linguistic weight HM and DHM, are proposed to integrate spherical fuzzy uncertain linguistic information in the third stage. In the experiment, a decision case is presented to illustrate the applicability of the proposed method, and results show the effectiveness, flexibility and advantages of the proposed method are demonstrated by numerical examples and comparative analysis. [ABSTRACT FROM AUTHOR]

In the existing conflict analysis models, they used a triangular fuzzy number on [0, 1] to describe the range of an agent's attitude towards an issue, but there are still some shortcomings in describing the specific attitude and degree of conflict represented by the triangular fuzzy number. In this paper, the conflict analysis model is extended, improved and perfected. Firstly, the expectation of triangular fuzzy number is used in the [-1, 1] triangular fuzzy information system to reasonably express the specific attitudes represented by a triangular fuzzy number. Secondly, the weights of each issue are obtained by using the Sugeno measure, which determines the total attitude of the agent towards all issues. Thirdly, the relationship between agents is obtained with the help of the weighted distance of triangular fuzzy numbers. Finally, the thresholds α and β are calculated by means of triangular fuzzy decision theory rough sets. [ABSTRACT FROM AUTHOR]

Bayesian decision models use probability theory as a commonly technique to handling uncertainty and arise in a variety of important practical applications for estimation and prediction as well as offering decision support. But the deficiencies mainly manifest in the two aspects: First, it is often difficult to avoid subjective judgment in the process of quantization of priori probabilities. Second, applying point-valued probabilities in Bayesian decision making is insufficient to capture non-stochastically stable information. Soft set theory as an emerging mathematical tool for dealing with uncertainty has yielded fruitful results. One of the key concepts involved in the theory named soft probability which is as an immediate measurement over a statistical base can be capable of dealing with various types of stochastic phenomena including not stochastically stable phenomena, has been recently introduced to represent statistical characteristics of a given sample in a more natural and direct manner. Motivated by the work, this paper proposes a hybrid methodology that integrates soft probability and Bayesian decision theory to provide decision support when stochastically stable samples and exact values of probabilities are not available. According to the fact that soft probability is as a special case of interval probability which is mathematically proved in the paper, thus the proposed methodology is thereby consistent with Bayesian decision model with interval probability. In order to demonstrate the proof of concept, the proposed methodology has been applied to a numerical case study regarding medical diagnosis. [ABSTRACT FROM AUTHOR]

This paper provides a novel target threat assessment model that utilizes TOPSIS and three-way decision-making under a single-valued neutrosophic environment. The presented model provides theoretical support for combat decision-making in complex battlefield environments with uncertain information. The model employs single-valued neutrosophic sets to handle uncertain data, which enhances the descriptive ability of information. The maximum deviation method is used to calculate attribute weight factors, which highlights the importance of each attribute. The final target threat ranking is obtained based on the relative closeness coefficient of each target. Furthermore, the proposed model constructs a multi-attribute aggregation loss function matrix for each target, sets the risk avoidance coefficient under the knowledge of the battlefield condition, and calculates the decision threshold of each target using three-way decision theory. This method produces the classification of the target choice. The numerical examples and comparison analysis demonstrate that the suggested model can handle ambiguous scenario information effectively and reasonably, transform traditional decision-making ranking results into three-way classification findings, and provide a rationale for choosing an attacking target. [ABSTRACT FROM AUTHOR]

Interval type-2 trapezoidal fuzzy (IT2TrF) number is a powerful tool to depict fuzzy information. Information measures methods have received more and more attention in recent years as they play an important role in decision-making theory. A new multi-attribute decision-making (MADM) method supported by IT2TrF information measures is investigated in this paper under the IT2TrF information environment. Firstly, three axiomatic definitions of IT2TrF information measures are introduced, which include information entropy, similarity measure and cross-entropy. Secondly, with the help of the exponential function, we formulate some information measure formulas, which are followed by the proofs that the exponential entropy, exponential similarity measure and exponential cross-entropy fit the three axiomatic definitions. Subsequently, a novel IT2TrF MADM method is designed, in which the IT2TrF exponential entropy and cross-entropy are utilized to generate the attribute weights, the IT2TrF exponential similarity measure is employed to obtain the closeness degree of the ideal solution and derive the most satisfying solution. Lastly, we provide a numerical example of corporate investment to demonstrate the applicability and feasibility of the proposed MADM method. The robustness and merits of the developed MADM method are highlighted by the comparative analysis. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the three-way decision model on incomplete single-valued neutrosophic information tables. Firstly, we define the minimum and maximum similarity measures between single-valued neutrosophic numbers (SVNNs) which may contain unknown values. On this basis, the notion of θ-weak similarity measure is given. Then, we introduce the conception of an incomplete single-valued neutrosophic information table (ISVNIT). For an incomplete single-valued neutrosophic information table, a new similarity relation is proposed based on the θ-weak similarity measure. Some properties are also studied. By using Bayesian decision theory and this similarity relation, we construct a three-way decision model on an ISVNIT. Finally, an example of choosing product service providers is explored to illustrate the rationality and feasibility of the proposed model. We also discuss the influence of parameters in the model on decision results. [ABSTRACT FROM AUTHOR]

In the existing conflict analysis models, they used a triangular fuzzy number on [0, 1] to describe the range of an agent's attitude towards an issue, but there are still some shortcomings in describing the specific attitude and degree of conflict represented by the triangular fuzzy number. In this paper, the conflict analysis model is extended, improved and perfected. Firstly, the expectation of triangular fuzzy number is used in the [-1, 1] triangular fuzzy information system to reasonably express the specific attitudes represented by a triangular fuzzy number. Secondly, the weights of each issue are obtained by using the Sugeno measure, which determines the total attitude of the agent towards all issues. Thirdly, the relationship between agents is obtained with the help of the weighted distance of triangular fuzzy numbers. Finally, the thresholds α and β are calculated by means of triangular fuzzy decision theory rough sets. [ABSTRACT FROM AUTHOR]

Online health communities (OHCs) have emerged as a significant platform for people communicating health information and self-healthcare management. In recent, the researches focusing on its performance measurement and the service quality evaluation have drawn intensive attention. Although some qualitative methods have made evaluation and analyses for the OHCs performance, the studies based on fuzzy multi-attribute decision making theory are rarely developed in the service quality evaluation of OHCs. In view of the complexity and uncertainty of evaluation mission, this paper develops an integrated evaluation approach of the OHC service quality based on the q-rung orthopair fuzzy linguistic aggregation operators. Firstly, we propose the cross-entropy of q-rung orthopair fuzzy numbers, which is applied in solving the optimal weight of indicators by a linear programming model. Next, the q-rung orthopair fuzzy linguistic power average (q-ROFLPA) and q-rung orthopair fuzzy linguistic partitioned dual Maclaurin symmetric mean (q-ROFLPDMSM) operators are developed for aggregating the assessment information and ranking the OHCs. Based on the proposed aggregation operators, the evaluation indicator system and an evaluation framework are constructed to accomplish the service quality evaluation of OHCs. Finally, a practical evaluation case of OHCs is provided to demonstrate the reliability and advantages of the proposed approach. [ABSTRACT FROM AUTHOR]

Some risky multi-criteria group decision making problems include payoff and probability information. To deal with these problems, this study introduces a large scale multi-criteria group decision making model based on focus theory of choice. In this model, a group of experts' linguistic evaluations on multiple criteria are first collected to form linguistic distributions. The positive foci of the linguistic distributions are computed and aggregated into the alternatives' scores. It is noted that in this process the linguistic terms and probabilities are aggregated by using different rules. The positive foci of the alternatives' scores are computed and the optimal alternative is selected. A pollution treatment evaluation problem is solved by using the proposed model, and simulation experiments and comparative analysis are given. [ABSTRACT FROM AUTHOR]

The quality of the input data is amongst the decisive factors affecting the speed and effectiveness of recurrent neural network (RNN) learning. We present here a novel methodology to select optimal training data (those with the highest learning capacity) by approaching the problem from a decision making point of view. The key idea, which underpins the design of the mathematical structure that supports the selection, is to define first a binary relation that gives preference to inputs with higher estimator abilities. The Von Newman Morgenstern theorem (VNM), a cornerstone of decision theory, is then applied to determine the level of efficiency of the training dataset based on the probability of success derived from a purpose-designed framework based on Markov networks. To the best of the author's knowledge, this is the first time that this result has been applied to data selection tasks. Hence, it is shown that Markov Networks, mainly known as generative models, can successfully participate in discriminative tasks when used in conjunction with the VNM theorem. The simplicity of our design allows the selection to be carried out alongside the training. Hence, since learning progresses with only the optimal inputs, the data noise gradually disappears: the result is an improvement in the performance while minimising the likelihood of overfitting. [ABSTRACT FROM AUTHOR]

This study examines decision theory based on interval type-2 fuzzy sets with linguistic information for the three-way decision approach by addressing the challenge of uncertainty for information analysis and fusion in subjective decision-making processes. First, the interval type-2 fuzzy linguistic term sets (IT2 FLTSs) are defined to represent and normalize the uncertain preference information in linguistic decision-making. Subsequently, perception computing based on computing with words paradigm is introduced to implement information fusion among different decision-makers in the linguistic information-based fuzzy logic reasoning process. Then, a three-way decision (3WD) theory based on IT2 FLTSs with fuzzy neighborhood covering is proposed, and the corresponded tri-partitioning strategies that satisfy Jaccard similarity of membership distributions are given. Finally, 3WD theory is applied to multi-criteria group decision-making with linguistic terms, and the algorithm steps are illustrated by a promising application under the background of coronavirus disease 2019 to reveal the feasibility and practicability of the proposed approach. [ABSTRACT FROM AUTHOR]

As everyday problems contain a lot of data and ambiguity, it has become necessary to develop new mathematical approaches to address them and soft set theory is the best tool to deal with such problems. Hence, in this article, we introduce a non-continuous mapping in soft settings called soft U -continuous. We mainly focus on studying soft U -continuity and its connection to soft continuity. We further show that soft U -continuity preserves soft compact sets and soft connected sets. The later sets have various applications in computing science and decision making theory. In the end, we show that if each soft U -continuous mapping f from a soft space X into a soft T0-space Y is soft continuous, then Y is soft T1. [ABSTRACT FROM AUTHOR]