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We discuss the three-way rough set based approach for approximation of decision granules in Intelligent Systems (IS's). The novelty of the approach is in presenting a new concept of approximation space which is based on advanced reasoning tools. Many generalisations of the rough set approaches developed over the years are mainly concentrated around reasoning concerning (partial) inclusion of sets. However, such approximation spaces are not satisfactory to deal with important aspects of approximate reasoning by IS's aiming to construct of the high quality approximations of compound decision granules. We demonstrate a number of examples supporting this claim. In particular, in solving the considered in the paper problems are involved complex algorithmic optimization processes directed by reasoning tools supporting searching for (semi-)optimal approximations of decision granules in huge spaces. This paper is a step toward developing tools for derivation of granules supporting IS's in perceiving situations to a degree satisfactory for making the right decisions. [ABSTRACT FROM AUTHOR]

Let A be a pairwise comparison matrix obtained from a consistent one by perturbing three entries above the main diagonal, x , y , z , and the corresponding reciprocal entries, in a way that there is a submatrix of size 2 containing the three perturbed entries and not containing a diagonal entry. In this paper we describe the relations among x , y , z with which A always has its principal right eigenvector efficient. Previously, and only for a few cases of this problem, R. Fernandes and S. Furtado (2022) proved the efficiency of the principal right eigenvector of A. In this paper, we continue to use the strong connectivity of a certain digraph associated with A and its principal right eigenvector to characterize the vector efficiency. For completeness, we show that the existence of a sink in this digraph is equivalent to the inefficiency of the principal right eigenvector of A. [ABSTRACT FROM AUTHOR]

Multidimensional fuzzy sets (MFS) is a new extension of fuzzy sets on which the membership values of an element in the universe of discourse are increasingly ordered vectors on the set of real numbers in the interval [ 0 , 1 ]. This paper aims to investigate fuzzy negations on the set of increasingly ordered vectors on [ 0 , 1 ] , i.e. on L ∞ ([ 0 , 1 ]) , MFN in short, with respect to some partial order. In this paper we study partial orders, giving special attention to admissible orders on L n ([ 0 , 1 ]) and L ∞ ([ 0 , 1 ]). In addition, we study the possibility of existence of strong multidimensional fuzzy negations and some properties and methods to construct such operators. In particular, we define the ordinal sums of n-dimensional negations and ordinal sums of multidimensional fuzzy negations on a multidimensional product order. A multi-attribute group decision making algorithm is presented. [ABSTRACT FROM AUTHOR]

Fuzzy and intuitionistic fuzzy β covering has attracted the interest of many researchers recently. However, some of the factors namely 1. the lack of inclusion relationship between lower and upper approximation, 2. Inability to fit real valued dataset i.e. misclassification, hinder its application in decision making. Also, majority of these approaches are affected by noise. All these factors have created the need for a robust model. This paper proposes a novel intutitionistic fuzzy β covering model which is robust, combining intuitionistic fuzzy set, β covering and multigranulation rough sets. A new intuitionistic fuzzy β covering based multigranulation model is proposed which satisfies inclusion relationship between two approximations. This robust model is used to formulate dependency degree, which is evaluated at various granularity levels and is thereby employed for feature subset selection. Series of experiments are conducted on real valued datasets to illustrate the robustness and effectiveness of the underlying model. Furthermore, a comparative analysis with state of art approaches followed by statistical test lays down the superiority of the proposed model. [ABSTRACT FROM AUTHOR]

Three-way decision (3WD) and rough set are two influential theories of study knowledge discovery and uncertain artificial intelligence. A central notion of 3WD is a tri-level thinking paradigm consisting of trisecting, acting, and outcome (i.e., TAO model). As is well known, movement-based on three-way decision (M-3WD) and change-based TAO model, mainly started from the perspective of effectiveness measure, are two outcome evolution studies about the three-way decision, which could lead to some limitations in application. This paper builds a change-based three-way decision (C-3WD) based on confidence level, and an application to rough set is also discussed. Furthermore, the (α , β) -approximate probability regions of rough set are re-decided by the change model, and a medical decision example is introduced to explain how to make C-3WD in the classification of rough set. By comparing the effectiveness of the traditional three-way decision method with ours, it is again verified from the two aspects of cost and earns and concludes that the model in this paper is more suitable for the decision process that includes trisecting and acting. Some experiments on various datasets to demonstrate the effectiveness of our methods. [ABSTRACT FROM AUTHOR]

Explaining black-box classification models is a hot topic in AI, with the overall goal of improving trust in decisions made by such models. Several works have been done and diverse functions have been proposed. However, their formal properties and links have not been sufficiently studied. This paper presents four contributions: The first consists of investigating global explanations of black-box classifiers. We provide a formal and unifying framework in which such explanations are defined from the whole feature space. The framework is based on two concepts, which are seen as two types of global explanations: arguments in favour of (or pro) predictions and arguments against (or con) predictions. The second contribution consists of defining various types of local explanations (abductive explanations, counterfactuals, contrastive explanations) from the whole feature space, investigating their properties, links and differences, and showing how they relate to global explanations. The third contribution consists of analysing and defining explanation functions that generate (global, local) abductive explanations from incomplete information (i.e., from a subset of the feature space). We start by proposing two desirable properties that an explainer would satisfy, namely success and coherence. The former ensures the existence of explanations while the latter ensures their correctness. We show that in the incomplete case, the two properties cannot be satisfied together. The fourth contribution consists of proposing two functions that generate abductive explanations and which satisfy coherence at the expense of success. [ABSTRACT FROM AUTHOR]

Conflict occurs in all aspects of life, and people tend to consider a variety of factors in the face of it and hesitate to make decisions among multiple choices. This paper performs a three-way conflict analysis in the dual hesitant fuzzy case. Firstly, we propose the concept of dual hesitant fuzzy situation tables (DHFSTs). Subsequently, we trisect the pairs of agents and objectively calculate issue weights by CRITIC method rather than subjective assignments. According to Bayesian minimum risk theory, we derive trisection of agents, in which the state set is calculated objectively. Then, we analyze three issue sets through the conflicting characters of issues, which provides a new way to consider the trisection of issues. In addition, we put forward the definition of maximal coalitions in DHFSTs and give an effective calculation method. Finally, we illustrate the feasibility of the proposed model by analyzing the development plan in Gansu Province, and conduct a brief comparative analysis. [ABSTRACT FROM AUTHOR]

The main aim of the paper is to discuss the architecture for the future Intelligent Systems (IS's) and Decision Support Systems (DS's) dealing with complex phenomena such as supporting medical decisions (diagnosis and therapy) and to emphasize challenges in designing such systems. More precisely, the paper presents arguments for developing a specialized computing model based on the interactive granular computing paradigm which can help to design IS's and DS's more close to the prototypes of real life decision making. In this regard, the paper brings to the fore different experiences faced during designing other medical IS's or DS's.As a starting step, the paper considers the experience of developing the OvuFriend platform and outlines some possible extension of it in the framework of the proposed architecture on the basis of Interactive Granular Computing (IGrC) model. Specifically, our attempt is to analyze a scheme, which is being used in the platform of OvuFriend for determining health risks and possibilities of a woman to conceive a child, from the perspective of IGrC. The target of the paper is two fold. Firstly, to show how the underlying AI algorithm of this scheme can be related with the notion of computing in the context of IGrC. Secondly, to identify possible extensions of the existing scheme so that it becomes more dynamic, interactive, and close to personalized medicine. [ABSTRACT FROM AUTHOR]

Conflict analysis has become a hot issue in management science. In the context of conflict analysis, there are three attitudes for agents to describe the opinion, including supportive, opposite, and neutral. Then, the conflict situation is discussed and analyzed. In this paper, we propose an extended Pawlak conflict model concerning the trust mechanism to solve the problem of the reaching consensus process. Firstly, the degree of conflict is defined by the weights of agents considering the penalty factors, and an extended Pawlak conflict model is presented. Then, the trust recommendation mechanism is proposed to modify the opinions of agents and reach conflict consensus. Four kinds of feedback mechanism are discussed by using four perspectives: 1) without the penalty factors and no limit to the range of adjustments; 2) without the penalty factors and the attitude of agents vary from pessimistic to neutral; 3) with the penalty factors and no limit to the range of adjustments; 4) with the penalty factors and the attitude of agents vary from pessimistic to neutral. Furthermore, this paper presents a process of reaching consensus based on the trust recommendation mechanism for the conflict analysis problem. Finally, a case study is used to validate the effectiveness and superiority of the proposed method. A comparative analysis is completed for the parameters and the maximum alliances could be obtained with the original Pawlak conflict model. [ABSTRACT FROM AUTHOR]

As an important uncertainty reasoning method, Dempster-Shafer (D-S) evidence theory has been widely applied to expert system, comprehensive evaluation, information fusion and decision analysis. However, it has not been fully valued in uncertainty measurement. A hybrid information system (HIS) means an information system that contains many types of attributes (e.g., categorical attribute, real-valued attribute and attribute with missing values, etc.). It is more difficult to measure an HIS than an ordinary IS. This paper studies the use of evidence theory to measure the uncertainty of an HIS. Firstly, a novel distance between two objects in an HIS considering decision attributes is constructed, and secondly, the tolerance relation based on the constructed distance is established in an HIS. And then, belief and plausibility functions are defined by the tolerance relation. Furthermore, several algorithms for attribute reduction are designed on the basis of the defined belief and plausibility functions. In addition, we come to a series of conclusions on the relation among θ -reduction by using decision attributes, θ -belief reduction and θ -plausibility reduction, which further confirms the effectiveness of the designed attribute reduction algorithms. Finally, the experimental results and statistical test show that the defined belief and plausibility functions work well in measuring the uncertainty of an HIS and the designed reduction algorithm is superior to several state-of-the-art algorithms in classification accuracy. These results will provide a wider perspective on the uncertainty of an HIS. [ABSTRACT FROM AUTHOR]

Considering L to be a complete residuated lattice, by introducing the notion of L -valued covering on an L -set (as a universe), and then an L -valued neighborhood based on it, we present the concept of L -valued covering-based rough sets. We mainly address the following issues in this paper: Firstly, we present four types of L -valued neighborhood operators and study some of their respective properties. Secondly, we construct L -valued lower (resp., upper) approximation operators and then discuss some of their properties. Finally, we try to propose a kind of MADM problem based on an L -valued covering-based rough set model (for L = [ 0 , 1 ]). [ABSTRACT FROM AUTHOR]

In the context of multicriteria decision analysis, Pairwise Comparison Matrices (PCMs) represent a widely-used mathematical structure to capture comparisons about criteria or alternatives. When a confidence (or uncertainty) level is associated to the provided comparison measures, PCMs are naturally extended to the so-called Interval Pairwise Comparison Matrices (IPCM). Classical approaches, based on the eigenvector associated to the largest eigenvalue of the matrix (Analytic Hierarchy Process) or optimization problems (e.g. the Logarithmic Least Squares approach), are frequently adopted in order to estimate absolute utilities from relative judgements in absence of expert's uncertainty. Conversely, in the presence of uncertain measures, computationally intensive approaches based on Monte Carlo analysis have been adopted. In this paper, starting from a given PCM, we provide an approach able to find the smallest multiplicative perturbations of its elements able to perturb the obtained ranking from the ordinal perspective. On the basis of such approach, we provide theoretical results which can be adopted also in the case of uncertain measures (e.g., IPCMs) with the aim to characterize the stability of the obtained ranking on the basis of the given uncertainty. As testified by numerical examples that conclude the paper, the proposed framework can greatly simplify the classical approaches by providing the possibility to make direct assumptions on the final outcome of Monte Carlo analysis and reducing or avoiding its required computational effort. [ABSTRACT FROM AUTHOR]

In this paper we propose efficient methods for elicitation of complexly structured preferences and utilize these in problems of decision making under (severe) uncertainty. Based on the general framework introduced in Jansen et al. (2018) [37] , we now design elicitation procedures and algorithms that enable decision makers to reveal their underlying preference system (i.e. two relations, one encoding the ordinal, the other the cardinal part of the preferences) while having to answer as few as possible simple ranking questions. Here, two different approaches are followed. The first approach directly utilizes the collected ranking data for obtaining the ordinal part of the preferences, while their cardinal part is constructed implicitly by measuring the decision maker's consideration times. In contrast, the second approach explicitly elicits also the cardinal part of the decision maker's preference system, however, only an approximate version of it. This approximation is obtained by additionally collecting labels of preference strength during the elicitation procedure. For both approaches, we give conditions under which they produce the decision maker's true preference system and investigate how their efficiency can be improved. For the latter purpose, besides data-free approaches, we also discuss ways for statistically guiding the elicitation procedure if data from elicitations of previous decision makers is available. Finally, we demonstrate how the proposed elicitation methods can be utilized in problems of decision under (severe) uncertainty. Precisely, we show that under certain conditions optimal decisions can be found without fully specifying the preference system. [ABSTRACT FROM AUTHOR]

Granular computing is becoming a very hot research field, which has received extensive attention in recent years. It helps us to analyze and solve problems better by dividing complex problems into several simpler ones. Three-way granular concept is an important concept proposed by combining granular computing, formal concept analysis and three-way decision. Using traditional updating methods of three-way granular concepts, a lot of time and space resources are needed when multiple attributes or objects are deleted in formal context. In order to improve the efficiency and flexibility of obtaining three-way concepts, this paper discusses a novel dynamic update method of three-way granular concepts. In this paper, we firstly introduce the related knowledge of three-way granular concepts. Secondly, the update rules of the extension and connotation of attribute-induced three-way granular concepts are discussed in the dynamic formal context to construct three-way granular concepts. Moreover, we develop a method for establishing attribute-induced three-way granular concept by dynamic changes in the case of deleting multiple objects and attributes in the formal context. Furthermore, we design four algorithms to compare between the proposed approaches and traditional updating ways of three-way granular concepts. Finally, the validity of dynamic update method of attribute-induced three-way granular concept is verified through the experimental evaluation using six datasets coming from the University of California-Irvine (UCI) repository. [ABSTRACT FROM AUTHOR]

This paper proposes a sequential three-way decision-making approach based on BWM (best-worst method) and MULTIMOORA for multiple levels of granularity to deal with the multi-attribute group decision-making problems under uncertainty. First, using BWM to preprocess the attribute indicators of the decision problem, the relationship between the criteria important for decision problem is determined. Then, according to the importance of the determined level of granularity, from rough to clear, three-way decisions are made in sequence at each level. In this way, we obtain a lattice based three-way decision-making process. Also, in the process at each granularity, we consider the costs of both the decision process and the decision result. Thus, this paper builds a multigranulation sequential three-way decisions model with cost-sensitive. Next, based on the above-mentioned model, we propose a decision procedure and an algorithm for multi-attribute group decision making. It is worth noting that according to the research goals of the decision problem, MULTIMOORA is used to sort the classified alternatives. And a ranking result of the decision problem is given. Finally, the effectiveness and validity of the proposed model is verified by a multi-attribute group decision problem. The problem is the case of emergency diagnosis and treatment after a highway accident. And put forward reasonable suggestions for further development direction. [ABSTRACT FROM AUTHOR]

Subject-specific causal discovery methods could help to make better decisions in domains where there are variations on causal relations across subjects, such as neuroscience and genetics. However, discovering subject-specific causal models from limited data sets could be challenging. Although there are several causal discovery methods, most of them are focused on finding the common causal relations of a population from data sets with enough samples. The issue of discovering subject-specific causal relations from limited data sets has not been sufficiently explored. In this paper, we propose a knowledge transfer method for discovering subject-specific causal models. Our method discovers causal probabilistic graphical models, up to Markov equivalence classes, from discrete and continuous data sets. We hypothesized that transferring weighted instances of additional sources according to their discrepancy with target instances helps to compensate for the lack of target data and improves the performance of a scored-based causal discovery method. Experimental results on synthetic data sets and benchmark causal Bayesian networks show that our proposal, under few target samples, outperforms significantly in adjacency and arrowhead recovery the baseline and alternative methods. [ABSTRACT FROM AUTHOR]

Interval sets, as a particular knowledge representation, are composed of the lower set and the upper set to represent more general uncertain qualitative information. In this paper, we aim at investigating multi-expert multi-criterion decision making (MEMCDM) based on the interval set information. In the process of MEMCDM, by comparing positive, negative and boundary regions of interval sets, we firstly propose the similarity and dissimilarity measures of interval set to describe the closeness and deviation between interval sets. Secondly, with the aid of dissimilarity, we determine the criterion weight by combining the dissimilarity difference of the judgement matrix and the result of the maximum deviation of dissimilarity. For dealing with the hesitant problem of experts, we design transformation algorithm, which provides technical support for transforming experts' evaluation tables into an interval set information table. In view of the wide applicability of alternative queuing method (AQM), we extend AQM based on 0 − 1 precedence relationship matrix to address MEMCDM. The 0 − 1 precedence relationship matrix of AQM exists the incomparable situation, which can lead to the indiscernible alternatives. To reduce indiscernible alternatives and increase efficiency, we design a possibility degree of interval sets and deeply construct precedence relationship matrix. Further, we improve AQM by using possibility degree matrix and aggregating precedence relationship matrix on each alternative by weight arithmetic average (WAA). Finally, we use an example and simulation experiment of former e-commerce platform selection to elaborate and validate our proposed method. [ABSTRACT FROM AUTHOR]

Pairwise comparisons have been a long standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern multi-criteria decision analysis methods; they represent a useful tool for deriving a weighting vector which establishes a cardinal ranking of the alternatives/criteria. The weighting vector used in this paper gained popularity due to its mathematical properties and satisfies fundamental requirements, such as the immunity to rank reversal and preservation of the algebraic structure of the problem. Under consistency condition, that represents the full decision maker's coherence, this vector is completely reliable because it exactly represents the decision maker's preferences expressed by means of the pairwise comparisons. Unfortunately, the consistency is hard to reach in real situation; thus, in a previous paper, we provided a condition weaker than consistency so that the weighting vector at least preserves the preferences order expressed by means of inconsistent pairwise comparisons. This paper deals with a further crucial step in multi-criteria decision analysis, that is to ensure that the weighting vector preserves the preferences intensity, in addition to the preferences order, expressed by means of inconsistent pairwise comparisons. Thus, firstly, we introduce a necessary condition so that the weighting vector preserves the preferences intensity. Then, we show that this condition is a necessary but not a sufficient condition. Finally, we propose a sufficient condition so that the weighting vector preserves the preferences intensity. In order to provide a general unified framework, we deal with pairwise comparison matrices defined over Abelian linearly ordered groups. [ABSTRACT FROM AUTHOR]

The Multi-Granulation Decision-Theoretic Rough Set (MG-DTRS) is an effective method for cost-sensitive decision making from multi-view and multi-level. However, the inherent weak point of MG-DTRS model is to compute three regions with a subjectively given pair of probabilistic parameters (i.e., α and β). To overcome this issue, this paper first proposes a generalized MG-DTRS model called Adaptive Multi-Granulation Decision-Theoretic Rough Sets (AMG-DTRS), which can adaptively obtain a pair of probabilistic thresholds by setting a compensation coefficient ζ. Then, three types of mean AMG-DTRS models are investigated, which provide a novel perspective on multi-granulation method for information fusion. Finally, the connections and differences between the proposed AMG-DTRS and the existing MGRS models are analyzed, which show the advantages and generalization of the AMG-DTRS model. In addition, there are numerous existing MGRS models can be derived explicitly by considering various MG-DTRS, MGRS and VP-MGRS based on our model. These results will be conducive to establishing the framework of information fusion for granular computing. [ABSTRACT FROM AUTHOR]

Conflict occurs naturally in all walks of life at any time. When agents face a conflict, they usually have multiple alternatives and hesitate to make a decision. This paper studies conflict analysis in the case of hesitant fuzzy setting, i.e. the attitude of an agent on an issue has multiple choices. We first propose a conflict analysis model based on hesitant fuzzy information systems. Subsequently, we present the concepts of conflict, neutrality and alliance sets on one issue and multiple issues respectively, and introduce a method to compute the three sets via Bayesian decision theory. Moreover, the degree of conflict, neutrality and alliance among agents with respect to an issue are defined respectively. According to the conflict and alliance degrees, the set of issues is divided into three parts: the main reason, secondary reason and irrelevant reason. Finally, two methods of computing coalitions are discussed. One is based on Bayesian decision theory. The other is to find a complete subgraph of the coalition graph. [ABSTRACT FROM AUTHOR]

The notion of q-rung orthopair fuzzy sets (q-ROFSs) enables decision makers to record diverse uncertain information in a larger scope by easing the limitation of membership and non-membership degrees. The paper introduces q-ROFSs into the framework of multi-granularity three-way decisions (MG-3WD) and explores a novel multi-attribute group decision making (MAGDM) approach in q-rung orthopair fuzzy (q-ROF) information systems. After reviewing some fundamental issues on q-ROFSs and MG-3WD, we first propose different types of multigranulation q-ROF probabilistic models and discuss some of their theoretical properties. Afterwards, a q-ROF MAGDM approach is constructed in light of the proposed multigranulation q-ROF probabilistic models and decision making-based 3WD methods. Then, we provide an example of corporate financial quality matching (CFQM) to show the practicability of the established q-ROF MAGDM approach. At last, corresponding sensitivity analysis, validity tests, comparative analysis and experimental analysis are arranged to reveal the applicability of the established approach from the aspect of MG-3WD. [ABSTRACT FROM AUTHOR]

Multi-attribute three-way decision (MA3WD) has been a novel tool to solve multi-attribute decision-making (MADM) problems by considering the transforming relationship between loss functions and decision matrix. However many practical decision-making problems face the information with uncertainty and complexity, which makes it impossible to obtain relative loss functions in MA3WD. By introducing the thinking of ideal solutions (IS), this study extends MA3WD to interval-valued intuitionistic fuzzy environment, giving a more flexible and general model to handle with uncertain MADM problems. In this paper, we firstly propose an interval-valued intuitionistic fuzzy three-way decision (IVIF3WD) model by obtaining relative loss functions derived from evaluation values, and introduce ideal solutions to construct an ideal-solution based three-way decision model with single interval-valued intuitionistic fuzzy attribute. Then in consideration of all the attributes, two multi-attribute IVIF3WD models are proposed in the perspectives of individual ideal solutions and global ideal solutions respectively. Finally, two cases of investment with different fuzzy information are utilized to illustrate the application and superiority of proposed models. [ABSTRACT FROM AUTHOR]

When using several possible linguistic terms with different weights (represented by probability values) to express preferences, the probability distribution of those linguistic terms is usually hard to be obtained. In this paper, we utilize degree values to reflect the weights of possible linguistic terms and first propose a novel concept called degree-based linguistic term set (DLTS) from the perspective of degree. Then we present a new multi-attribute three-way decision method under the environment of DLTSs. Furthermore, considering that if only one person is involved in decision-making process, it may produce unreasonable or unfair evaluation results. We choose multiple decision-makers to participate in the decision-making process, and propose a multi-attribute group three-way decision method by utilizing the idea of TOPSIS method under the environment of DLTSs. Since the weights of multiple decision-makers (DMs) may be different, we give a method to determine the weights by using the idea of information gain based on the three-way decision results of each decision-maker (DM). Finally, we compare our decision method with an existing decision method, and illustrate the effectiveness of our method through a concrete example. [ABSTRACT FROM AUTHOR]

n -Dimensional fuzzy sets are a fuzzy set extension where the membership values are n -tuples of real numbers in the unit interval [ 0 , 1 ] increasingly ordered, called n -dimensional intervals. The set of n -dimensional intervals is denoted by L n ([ 0 , 1 ]). This paper aims to investigate semi-vector spaces over a weak semifield and aggregation functions concerning an admissible order on the set of n -dimensional intervals and the construction of aggregation functions on L n ([ 0 , 1 ]) based on the operations of the semi-vector spaces. In particular, extensions of the family of OWA and weighted average aggregation functions are investigated. Finally, we develop a multi-criteria group decision-making method based on n -dimensional aggregation functions with respect to an admissible order and give an illustrative example. [ABSTRACT FROM AUTHOR]

Choquet Expected Utility framework for decision making under uncertainty is compared with the Expected Utility framework in a scenario involving rare events with potentially catastrophic consequences. The scenario involves detection of suspected criminal activity in a surveillance system. The results of simulation studies show the advantages of using the Choquet framework to model pessimistic attitude of decision maker. The Choquet approach detects threats earlier and with higher probability of detection when compared to Expected Utility approach. The paper outlines the relevant decision theory, provides details of simulation design, and experimental results. [ABSTRACT FROM AUTHOR]

Successful decision-making analysis needs to take both advantages of human analysts and computers, and human knowledge is usually expressed in a qualitative way. Computer based approaches are good at handling quantitative data, while it is still challenging on how to well structure qualitative knowledge and incorporate them as part of decision analytics. This paper develops a logical reasoning based decision-making framework for handling qualitative human knowledge. In this framework, an algebraic structure is adopted for modelling qualitative human knowledge in a systematic way, and a logic based approximate reasoning method is then proposed for inferring the final decision based on the structured qualitative knowledge. By taking a non-classical logic as its formal foundation, the proposed logical reasoning based decision making method is able to model and infer with qualitative human knowledge directly without numerical approximation in a strict way. [ABSTRACT FROM AUTHOR]

Credal networks generalize Bayesian networks to allow for imprecision in probability values. This paper reviews the main results on credal networks under strong independence, as there has been significant progress in the literature during the last decade or so. We focus on computational aspects, summarizing the main algorithms and complexity results for inference and decision making. We address the question "What is really known about strong extensions of credal networks?" by looking at theoretical results and by presenting a short summary of real applications. [ABSTRACT FROM AUTHOR]

The n -dimensional fuzzy logic (n -DFL) has been contributed to overcome the insufficiency of traditional fuzzy logic in modeling imperfect and imprecise information, coming from different opinions of many experts by considering the possibility to model not only ordered but also repeated membership degrees. Thus, n -DFL provides a consolidated logical strategy for applied technologies since the ordered evaluations provided by decision makers impact not only by selecting the best solutions for a decision making problem, but also by enabling their comparisons. In such context, this paper studies the n -dimensional fuzzy implications (n -DI) following distinct approaches: (i) analytical studies, presenting the most desirable properties as neutrality, ordering, (contra-)symmetry, exchange and identity principles, discussing their interrelations and exemplifications; (ii) algebraic aspects mainly related to left- and right-continuity of representable n -dimensional fuzzy t-conorms; and (iii) generating n -DI from existing fuzzy implications. As the most relevant contribution, the prospective studies in the class of n -dimensional interval (S,N)-implications include results obtained from t-representable n -dimensional conorms and involutive n -dimensional fuzzy negations. And, these theoretical results are applied to model approximate reasoning of inference schemes, dealing with based-rule in n -dimensional interval fuzzy systems. A synthetic case-study illustrates the solution for a decision-making problem in medical diagnoses. [ABSTRACT FROM AUTHOR]

The paper presents the proposed research methodology, dedicated to the application of greedy heuristics as a way of gathering information about available features. Discovered knowledge, represented in the form of generated decision rules, was employed to support feature selection and reduction process for induction of decision rules with classical rough set approach. Observations were executed over input data sets discretised by several methods. Experimental results show that elimination of less relevant attributes through the proposed methodology led to inferring rule sets with reduced cardinalities, while maintaining rule quality necessary for satisfactory classification. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to describe an axiomatic utility theory for Dempster-Shafer belief function lotteries. The axiomatic framework used is analogous to von Neumann-Morgenstern's utility theory for probabilistic lotteries as described by Luce and Raiffa. Unlike the probabilistic case, our axiomatic framework leads to interval-valued utilities, and therefore, to a partial (incomplete) preference order on the set of all belief function lotteries. If the belief function reference lotteries we use are Bayesian belief functions, then our representation theorem coincides with Jaffray's representation theorem for his linear utility theory for belief functions. We illustrate our representation theorem using some examples discussed in the literature, and we propose a simple model for assessing utilities based on an interval-valued pessimism index representing a decision-maker's attitude to ambiguity and indeterminacy. Finally, we compare our decision theory with those proposed by Jaffray, Smets, Dubois et al., Giang and Shenoy, and Shafer. [ABSTRACT FROM AUTHOR]

Rough set model with double quantification satisfies the requirement of quantitative information in practical applications, it has better fault tolerance than probabilistic rough set model considering only relative quantification and graded rough set model considering only absolute quantification. In this paper, two kinds of consistency levels are introduced from the perspective of double quantification in an ordered information system, namely relative quantitative consistency level and absolute quantitative consistency level. The single-quantitative variable consistency dominance-based rough set models based on these two kinds of quantitative consistency levels and their basic properties with the relevant three-way decision rules are discussed respectively in an ordered information system. Moreover, two kinds of double-quantitative variable consistency dominance-based rough set models and their basic properties with the relevant decision rules based on these two kinds of quantitative consistency levels are introduced. A consistency analysis of decision making in a practical case study is used to illustrate and interpret the double-quantitative variable consistency rough set models and the related decision rules in the ordered information system. The obvious shortcomings of dominance-based rough set approach (DRSA) without quantitative information are compared to explain the advantages of the quantitative variable consistency dominance-based rough sets with the two consistency levels in the practical case study. [ABSTRACT FROM AUTHOR]

Since Aczél studied the distributive law between two operations, the distributive laws among different binary aggregation functions become an interesting and vast research field. This paper is mainly devoted to solving the distributivity equations between 2-uninorms and overlap(grouping) functions, which are two classes of special aggregation functions found to possess wide applications in image processing, decision making, classification and fuzzy detection problems. We obtain the sufficient and necessary conditions of the distributivity equations between five classes of basic 2-uninorms and overlap(grouping) functions. [ABSTRACT FROM AUTHOR]

This paper focuses on sequential qualitative decision problems, where no probability distribution on the states that may follow an action is available. New qualitative criteria that are based on ordinal uninorms and namely R ⁎ and R ⁎ are proposed. Like the Hurwicz criterion, the R ⁎ and R ⁎ uninorms arbitrate between pure pessimism and pure optimism, and generalize the Maximin and Maximax criteria. But contrarily to the Hurwicz criterion they are associative, purely ordinal and compatible with Dynamic Consistency and Consequentialism. These important properties allow the construction of an optimal strategy in polytime, following an algorithm of Dynamic Programming. Making a step further, we then generalize R ⁎ to qualitative decision under possibilistic uncertainty, proposing an alternative to the classical optimistic and pessimistic criteria used for the computation of optimal strategies in possibilistic decision trees. [ABSTRACT FROM AUTHOR]

Three-way concept analysis is a mathematical theory, which combines formal concept analysis and three-way decision. The existing models, i.e., three-way concept lattices and three-way object oriented concept lattices, have been used successfully in many fields. However, these two models are established to cater some specific applications and cannot fulfill some special requirements such as the needs to seek potential collaborators in international import and export transactions. In this paper, a novel type of three-way concept lattices is presented based on dual concept analysis, which enables ones to characterize specific set by pointing out the attributes that are not possessed by at least one object in the complement of this specific set. And then, the connections between three-way dual concept lattices and classical dual concept lattices are explored. Besides, the relationships among four types of three-way concept analysis models, i.e., three-way concept lattices, three-way dual concept lattices, three-way object oriented concept lattices and three-way property oriented concept lattices, are investigated. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel representative of the existing family of ordered weighted aggregation (OWA) operators with constant orness (optimism/pessimism level). In other words, orness value of weight vectors generated using the proposed operator is independent of the total number of arguments. The proposed OWA operator is the operator that is based on the beta function. Two different types of operators have been proposed with respect to the level of optimism ("or-like") and pessimism ("and-like") each. In addition to that the proposed operators discussed here are bi-parametric and real-valued in nature in terms of their parameters. Hence, for a given orness value (optimism or pessimism), it provides an infinite number of weight vectors as the proposed operator's orness depends on the value of one of its parameters. These properties lead to lots of flexibility for the Decision-Maker (DM). Its comparison and advantages over other existing members of the OWA family with constant orness such as S-OWA operators have been elaborated. Also, the maximum Rényi entropy of the OWA (MRE-OWA) operator and the maximum Rényi entropy of the proposed OWA operator are compared and evaluated for a specified orness level. Several other important properties and applications of the family of the proposed operators have also been analyzed in detail. [ABSTRACT FROM AUTHOR]

Three-way concept analysis is an integration of formal concept analysis and three-way decision, which has been found wide applications in knowledge representation, cognitive computing and decision sciences. There have been already a huge number of literature on theory and applications on such topics. Most researches on formal concept analysis focus, independently, on specific scenarios such as Boolean formal contexts and fuzzy formal contexts. In this paper, a unified framework for three-way concept analysis is built in lattice-valued formal contexts. The notions of positive concept and negative concept are given in a lattice-valued formal context based on an overlapping function, one of significant operators for information fusion. Two pairs of object induced adjunctive three-way concept operators and attribute induced adjunctive three-way concept operators are introduced. Their properties have been fully investigated. With those operators, the algebraic structures of adjunctive three-way concepts, their extensions and intensions have been explored. Specifically, the local structure within pairs of sub-concept and sup-concept has been finely characterized. The derived results provide ones a way to construct the complete lattice of a lattice-valued formal context or its sublattice by determining all pairs of sub-concept and sup-concept provided that an object fuzzy set or an attribute fuzzy set is given. A case analysis on a real world dataset from UCI repository is presented to verify the rationality and significance of obtained results. [ABSTRACT FROM AUTHOR]

This paper concerns itself with decision making under uncertainty and the consideration of risk. Type-1 fuzzy logic by its (essentially) crisp nature is limited in modelling decision making as there is no uncertainty in the membership function. We are interested in the role that interval type-2 fuzzy sets might play in enhancing decision making. Previous work by Bellman and Zadeh considered decision making to be based on goals and constraints. They deployed type-1 fuzzy sets. This paper extends this notion to interval type-2 fuzzy sets and presents a new approach to using interval type-2 fuzzy sets in a decision making situation taking into account the risk associated with the decision making. The explicit consideration of risk levels increases the solution space of the decision process and thus enables better decisions. We explain the new approach and provide two examples to show how this new approach works. [ABSTRACT FROM AUTHOR]

In this paper, we show how the impact of norms on the sequential decision making of agents can be formally modeled, computationally determined and quantitatively assessed. For this purpose, we put forward the Normative Markov Decision Process (NMDP) framework – an extension of Markov Decision Processes (MDPs). NMDPs provide an explicit declarative representation of obligation and prohibition as penalties associated to states and conditions on the accessibility of states. Furthermore, NMDPs make an explicit representation of the probability that whoever is responsible for enforcing the norms detects a violation, thus modeling enforcement effectiveness and cost. Then, we approach the problem of reasoning with the NMDP framework by proposing two types of agent: norm-compliant and self-interested . Using these agents, this paper shows how this framework may be employed to study the impact of norms on agent behavior by providing a quantitative measure of the cost of norm abidance and, by the same token, to what extent norms affect reasoning complexity. In particular, we illustrate the use of the NMDP framework through experimental analysis in a simulated environment where the chances of norm violation being detected and penalties are varied. [ABSTRACT FROM AUTHOR]

Approaches to decision-making under uncertainty in the belief function framework are reviewed. Most methods are shown to blend criteria for decision under ignorance with the maximum expected utility principle of Bayesian decision theory. A distinction is made between methods that construct a complete preference relation among acts, and those that allow incomparability of some acts due to lack of information. Methods developed in the imprecise probability framework are applicable in the Dempster-Shafer context and are also reviewed. Shafer's constructive decision theory, which substitutes the notion of goal for that of utility, is described and contrasted with other approaches. The paper ends by pointing out the need to carry out deeper investigation of fundamental issues related to decision-making with belief functions and to assess the descriptive, normative and prescriptive values of the different approaches. [ABSTRACT FROM AUTHOR]

This paper presents a general framework for learning with imprecise probabilities, consisting of a hierarchical approach with two sets of parameters. In the top set we have imprecise information, and conditioned on this set we have precise Bayesian information about the other set of parameters. Given a set of observations, the information about both sets of parameters is updated by conditioning, and a model selection method is applied to compute a reduced top set. This model selection method is based on decisions with imprecise probabilities. It will be shown that many existing approaches can be fitted in this general procedure, and a theoretical justification will be provided. Finally, the method will be applied to the problem of learning credal networks. [ABSTRACT FROM AUTHOR]

Abstract Based on results from cognitive science, this paper examines the two fields of three-way decision and granular computing, as well as their interplay. The ideas from one field shed new light on the other field. The integration of the two gives rise to three-way granular computing, that is, thinking, problem solving, and information processing in threes. We discuss a wide sense of three-way decision and propose a trisecting–acting–outcome (TAO) model. We explain fundamental notions of granular computing based on the philosophy of three-way decision as thinking in threes. We discuss a model of three-way granular computing by making use of two particular types of granular structures represented, respectively, by three granules and three levels. We use examples across different disciplines to demonstrate the values of the two types. Our investigation suggests that, in many situations, the power of granular computing is indeed the power of three-way decision, i.e., thinking in threes. Highlights • Discuss a wide sense of three-way decision as thinking in threes. • Propose a TAO (trisecting–acting–outcome) model of three-way decision. • Explore the interplay of three-way decision and granular computing in the context of cognitive science. • Explain granular computing according to a philosophy of thinking in threes. • Illustrate the value of three-way decision by many examples. [ABSTRACT FROM AUTHOR]

Abstract Possibilistic Markov Decision Processes offer a compact and tractable way to represent and solve problems of sequential decision under qualitative uncertainty. Even though appealing for its ability to handle qualitative problems, this model suffers from the drowning effect that is inherent to possibilistic decision theory. The present 1 paper proposes to escape the drowning effect by extending to stationary possibilistic MDPs the lexicographic preference relations defined by Fargier and Sabbadin [13] for non-sequential decision problems. We propose a value iteration algorithm and a policy iteration algorithm to compute policies that are optimal for these new criteria. The practical feasibility of these algorithms is then experimented on different samples of possibilistic MDPs. [ABSTRACT FROM AUTHOR]

The behaviour of norm-autonomous agents is determined by their goals and the norms that are explicitly represented inside their minds. Thus, they require mechanisms for acquiring and accepting norms, determining when norms are relevant to their case, and making decisions about norm compliance. Up until now the existing proposals on norm-autonomous agents assume that agents interact within a deterministic environment that is certainly perceived. In practise, agents interact by means of sensors and actuators under uncertainty with non-deterministic and dynamic environments. Therefore, the existing proposals are unsuitable or, even, useless to be applied when agents have a physical presence in some real-world environment. In response to this problem we have developed the n-BDI architecture. In this paper, we propose a multi-context graded BDI architecture (called n-BDI) that models norm-autonomous agents able to deal with uncertainty in dynamic environments. The n-BDI architecture has been experimentally evaluated and the results are shown in this paper. [ABSTRACT FROM AUTHOR]

Modelling the preferences of a decision maker about alternatives having multiple criteria usually starts by collecting preference information (comparisons of alternatives, importance of criteria, …), which are then used to fit a preference model issued from some set of hypothesis (weighted average, CP-net, lexicographic orderings, AHP, …). In practice, this process often leads to inconsistencies that may be due to inaccurate information provided by the decision maker, who can be unsure about the provided information, or to a poor choice of hypothesis set, which can be too restrictive or not well adapted to the decision process. In this paper, we propose to use belief functions as a way to quantify and resolve such inconsistencies, notably by allowing the decision maker to express her/his certainty about the provided preferential information. Our framework is generic, in the sense that it does not assume a given set of hypothesis a priori, and is consistent with precise methods, in the sense that in the absence of uncertainty and inconsistencies in the information, precise models are ultimately retrieved. [ABSTRACT FROM AUTHOR]

We introduce three different approaches for decision making under uncertainty if (I) there is only partial (both cardinally and ordinally scaled) information on an agent's preferences and (II) the uncertainty about the states of nature is described by a credal set (or some other imprecise probabilistic model). Particularly, situation (I) is modeled by a pair of binary relations, one specifying the partial rank order of the alternatives and the other modeling partial information on the strength of preference. Our first approach relies on decision criteria constructing complete rankings of the available acts that are based on generalized expectation intervals. Subsequently, we introduce different concepts of global admissibility that construct partial orders between the available acts by comparing them all simultaneously. Finally, we define criteria induced by suitable binary relations on the set of acts and, therefore, can be understood as concepts of local admissibility. For certain criteria, we provide linear programming based algorithms for checking optimality/admissibility of acts. Additionally, the paper includes a discussion of a prototypical situation by means of a toy example. [ABSTRACT FROM AUTHOR]

This paper presents decision analysis networks (DANs) as a new type of probabilistic graphical model. Like influence diagrams (IDs), DANs are much more compact and easier to build than decision trees and can represent conditional independencies. In fact, for every ID there is an equivalent symmetric DAN, but DANs can also represent asymmetric problems involving partial orderings of the decisions (order asymmetry), restrictions between the values of the variables (domain asymmetry), and conditional observability (information asymmetry). Symmetric DANs can be evaluated with the same algorithms as IDs. Every asymmetric DAN can be evaluated by converting it into an equivalent decision tree or, much more efficiently, by decomposing it into a tree of symmetric DANs. Given that DANs can solve symmetric problems as easily and as efficiently as IDs, and are more appropriate for asymmetric problems—which include virtually all real-world problems—DANs might replace IDs as the standard type of probabilistic graphical model for decision support and decision analysis. We also argue that DANs compare favorably with other formalisms proposed for asymmetric decision problems. In practice, DANs can be built and evaluated with OpenMarkov, a Java open-source package for probabilistic graphical models. [ABSTRACT FROM AUTHOR]

This paper investigates the decision-theoretic rough sets involved multiple decision-makers with linguistic evaluation information for the uncertainty and risk under the framework of three-way decisions theory. We first discuss the probabilistic rough fuzzy set model with linguistic information for the value of objects on the universe about the attribute set. Subsequently, we present the decision-theoretic rough fuzzy set with linguistic information for the loss functions. Then, we establish the three-way decisions based on linguistic information-based decision-theoretic rough fuzzy set as well as the corresponded decision rules that satisfy minimum risk are given. Furthermore, we consider a kind of multiple attribute group decision making problem with linguistic information and then present a new decision model using the decision-theoretic rough fuzzy set with linguistic information-based three-way decisions. Finally, the proposed decision model and method is applied to an emergency decision making problem of unconventional emergency events, the steps and the principle of the proposed method are illustrated by a numerical example with the background of emergency decision-making. [ABSTRACT FROM AUTHOR]

Any decision taken by an agent requires some knowledge of its environment. Communication with other agents is a key issue for assessing the overall quality of its own knowledge. This assessment is a challenge itself as the agent may receive information from unknown agents. The aim of this paper is to propose a framework for assessing the reliability of unknown agents based on communication. We assume that information is represented through logical statements and logical inconsistency is the underlying notion of reliability assessment. In our context, assessing consists of ranking the agents and representing reliability through a total preorder. The overall communication set is first evaluated with the help of inconsistency measures. Next, the measures are used for assessing the contribution of each agent to the overall inconsistency of the communication set. After stating the postulates specifying the expected properties of the reliability preorder, we show through a representation theorem how these postulates and the contribution of the agent are interwoven. We also detail how the properties of the inconsistency measures influence the properties of the contribution assessment. Finally we describe how to aggregate different reliability preorders, each of them may be based on different inconsistency measures. [ABSTRACT FROM AUTHOR]

Multigranulation spaces provide a unified framework for representing multigranulation knowledge. In this paper, we aim to construct belief structures and characterize knowledge reduction in terms of evidence theory for the multigranulation spaces where decision attributes are considered. First, we introduce a type-1 belief structure for a multigranulation space, and prove that a pair of lower and upper pessimistic multigranulation approximations correspond to a pair of belief and plausibility functions under this belief structure. Second, we point out that no belief structure can be induced when using the optimistic multigranulation approximations in general. By adding a special sufficient condition, a second type of belief structure is further explored to study those that cannot be induced. Third, we develop several measurements by using the belief and plausibility functions, and characterize knowledge reduction of multigranulation spaces based on these measurements. In the end, a numerical algorithm for reducing redundant granular structures in multigranulation spaces is designed. An example is used to examine the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Three-way decisions are a fundamental methodology with extensive applications, while attribute reducts play an important role in data analyses. The combination of both topics has theoretical significance and applicable prospects, but rarely gains direct research at present. In this paper, three-way decisions are introduced into attribute reducts and thus three-way attribute reducts are systematically investigated. Firstly, classical qualitative reducts are reviewed by the dependency degree. Then, the dependency degree implements approximation analyses to be improved to a controllable measure: the relative dependency degree, which is monotonic to relatively measure the attribute dependency. Given an approximate bar, the relative dependency degree defines the applicable quantitative reducts, which approach, expand, and weaken the classical qualitative reducts. This type of quantitative reducts is actually the positive quantitative reducts for three-way reducts. Thus, three-way quantitative reducts are established by the relative dependency degree and dual thresholds. The positive, boundary, and negative quantitative reducts divide the power set of the condition attribute set and thus gain acceptance, noncommitment, and rejection decisions, respectively; they exhibit the potential derivation from the higher level to the lower level. Furthermore, three-way qualitative reducts are established by degeneration to implement three-way decisions, and three-way quantitative and qualitative reducts exhibit the approximation, expansion, and strength; by virtue of superiority analyses, three-way reducts improve the latent two-way reducts with only acceptance and rejection decisions. Finally, three-way reducts are practically illustrated by observing an example of decision tables. By developing the relative dependency degree with controllability, three-way reducts implement both a quantitative generalization for qualitative reducts and a structural completion for attribute reducts. The relevant study provides a new insight into both three-way decisions and attribute reducts. [ABSTRACT FROM AUTHOR]