Dempster’s rule of combination serves as a cornerstone in evidence theory for integrating uncertain information from multiple sources. Despite its theoretical appeal, practical implementations remain computationally demanding, especially when relying on recursive algorithms or the Fast Möbius Transform. In this paper, we introduce a novel tensor-based framework for efficient evidence combination under Dempster’s rule. By reformulating mass function aggregation as a tensor operation, our approach enables seamless integration with modern machine learning and data processing pipelines that natively support tensor computations. The core mechanism involves applying a projection matrix to the dyadic product of two encoded mass functions, precisely emulating traditional combination behavior. Extensive empirical evaluations demonstrate significant computational advantages, including up to a 1000-fold acceleration in worst-case scenarios compared to classical recursive methods. This work not only provides a computationally efficient and tensor-compatible alternative for real-time information fusion tasks but also lays the foundation for future research at the intersection of evidential reasoning and tensor-based computation. To support reproducibility and facilitate further research, we also provide our implementation of the developed tensor-based methodology as open-source software which is publicly accessible. 1 1 https://pypi.org/project/TensorBeliefFunction/ .

We consider the problem of choosing new focal elements to supplement the given evidence within the framework of the Dempster-Shafer evidence theory. We propose and analyze some selection rules to solve this problem under the assumption that the final goal is to add evidence to make the pignistic transformation of the new body of evidence as representative as possible of the underlying distribution of evidence. Given the current absence of selection rules, we used the random choice of the next focal element as a benchmark, and then we formalized some possible selection rules, some of them based on the maximization or minimization of uncertainty. Then, we used a Monte Carlo simulation to compare the proposed selection rules with the benchmark represented by the random selection. Numerical results show that the selection rule that balances the occurrence of elements of the frame of discernment within the set of focal elements outperforms the others, on average, as well as in a worst-case scenario, and consequently may reasonably serve as a guiding rule for the selection of new focal elements. • The problem of updating evidence as additional data is available is addressed. • A framework based on the Dempster-Shafer theory is proposed. • Within the proposed framework we focus on the Transferable Belief Model. • Several rules for selection of the “best” new focal elements are introduced. • The rule balancing the occurrence of elementary events outperforms the others.

Consumer preference studies in economics rest heavily on the behavioural interpretation of preference especially in the form of Revealed Preference Theory (RPT). Viewing purchasing decisions as a kind of human reasoning, in this paper we are interested in generalising behaviourism to preference-based argumentation where existing frameworks are arguably governed by the opposing mentalistic interpretation of preference. Concretely our contributions are three-fold. First we re-construct and unify two main approaches to RPT in argumentation terms by developing a Revealed Preference Argumentation (RPA) framework. We show that key RPT-based consumer analyses such as different rationality checks of a consumer behaviour and various kinds of such behaviour's extrapolations can be translated to computational tasks in RPA. RPA is in turn subsumed by the second contribution - an Integrated Preference Argumentation (IPA) framework which fully integrates mentalism and behaviourism. In particular we show that RPA is just a special case of IPA with only revealed preference, while existing preference-based argumentation frameworks can be viewed as IPA frameworks with only stated preference. As the third contribution, we develop a complete set of IPA algorithms and establish their correctness and termination for a general class of IPA frameworks. For demonstration we implement the algorithms in Prolog to obtain an IPA reasoning engine and test the engine with various RPT-based consumer behaviour analyses. In sum, it is argued that the current paper provides not only a theory of Integrated Preference Argumentation, but also a related development tool for future applications of argumentation to behavioural economics - a largely unexplored area so far though Dung used the stable marriage problem in microeconomic game theory to partly motivate the argumentation theory.

Seeking an efficient solution for the problem of dynamic user preferences on social networks is challenging because the input data areshort textsand user preferences usuallychangeover time. This work proposes a novel framework that tackles these challenges based on deep neural networks and the Dempster-Shafer theory of evidence. The framework consists of three primary phases: (1) learning the hidden space of user texts; (2) word generation and mass inference; and (3) mass combination and keyword extraction. In the first phase, user texts are grouped into small batches according to timestamps. Each batch is used for separately training two types of neural networks, the Variational Autoencoder (VAE) and the Generative Adversarial Network (GAN). In the second phase, the generators in the trained VAE and GAN work independently as twoexpertsto generate bunches of tokens for modeling user preferences. Each bunch is considered as one piece of evidence, and is transformed into the so-called mass function in Dempster-Shafer theory by maximum a posterior estimation. In the final phase, Dempster’s rule of combination is utilized for fusing the two independent pieces of evidence into an overall mass. This mass is used for extracting top keywords to form the user preferences within a specific time span. The experiments on short text datasets verified that the proposed method outperforms baseline models on many evaluation metrics. Additionally, the output of the proposed framework could be used for visualization, which is useful in many practical applications.

There is a need for a probabilistic linguistic term set model for go/no-go product screening problem for new product development to meet a firm’s expectation. This paper develops a novel 3-tuple linguistic distance-based model to evaluate whether an overall respondents perception meets a firm’s expectation (“go”) for new product development. The respondent’s perception is collected by a Kansei-based survey as an interval-linguistic term. Then, an expected distance between the firm’s expectation and the respondent’s perception is computed by a target-based Manhattan distance measure. The expected distance is compared with a threshold to shows that what product attribute meets the firm’s expectation based on customers’ perceptions. A real case study of Thai-tea soy milk packaging design is provided. The proposed model is compared to the existing model to show its effectiveness and applicability. Experimental results show that the proposed model can effectively point out the inferior product attributes, which leads to redesign the product until all product concepts meet the target attributes before launching the product to the market. Thus, it can significantly reduce the risk of failure of the product in a real market. This paper has significant contributions in that it allows respondents to provide their opinions with uncertainty by providing an interval linguistic assessment, handles a bias of the heterogeneity of respondents by determining the weight of respondents, and overcomes limitations of existing models by applying target-oriented linguistic terms.

Fuzzy cluster analysis plays an essential role in addressing unclear boundaries between clusters in data and aims to group objects into fuzzy clusters based on their similarities. In this paper, we propose a new method for fuzzy clustering of data with categorical attributes. Specifically, we first introduce a method for kernel-based representation of cluster centers in which the underlying distribution of categorical values within a cluster center is estimated as a weighted sum of the uniform distribution and their frequency distribution. We then extend the k-centers clustering method by applying this newly proposed method of cluster center presentation for fuzzy clustering of categorical data. The effectiveness and efficiency of the proposed method are demonstrated by conducting experiments on 16 realworld datasets and comparing the results with those of existing methods. In addition, our research can be regarded as the first attempt to apply a fuzzy silhouette scoring method that includes internal coherence and external separation of fuzzy clusters into clustering of categorical data.

Argumentative agents in AI are inspired by how humans reason by exchange of arguments. Given the same set of arguments possibly attacking one another (Dung's AA framework) these agents are bound to accept the same subset of those arguments (aka extension) unless they reason by different argumentation semantics. However humans may not be so predictable, and in this paper we assume that this is because any real agent's reasoning is inevitably influenced by her own preferences over the arguments. Though such preferences are usually unobservable, their effects on the agent's reasoning cannot be washed out. Hence by reconstructing her reasoning process, we might uncover her hidden preferences, which then allow us to predict what else the agent must accept. Concretely we formalize and develop algorithms for such problems as uncovering the hidden argument preference relation of an agent from her expressed opinion, by which we mean a subset of arguments or attacks she accepted from a given AA framework; and uncovering the collective preferences of a group from a dataset of individual opinions. A major challenge we addressed in this endeavor is to deal with “answer sets” of argument preference relations which are generally exponential or even infinite. So we start by developing a compact representation for such answer sets called preference states. Preference revelation tasks are then structured as derivations of preference states from data, and reasoning prediction tasks are reduced to manipulations of derived preference states without enumerating the underlying (possibly infinite) answer sets. We also apply the presented results to two non-trivial problems: learning preferences over rules in structured argumentation with priorities – an open problem so far; and analyzing public polls in apparently deeper ways than existing social argumentation frameworks allow.

Clustering categorical data remains a challenging problem in the era of big data, due to the difficulty in measuring dis/similarity meaningfully for categorical data and the high computational complexity of existing clustering algorithms that makes it difficult to be applied in practical use for big data mining applications. In this paper, we propose an integrated approach that incorporates the Locality-Sensitive Hashing (LSH) technique into the k-means-like clustering so as to make it capable of predicting the better initial clusters for boosting clustering effectiveness. To this end, we first utilize a data-driven dissimilarity measure for categorical data to construct a family of binary hash functions that are then used to generate the initial clusters. We also propose to use a nearest neighbor search at each iteration for cluster reassignment of data objects to improve the clustering complexity. These solutions are incorporated into the k-representatives algorithm resulting in the so-called LSH-k-representatives algorithm. Extensive experiments conducted on multiple real-world and synthetic datasets have demonstrated the effectiveness of the proposed method. It is shown that the newly developed algorithm yields comparable or better clustering results in comparison to the existing closely related works, yet it is significantly more efficient by a factor of between 2× and 32×.

This paper proposes a novel framework for clustering mixed numerical and categorical data with missing values. It integrates the imputation and clustering steps into a single process, which results in an algorithm named Clustering Mixed Numerical and Categorical Data with Missing Values (k-CMM). The algorithm consists of three phases. The initialization phase splits the input dataset into two parts based on missing values in objects and attributes types. The imputation phase uses the decision-tree-based method to find the set of correlated data objects. The clustering phase uses the mean and kernel-based methods to form cluster centers at numerical and categorical attributes, respectively. The algorithm also uses the squared Euclidean and information-theoretic-based dissimilarity measure to compute the distances between objects and cluster centers. An extensive experimental evaluation was conducted on real-life datasets to compare the clustering quality of k-CMM with state-of-the-art clustering algorithms. The execution time, memory usage, and scalability of k-CMM for various numbers of clusters or data sizes were also evaluated. Experimental results show that k-CMM can efficiently cluster missing mixed datasets as well as outperform other algorithms when the number of missing values increases in the datasets.

In this paper, we aim at developing a new collaborative filtering recommender system using soft ratings, which is capable of dealing with both imperfect information about user preferences and the sparsity problem. On the one hand, Dempster-Shafer theory is employed for handling the imperfect information due to its advantage in providing not only a flexible framework for modeling uncertain, imprecise, and incomplete information, but also powerful operations for fusion of information from multiple sources. On the other hand, in dealing with the sparsity problem, community context information that is extracted from the social network containing all users is used for predicting unprovided ratings. As predicted ratings are not a hundred percent accurate, while the provided ratings are actually evaluated by users, we also develop a new method for calculating user-user similarities, in which provided ratings are considered to be more significant than predicted ones. In the experiments, the developed recommender system is tested on two different data sets; and the experiment results indicate that this system is more effective than CoFiDS, a typical recommender system offering soft ratings.

The success rate of delivering services in tourism business depends on the successful collaboration with suitable supply chain partners. It makes partner evaluation process critically very important, yet there is currently no available unified evaluation framework in the existing research. Limited by the qualitative nature of evaluation criteria and the incompleteness of available information, the selection process has to deal with complexity on measuring subjective variables, and also uncertainty of imprecise judgments. This study aims at developing the partner evaluation model for tourism partner selection problem, by applying the Dempster-Shafer (D-S) theory of evidence and Satisfactory principle as alternative framework. The result shows that the proposed hybrid approach provides a consistent evaluation result. The contribution of our study depicts that the linguistic evaluation model can deal with not only the uncertain information assessments, but also the ambiguity of sources providing information, while maintaining the flexibility for managers in making their decisions using randomly linguistic preferences. A practical case study in Thai tourism industry is used to illuminate the applicability of the proposed technique.

In this paper, we address the problem of combining information in recommender systems (RSs) based on Dempster-Shafer theory (DST). We first discuss the characteristics of this problem, and then analyze six popular combination methods in the context of RSs. Based on the analysis, we propose two new mixed combination methods which can be considered as useful tools for fusing information in the systems. To evaluate the proposed methods, we integrate them into a typical RS based on DST, and then measure recommendation performances on MovieLens data set. The experimental results show that, comparing to the baselines, the new methods outperform with regards to DS-MAE and DS-Recall, and can be comparable in terms of DS-Precision and DS-F1.

This paper proposes a new method for combining information in recommender systems based on Dempster-Shafer theory. Within this method, focal elements whose probabilities are less than or equal to an infinitesimal threshold are considered as noise that may be caused by the process of fusing information, and then eliminated. Comparing with two baselines, known as 2-points focused and 2-probabilities focused combination methods, the new method is more effective because it does not eliminate focal elements whose probabilities are not very small. Moreover, the new method is tested in a wide range of experiments on MovieLens data set, and the experimental results indicate that the proposed method is much better than the baselines in accuracy of recommendations.

In a recent paper, Liu have proposed the so-called F -algorithm which conditionally reduces the computational complexity of the Meyerowitz-Richman-Walker algorithm for the computation of the aggregate-uncertainty measure in the Dempster-Shafer theory of evidence, along with an illustration of its application in a practical scenario of target identification. In this correspondence, we will point out several technical mistakes, which some of them lead to some inexact or incomplete statements in the paper of Liu The corrections of these mistakes will be made, and some further improvement and results will be derived.

Though probability weather forecasts such as seasonal forecasts offer several benefits over categorical forecasts, they have not been used effectively in practical application. Recently, a new type of probability forecast named early warning information on extreme weather has started service in Japan. It has much more information available than previous seasonal forecasts. This paper describes a way of decision making using early warning information on extreme weather, and considers inventory management at a small shop as an example.

The main focus of this paper is for decision analysis from the target-oriented point of view. Firstly, the target achievement computation method is revised, in which the resulting value function can have four shapes: concave, convex, S-shaped, inverse S-shaped. In addition, it is now more and more widely acknowledged that all facets of uncertainty cannot be captured by a single probability distribution. A fuzzy uncertain target-oriented method is also proposed, in which the proportional approach is selected to transform a possibility distribution into its associated probability distribution, and then based on the random target-oriented model, we can obtain the probability of meeting targets. Three types of fuzzy targets, widely used in Bellman-Zadeh paradigm, are selected to illustrate the fuzzy target-oriented model.

This paper introduces a linguistic evaluation approach to new-product go/nogo evaluation at the front end in new-product development, based on the 2-tuple linguistic representation and the so-called preference-preserving 2-tuple transformation. A case study taken from the literature is used to illuminate the proposed technique and for a comparative study.

In this paper, we introduce a new comparison relation on fuzzy numbers based on their alpha-cut representation and comparison probabilities of interval values. Basically, this comparison process combines a widely accepted interpretation of fuzzy sets together with the uncertain characteristics inherent in the representation of fuzzy numbers. The proposed comparison relation is then applied to the issue of ranking fuzzy numbers using fuzzy targets in terms of target-based evaluations. Some numerical examples are used to illuminate the proposed ranking technique as well as to compare with previous methods. More interestingly, according to the interpretation of the new comparison relation on fuzzy numbers, we provide a fuzzy target-based decision model as a solution to the problem of decision making under uncertainty, with which an interesting link between the decision maker's different attitudes about target and different risk attitudes in terms of utility functions can be established. Moreover, an application of the proposed comparison relation to the fuzzy target-based decision model for the problem of fuzzy decision making with uncertainty is provided. Numerical examples are also given for illustration.

Traditionally, decision-making problems that manage preferences from different experts follow a common resolution scheme composed of two phases: an aggregation phase that combines the individual preferences to obtain a collective preference value for each alternative; and an ex ploitation phase that orders the collective preferences according to a given criterion, to select the best alternative/s. In this paper, instead of using an aggregation operator to obtain a collective preference value, a random preference is defined for each alternative in the aggregation phase. To this end, a probability-based interpretation of weights is assumed. Then, the independent assumption imposed on alternatives allows us to work out probabilities of pairwise comparisons of random preferences. In order to obtain a raking order of alternatives for the exploitation phase, we define a choice function based on the ordered weight averaging (OWA) operator with help of the fuzzy majority.

In this paper, we aim at bringing fuzzy targets within the reach of the target-based decision model in decision analysis with uncertainty. After introduced the target-based interpretation of the expected value on which it is implicitly assumed a neutral behavior on attitude about target, we extend the target-based model for decision making under uncertainty using fuzzy targets, making use of Yager's procedure of converting possibility distributions into probability ones via a simple normalization. We also discuss a target-based framework of attitudinal decision making with uncertainty developed recently by Yager (1999).

In multiple-attribute decision making (MADM) problems, one often needs to deal with decision information with uncertainty. During the last decade, Yang and Singh (1994) have proposed and developed an evidential reasoning (ER) approach to deal with such MADM problems. Essentially, this approach is based on an evaluation analysis model and Dempster's rule of combination in the Dempster-Shafer (D-S) theory of evidence. This paper reanalyzes the ER approach explicitly in terms of D-S theory and then proposes a general scheme of attribute aggregation in MADM under uncertainty. In the spirit of such a reanalysis, previous ER algorithms are reviewed and two other aggregation schemes are discussed. Theoretically, it is shown that new aggregation schemes also satisfy the synthesis axioms, which have been recently proposed by Yang and Xu (2002) for which any rational aggregation process should grant. A numerical example traditionally examined in published sources on the ER approach is used to illustrate the discussed techniques.

This paper proposes a multiexpert decision-making (MEDM) method with linguistic assessments, making use of the notion of random preferences and a so-called satisfactory principle. It is well known that decision-making problems that manage preferences from different experts follow a common resolution scheme composed of two phases: an aggregation phase that combines the individual preferences to obtain a collective preference value for each alternative; and an exploitation phase that orders the collective preferences according to a given criterion, to select the best alternative/s. For our method, instead of using an aggregation operator to obtain a collective preference value, a random preference is defined for each alternative in the aggregation phase. Then, based on a satisfactory principle defined in this paper, that says that it is perfectly satisfactory to select an alternative as the best if its performance is as at least "good" as all the others under the same evaluation scheme, we propose a linguistic choice function to establish a rank ordering among the alternatives. Moreover, we also discuss how this linguistic decision rule can be applied to the MEDM problem in multigranular linguistic contexts. Two application examples taken from the literature are used to illuminate the proposed techniques.

In rough-set-based data analysis, the roughness of a set is traditionally used to express the degree of inexactness of the set arose due to incompleteness of available knowledge. Recently, an attempt of integration between the theories of fuzzy sets and rough sets has resulted in providing a roughness measure for fuzzy sets (Banerjee and Pal, 1996). Essentially, Banerjee and Pal's roughness measure depends on parameters that are designed as thresholds of definiteness and possibility in membership of the objects to a fuzzy set. We introduce a parameter-free roughness measure for fuzzy sets based on the notion of the mass assignment of a fuzzy set. Several interesting properties of this new measure are proved. Furthermore, we also discuss some possible extensions of the so-called approximation quality, which may be used to describe the rough approximation quality of a fuzzy classification.

In this paper we first introduce a context-based interpretation of fuzzy concepts within which the modal-logic based formulation of fuzzy sets is related. Within the framework, we also establish an interpretation of the mass assignment of a fuzzy set. As a consequent, an alternative interpretation of linguistic variables is presented that is clearly related to voting model semantics of linguistic variables as developed by Lawry (2000, 2001). The relationship between the two interpretations is also established.

In this paper, firstly, processes of classical inference are reviewed as granular reasoning from a point of view of reconstructing Kripke-style models with granularity. The essential point of the reconstruction is that some possible worlds are amalgamated to generate granules of worlds and vice versa. It is also called zoom reasoning systems. Then, the idea is applied for fuzzy reasoning processes by considering fuzzily granularized possible worlds. There linguistic truth values with linguistic hedges can be naturally introduced.

People use natural languages to think, to reason, to deduce conclusions, and to make decisions. Fuzzy set theory introduced by L. A. Zadeh has been intensively developed and founded a computational foundation for modeling human reasoning processs. The contribution of this theory both in the theoretical and the applied aspects is well recognized. However, the traditional fuzzy set theory cannot handle linguistic terms directly. In our approach, we have constructed algebraic structures to model linguistic domains, and developed a method of linguistic reasoning, which directly manipulates linguistic terms, In particular, our approach can be applied to fuzzy control problems. In many applications of expert systems or fuzzy control, there exist numerous fuzzy reasoning methods. Intuitively, the effectiveness of each method depends on how well this method satisfies the following criterion: the similarity degree between the conclusion (the output) of the method and the consequence of an if-then sentence (in the given fuzzy model) should be the "same" as that between the input of the method and the antecedent of this if-then sentence. To formalize this idea, we introduce a "measure function" to measure the similarity between linguistic terms in a domain of any linguistic variable and to build approximate reasoning methods. The resulting comparison between our method and some other methods shows that our method is simple and more effective.