Evidence Theory (a.k.a. Dempster-Shafer theory) offers a quite general and powerful setting to reason under uncertainty. However, most of the approaches allowing one to instantiate mass functions, the basic building block of the theory, rely on measured, objective data, and there are very few approaches to instantiate them from subjective, expert opinions. Here we suggest a viable solution, based on the concept of pairwise comparisons, for the elicitation of such subjective information. The approach is based on the well-established body of knowledge on the theory of pairwise comparisons and shows its flexibility as it can incorporate multiple representations for the subjective judgments and multiple experts, just to cite two possible extensions.

We consider the problem of quantification of uncertainty in the framework of evidence theory. A large number of uncertainty measures have been proposed in the last 40 years to perform this task, and contributions, albeit numerous, are scattered in the literature, and it is difficult to have an idea of how many measures exist, let alone to know their formal definitions and their evolution in time. In this article, we provide a self-contained exposition of 65 uncertainty measures—out of which 43 were proposed in the last decade—and then we consider their development from the temporal point of view, as well as the lineage of each one from previous ones. These two analyses help us see that 2016 was anannus mirabilis, since the three measures proposed in that year would later on become extremely influential. Moreover, our analysis offers at least three insights that may hopefully open the floor for future research. First, the recent proliferation of uncertainty measures has not always been accompanied by sufficiently deep analyses on their formal properties. Second, the widely accepted behavioral requirement that the total uncertainty must be the sum of the contributions of non-specificity and conflict appears questionable in light of its necessary conditions. Third, and last, the choice of the most suitable measure cannot be detached from the interpretation that is given to the belief function.

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.

The traditional approach to deal with backorders and lost sales in reorder-level inventory control policies is either to model stockout cost or to constrain the problem through a service level definition. This paper aims at presenting a (r, Q) policy that combines these approaches by underlining the importance of both components in a lost-sale setting with stochastic customer demand. In fact, backlogging may not be representative of real customer behavior in many competitive environments, such as in a retailer or e-commerce context. Considering skewed customer demand, a generalization on average inventory is given for the formulation of the objective function of total costs for the considered optimization horizon. The impact of the implemented ready-rate service level on total costs and lost sale quantities for the novel approach are investigated for varying lost-sale costs.

We consider a wide range of measures of uncertainty that have been proposed within the Dempster–Shafer evidence theory. All these measures aim to quantify the uncertainty associated with a given basic probability assignment. As a preliminary step, we offer a study of the literature, which shows a recent resurgence of interest in the quantification of uncertainty in the evidence theory. Then, we compare a number of uncertainty measures by means of numerical simulations and analyze their similarities and differences using rank correlation coefficients, hierarchical clustering, and centrality analysis. The results show that uncertainty measures with similar formulations do not necessarily have similar numerical properties, and some original results are obtained. In particular, we demonstrate that numerical studies on uncertainty measures are necessary to obtain more insight and to enhance the interpretability of the values returned by the measures.

This study aims to develop a Multi-Attribute Decision-Making (MADM) method, the Best-Worst Tradeoff method, which draws on the underlying principles of two popular MADM methods (the Best-Worst Method (BWM) and the Tradeoff). The traditional Tradeoff procedure, which is based on the axiomatic foundation of multi-attribute value theory, considers the ranges of the attributes, but decision-makers/analysts find it hard to check the consistency of the paired comparisons when using this method. The traditional BWM, on the other hand, uses two opposite references (best and worst) in a single optimization, which not only frames the elicitation process in a more structured way, but helps decision-makers/analysts check the consistency. However, the BWM does not explicitly considers the attributes ranges in the pairwise comparisons. The method proposed in this study uses the “consider-the-opposite-strategy” and accounts for the range effect simultaneously. Specifically, the decision-maker considers the ranges of the attributes and provide two pairwise comparison vectors, then an optimization model is designed to determine the optimal weights of the attributes based on these two vectors. After that, consistency thresholds are constructed to check the consistency of the judgements. Finally, a case study is used to examine the feasibility of the proposed method.

This paper recalls the definition of consistency for pairwise comparison matrices and briefly presents the concept of inconsistency index in connection to other aspects of the theory of pairwise comparisons. By commenting on a recent contribution by Koczkodaj and Szwarc, it will be shown that the d iscussion on inconsistency indices is far from being over, and the ground is still fertile for debates.

Knowledge mobilization is a transition from the prevailing knowledge management to a new methodology through some innovative methods for knowledge representation, formation, and development and for knowledge retrieval and distribution. The context is industrial processes and finding solutions to complex problems that arise and for which at least partial solutions have been documented. The fact that a problem has been solved before normally makes it easier to solve it again and the existence of documents that describe how it was solved supports the problem-solving process. But documents that describe the problem solving have to be retrieved from a large database of documents and the information that describes the content of a document is not precise. We show that fuzzy ontology will be useful for finding a sufficiently small set of documents that are relevant for the problem solving even if they are imprecisely classified with keywords.

Knowledge mobilisation is a transition from the prevailing knowledge management technology to a new methodology and some innovative methods for knowledge representation, formation and development and for knowledge retrieval and distribution. We show that fuzzy ontology will be useful to represent real world knowledge and that approximate reasoning schemes can give us answers which are sufficiently good for real world situations in which we need sufficiently good knowledge. We demonstrate the knowledge mobilisation approach by showing how amateurs can become wine connoisseurs with support from the technology.

Adjacency relations for social network analysis have usually been tackled in their bidimensional form, in the sense that relations are computed over pairs of objects. Nevertheless, this paper considers the bidimensional case as restrictive and it proposes an approach where the dimension of the analysis is not limited to binary relations. With the aid of fuzzy logic and OWA operators, it is showed that the interpretation of m-ary adjacency relations is the same of binary relations and therefore they can consistently be employed in social network analysis and some novel results be derived. Besides justifying the use of m-ary relations, the paper proposes a way to characterize them and, eventually, it will provide the reader with an example section.