International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

As Dempster–Shafer theory spreads in different application fields, and as mass functions are involved in more and more complex systems, the need for algorithms randomly generating mass functions arises. Such algorithms can be used, for instance, to evaluate some statistical properties or to simulate the uncertainty in some systems (e.g., data base content, training sets). As such random generation is often perceived as secondary, most of the proposed algorithms use straightforward procedures whose sample statistical properties can be difficult to characterize. Thus, although such algorithms produce randomly generated mass functions, they do not always produce what could be expected from them (for example, uniform sampling in the set of all possible mass functions). In this paper, we briefly review some well-known algorithms, explaining why their statistical properties are hard to characterize. We then provide relatively simple algorithms and procedures to perform efficient random generation of mass functions whose sampling properties are controlled.

We study necessary and sufficient conditions for the continuous Scott-Suppes representability of a semiorder through a continuous real-valued map and a strictly positive threshold. In the general case of a semiorder defined on topological space, we find several necessary conditions for the continuous representability. These necessary conditions are not sufficient, in general. As a matter of fact, the analogous of the classical Debreu's lemma for the continuous representability of total preorders is no longer valid for semiorders. However, and in a positive direction, we show that if the set is finite those conditions are indeed sufficient. In particular, we characterize the continuous Scott-Suppes representability of semiorders defined on a finite set endowed with a topology.

Many emerging applications need continuous querying over uncertain event streams, mostly for online monitoring. These streaming uncertain events may come from radars, sensors, or even software hooks. The uncertainty is usually due to measurement errors, inherent ambiguities and privacy preserving reasons. To cover new requirements, we have designed and implemented a new system called Probabilistic Data Stream Management System (PDSMS) in Ref. 1. PDSMS is a data processing engine which runs continuous queries over probabilistic streams. However, lack of a semantics for probabilistic databases which supports continuous distributions prevented us from having a strong foundation for our query operators. It also precludes us from proving consistency and correctness of query operations especially after optimization and adaption. In fact, in the probabilistic database literature, there is no semantics available which covers continuous distributions. This limitation is very restrictive as in real-world, uncertainty is usually modeled by continuous distributions. In this paper, after presenting a basic probabilistic data model for PDSMS, we focus on querying and formally present the first semantics for probabilistic query operations which supports continuous distributions as well as discrete ones. Using this new semantics, we define our query operators (e.g. select, project, and join) formally without ambiguity and compatible with operators in relational algebra. Thus, we can leverage many transformation rules in relational algebra as well. This new semantics allows us to have different strictness levels and consistency between operators. We also proved many strictness theorems about different alternatives for query operators.

In this paper, we develop some new aggregation operators with pure linguistic information including the uncertain pure linguistic weighted geometric mean (UPLWGM) operator, the induced uncertain pure linguistic ordered weighted geometric mean (IUPLOWGM) operator, and the induced uncertain pure linguistic hybrid geometric mean (IUPLHGM) operator. These developed aggregation operators are very suitable to deal with the situation where the input arguments are represented in uncertain pure linguistic variables. Also, as a more general type of aggregation operator, the IUPLHGM operator is based on the UPLWGM and IUPLOWGM operators, and it can reflect the importance degrees of both the given uncertain linguistic variables and their ordered positions. Moreover, in the situations where the information about all the attribute weights, the attribute values and the expert weights are expressed in the form of linguistic labels variables, we develop an approach based on the IUPLHGM operator for multiple attribute group decision making with pure linguistic information. Finally, an application of the developed approach to group decision making problem regarding the selection of investments is given. Also, we present a comparative analysis with other related decision making methods to demonstrate the effectiveness of the developed approach.

Entropy is a measure of the uncertainty associated with a variable whose value cannot be exactly predicated. In uncertainty theory, it has been quantified so far by logarithmic entropy. However, logarithmic entropy sometimes fails to measure the uncertainty. This paper will propose another type of entropy named sine entropy as a supplement, and explore its properties. After that, the maximum entropy principle will be introduced, and the arc-cosine distributed variables will be proved to have the maximum sine entropy with given expected value and variance.

In 1993, Yang first extended the classification maximum likelihood (CML) to a so-called fuzzy CML, by combining fuzzy c-partitions with the CML function. Fuzzy c-partitions are generally an extension of hard c-partitions. It was claimed that this was more robust. However, the fuzzy CML still lacks some robustness as a clustering algorithm, such as its in-ability to detect different volumes of clusters, its heavy dependence on parameter initializations and the necessity to provide an a priori cluster number. In this paper, we construct a robust fuzzy CML clustering framework that has a robust clustering method. The eigenvalue decomposition of a covariance matrix is firstly considered using the fuzzy CML model. The Bayesian information criterion (BIC) is then used for model selection, in order to choose the best model with the optimal number of clusters. Therefore, the proposed robust fuzzy CML clustering framework exhibits clustering characteristics that are robust in terms of the parameter initialization, robust in terms of the cluster number and also in terms of its capability to detect different volumes of clusters. Numerical examples and real data applications with comparisons are provided, which demonstrate the effectiveness and superiority of the proposed method.

Fuzzy number approximation has been investigated by many researchers. It is still useful to develop new approximations in order to better fit real world problems. This paper proposes a method for symmetric trapezoidal fuzzy number approximation which preserves the expected interval. Some properties of approximation are proved and a fuzzy partition is generated by using the proposed method.