International Journal of Approximate Reasoning最新文献

In this article, we investigate approximations of the inductive inference operator system W that has been shown to exhibit desirable inference properties and to extend both system Z, and thus rational closure, and c-inference. For versions of these inference operators that are extended to also cover inference from belief bases that are only weakly consistent, we first show that extended system Z and extended c-inference are captured by extended system W. Then we introduce general functions for generating inductive inference operators: the combination of two inductive inference operators by union, and the completion of an inductive inference operator by an arbitrary set of axioms. We construct the least inductive inference operator extending system Z and c-inference that is closed under system P and show that it is still strictly extended by extended system W. Furthermore, we introduce an inductive inference operator that strictly extends extended system W and that is strictly extended by lexicographic inference. This leads to a comprehensive map of inference relations between rational closure and extended c-inference on the one side and lexicographic inference on the other side with extended system W and its approximations at its centre, where all relationships also hold for the unextended versions.

Three-way decision spaces, as an important component of three-way decisions, greatly enrich their theoretical development and application prospects. Meanwhile, fuzzy implications, as a vital class of fuzzy logic connectives, have made great contributions to the solution of practical problems, especially complex decision-making problems. This paper considers the collaborative effect of the two, which inject new vitality into the theoretical development and application prospects of fuzzy implications and three-way decision spaces. As a vital component of three-way decision spaces, (semi-)decision evaluation functions have been widely studied based on fuzzy logic connectives and become a research hotspot. Specifically, this paper focuses on fuzzy implications-based transformation approaches from semi-three-way decision spaces to three-way decision spaces and their applications. Firstly, we present some novel fuzzy implications-based transformation approaches from semi-decision evaluation functions to decision evaluation functions, and construction approaches of semi-decision evaluation functions involving the existing semi-decision evaluation functions, fuzzy sets, interval-valued fuzzy sets and fuzzy relations. Secondly, we discuss the relationship between our approaches and the known construction approaches of three-way decision spaces. Notably, our approaches cover all existing approaches except the uninorms-based approaches. Finally, by the experiment results, we obtain our approaches are feasible, effective, superior to the known three-way decision spaces approaches and have good anti-noise ability. And, the parameter ρ of our approaches is also effective and stable.

In this paper, we introduce permutations dependent operators. The motivation for studying such a concept arises from standard fuzzy integrals, where permutations play a crucial role. In contrast to standard fuzzy integrals, our construction allows any permutation of the basic set in a formula to be considered, rather than limiting it to permutations that reorder the components of the input vector monotonically. We herein present an approach to integration with respect to sets of permutation pairs, i.e., databases in which each vector has a preselected permutation. This new operator generalizes several concepts known in the literature. We investigate the properties of this new concept and highlight its practical utility in image processing.

The theory of formal concept analysis (FCA) is an important mathematical method for knowledge representation and knowledge discovery. The Boolean formal context is proposed by introducing Boolean matrices and logical operations into FCA. Based on the concept lattice of the Boolean formal context and the column vector(row-vector)-oriented concept lattice of the Boolean formal context, this paper proposes the column vector(row vector)-induced three-way concept lattice of the Boolean formal context and the column vector(row vector)-induced three-way column vector(row vector)-oriented concept lattice of the Boolean formal context, and proves their rationality. Then, the isomorphism between the three-way concept lattice of the Boolean formal context and the three-way concept lattice of the general formal context is proved.

A qualitative conditional “If A then usually B” establishes a plausible connection between the antecedent A and the consequent B. As a semantics for conditional knowledge bases containing such conditionals, ranking functions order possible worlds by mapping them to a degree of plausibility. c-Representations are special ranking functions that are obtained by assigning individual integer impacts to the conditionals in a knowledge base $R$ and by defining the rank of each possible world as the sum of these impacts of falsified conditionals. c-Inference is the nonmonotonic inference relation taking all c-representations of a given knowledge base $R$ into account. In this paper, we show how c-inference can be realized as a satisfiability modulo theories problem (SMT), which allows an implementation by an appropriate SMT solver. Moreover, we show that this leads to the first implementation fully realizing c-inference because it does not require a predefined upper limit for the impacts assigned to the conditionals. We develop a transformation of the constraint satisfaction problem characterizing c-inference into a solvable-equivalent SMT problem, prove its correctness, and illustrate it by a running example. Furthermore, we provide a corresponding implementation using the SMT solver Z3. We develop and implement a randomized generation scheme for knowledge bases and queries, and evaluate our SMT-based implementation of c-inference with respect to such randomly generated knowledge bases. Our evaluation demonstrates the feasibility of our approach as well as the superiority in comparison to former implementations of c-inference.

This paper delves into logical syllogisms featuring intermediate quantifiers. In our previous works, we established the validity of logical syllogisms involving fundamental intermediate quantifiers “Almost all”, “Most”, and “Many”. In this paper, we focus on syllogisms incorporating also the quantifiers “Several” and “A few (A little)”.

Incomplete Argumentation Frameworks (IAFs) enrich classical abstract argumentation with arguments and attacks whose actual existence is questionable. The usual reasoning approaches rely on the notion of completion, i.e. standard AFs representing “possible worlds” compatible with the uncertain information encoded in the IAF. Recently, extension-based semantics for IAFs that do not rely on the notion of completion have been defined, using instead new versions of conflict-freeness and defense that take into account the (certain or uncertain) nature of arguments and attacks. In this paper, we give new insights on both the “completion-based” and the “direct” reasoning approaches. First, we adapt the well-known grounded semantics to this framework in two different versions that do not rely on completions. After determining that our new semantics are polynomially computable, we provide a principle-based analysis of these semantics, as well as the “direct” semantics previously defined in the literature, namely the complete, preferred and stable semantics. Finally, we also provide new results regarding the satisfaction of principles by the classical “completion-based” semantics.

Support function machines (SFMs) have been proposed to handle set-valued data, but they are sensitive to outliers and unstable for re-sampling due to the use of the hinge loss function. To address these problems, we propose a robust SFM model with proximity functions. We first define a family of proximity functions that are used to convert set-valued data into continuous functions in a Banach space, and then we use the margin maximization in a Banach space to construct the pinball SFMs (PinSFMs). We study some properties of the proposed model, and it is interesting to observe that the optimal measure of the proposed model has a specific representation under the total variation norm. Using the representation of the optimal measure, we convert an infinite-dimensional optimization problem into a finite-dimensional optimization problem. Unlike SFMs, we employ a sampling strategy to tackle the finite-dimensional optimization problem. We theoretically show that the sparse solution determines the sparsity of the sampling points though the sampling strategy causes uncertainty for the sampling points. In addition, we achieve kernel versions of proximity functions, and the attractive property of this kernelization is that the proposed model is convex even if indefinite kernels are employed. Experiments on a series of data sets are performed to demonstrate that the proposed model is superior to some existing models in the presence of outliers.