International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Partial periodic patterns are commonly seen in real-life applications and provide useful prediction with uncertainty. Most previous approaches have set a single minimum support threshold for all events to assume they have similar frequencies which is not practical for real-world applications. Instead of setting a single minimum support threshold for all events, Chen et al. proposed an FP-tree-like algorithm to allow multiple minimum supports for reflecting the natures of the events. However, such a tree-based algorithm encountered an efficiency problem while period length is long or event sequential orders in period segments are varied. Under the circumstance, many tree branches are created and much execution time is spent to find partial periodic patterns. In this paper, we thus propose a projection-based algorithm which examines only prefix subsequences and projects only corresponding postfix subsequences with multiple minimum supports to quickly find the partial periodic patterns in a recursive process. Experiments on both synthetic and real-life datasets show that the proposed algorithm is more efficient than the previous one.

Verifying and specifying multi-agent systems in an appropriate inconsistency-tolerant logic are of growing importance in Computer Science since computer systems are generally used by or composed of inconsistency-tolerant multi-agents. In this paper, an inconsistency-tolerant logic for representing multi-agents is introduced as a Gentzen-type sequent calculus. This logic (or calculus) has multiple negation connectives that correspond to each agent, and these negation connectives have the property of paraconsistency that guarantees inconsistency-tolerance. The logic proposed is regarded as a modified generalization of trilattice logics, which are known to be useful for expressing fine-grained truth-values in computer networks. The completeness, cut-elimination and decidability theorems for the proposed logic (or sequent calculus) are proved as the main results of this paper.

Similarity measures between generalized trapezoidal fuzzy numbers (GTFNs) are employed to indicate the degrees of similarity between GTFNs. Although several similarity measures of GTFNs have been proposed in the literature, none has considered using the Jaccard index. In general, the Jaccard index is a statistic used for comparing the similarity and diversity of sample sets. This paper presents a new similarity measure between GTFNs, which involves the Jaccard index. The proposed similarity measure is found to have better properties. Several examples are employed to compare the proposed measure with some existing methods. An experiment is performed using 15 sets of GTFNs to compare the proposed similarity measure with existing ones. Numerical results show that the proposed measure is more reasonable than those existing methods.

In this study, a problem for advertising policy to avoid the depreciation rate of sale, an imperfect production rate and environmental pollution control is formulated with reliability and rework over a finite time horizon. The advertisement and production rates are function of time which are taken as control variables. Also, recent studies indicate that industrial solid waste (ISW) in production period has been an important contributor to greenhouse gas (GHG) emissions. The company has agreed to invest a large amount of money to manage the ISW through technological up gradation, etc that reduce the GHG in environment. The unit production cost is a function of production rate and also dependent on raw material cost, development cost due to technological up gradation and reliability and wear-tear cost. The total profit which consists of the sales proceeds, marginal selling price, production cost, operating cost, pollution cost, inventory holding cost and advertisement cost is formulated as an optimal control problem. The selling price and all inventory costs are fuzzy rough in nature and using expectation of fuzzy rough technique, the problem is converted into equivalent crisp problem and solved using Pontryagin's Maximum Principle and Generalized Reduced Gradient Method (GRG). Finally numerical experiment, sensitivity analysis for marginal selling price, defective parameter, rework and depreciation rate of sale and graphical representation are provided to illustrate the model.

In this paper, we focus on the characterizations of some properties of fuzzy relations by using the notions of traces. The investigation is two-fold. On one hand, we attempt to reformulate the results obtained by Fodor under weakened conditions. On the other hand, we present some new characterizations of properties, mainly T-asymmetry, T-S-semitransitivity and T-S-Ferrers property, in terms of traces.

Based on the frequent pattern mining, closed frequent pattern mining and weighted frequent pattern mining have been studied to reduce the search space and discover important patterns. In the previous definition of weighted closed patterns, supports of patterns are only considered to compute the closures of the patterns. It means that the closures of weighted frequent patterns cannot be perfectly checked. Moreover, the usefulness of weighted closed frequent patterns depends on the presence of frequent patterns that have supersets with the exactly same weighted support. However, from the errors such as noise, slight changes in items' supports or weights by them have significantly negative effects on the mining results, which may prevent us from obtaining exact and valid analysis results since the errors can break the original characteristics of items and patterns. In this paper, to solve the above problems, we propose a concept of robust weighted closed frequent pattern mining, and an approximate bound is defined on the basis of the concept, which can relax requirements for precise equality among patterns' weighted supports. Thereafter, we propose a weighted approximate closed frequent pattern mining algorithm which not only considers the two approaches but also suggests fault tolerant pattern mining in the noise constraints. To efficiently mine weighted approximate closed frequent patterns, we suggest pruning and subset checking methods which reduce search space. We also report extensive performance study to demonstrate the effectiveness, efficiency, memory usage, scalability, and quality of patterns in our algorithm.

The notion of Best-Matching Unit (BMU) in the proposed Fuzzy Relational Self-Organizing (FRSOM) algorithm is replaced by a membership function where every neuron has a certain degree of matching to an input object. The FRSOM is an extension of the relational self-organizing map. In the proposed FRSOM we incorporate a monotonically increasing fuzzifier and a monotonically decreasing neighborhood kernel. Initially, FRSOM assigns winning neurons. However, as time progresses adjacent neurons begin communicating and sharing information about the stimulus received. The amount of information being shared at a given time is governed by the fuzzifier and the number of neurons sharing information is controlled by the neighborhood kernel. Additionally, in this paper we show that FRSOM is the relational dual of Fuzzy Batch SOM (FBSOM) followed by experimental results comparing both FBSOM and FRSOM on synthetic datasets. Then we will demonstrate the visualization and summarization capabilities of FRSOM on two real relational datasets, Gene Ontology and a patient data consisting of Activity of Daily Living score trajectories.