Due to the increasing occurrence of very large databases, mining useful information and knowledge from transactions is evolving into an important research area. In the past, many algorithms were proposed for mining association rules, most of which were based on items with binary values. Transactions with quantitative values are, however, commonly seen in real-world applications. In this paper, ...

A new learning method, the fuzzy kernel perceptron (FKP), in which the fuzzy perceptron (FP) and the Mercer kernels are incorporated, is proposed in this paper. The proposed method first maps the input data into a high-dimensional feature space using some implicit mapping functions. Then, the FP is adopted to find a linear separating hyperplane in the high-dimensional feature space. Compared wi...

Let d be a metric on the set FP(X) of fuzzy subsets of a set X. A midpoint of two fuzzy subsets μ, ν ∈ FP(X) is any fuzzy subset ξ ∈ FP(X) such that d(ξ, μ) = d(ξ, ν) = 1 2d(μ, ν). These midpoints can be used to describe “middle ways” or “compromises” between two situations described by the fuzzy subsets μ and ν. In this work we explicitly compute midpoints for weighted Hamming distances and fo...

The main objective of this paper is to model and optimize the parallel and relatively complex FuzzyP+FuzzyI+FuzzyD (FP+FI+FD) controller for simultaneous control of the voltage and frequency of a micro-grid in the islanded mode. The FP+FI+FD controller has three parallel branches, each of which has a specific task. Finally, as its name suggests, the final output of the controller is derived fro...

In this work, we first define relations on the fuzzy parametrized soft sets and study their properties. We also give a decision making method based on these relations. In approximate reasoning, relations on the fuzzy parametrized soft sets have shown to be of a primordial importance. Finally, the method is successfully applied to a problems that contain uncertainties. Keyword 0.1 Soft sets, fuz...

In the present paper, we redefine the concept of FPFS-sets in algebra systems, which is a novel way that is different from the definition of FPFS-sets in hemirings by Liu [10]. Based on the definition, we put forth FPFS-groups, FPFSnormal subgroups and FP -equivalent fuzzy soft normal subgroups of groups. Further, some properties and characterizations are investigated. Finally, aggregate fuzzy ...

Let d be a metric on the set FP(X) of fuzzy subsets of a finite set X. A midpoint of two fuzzy subsets μ, ν ∈ FP(X) is any fuzzy subset ξ ∈ FP(X) such that d(ξ, μ) = d(ξ, ν) = 1 2d(μ, ν). These midpoints can be used to represent “middle ways” or “compromises” between two situations described by the fuzzy subsets μ and ν. Now, the imprecise knowledge of a nucleic acid or protein sequence of leng...

In this paper a fuzzy logic (FL) based load frequency controller (LFC) called discrete FuzzyP+FuzzyI+FuzzyD (FP+FI+FD) is proposed to ensure the stability of a multi-source power system in restructured environment. The whale optimization algorithm (WOA) is used for optimum designing the proposed control strategy to reduce fuzzy system effort and achieve the best performance of LFC task. Further...

The satisfiability problem for the logic FP(Ł) (fuzzy probability logic over Łukasiewicz logic) is shown to be NP-complete; satisfiability in FP(ŁΠ) (the same over the logic joining Łukasiewicz and product logic) is shown to be in PSPACE.

A categorical approach to probability allows to put basic notions of probability into a broader mathematical perspective, to evaluate their roles, and mutual relationships. Classical probability theory and fuzzy probability theory lead to two particular categories and their relationship (in categorical terms) enable us to understand and explicitly formulate the difference between them. Using ou...