A closed form type reduction method for piecewise linear interval type-2 fuzzy sets

In this study, a new centroid type reduction method is proposed for piecewise linear interval type-2 fuzzy sets based on geometrical approach. The main idea behind the proposed method relies on the assumption that the part of footprint of uncertainty (FOU) of an interval type-2 fuzzy set (IT2FS) has a constant width where the centroid is searched. This constant width assumption provides a way to calculate the centroid of an IT2FS in closed form by using derivative based optimization without any need of iterations. When the related part of FOU is originally constant width, the proposed method finds the accurate centroid of an IT2FS; otherwise, an enhancement can be performed in the algorithm in order to minimize the error between the accurate and the calculated centroids. Moreover, only analytical formulas are used in the proposed method utilizing geometry. This eliminates the need of using discretization of an IT2FS for the type reduction process which in return naturally improves the accuracy and the computation time. The proposed method is compared with Enhanced Karnik–Mendel Iterative Procedure (EKMIP) in terms of the accuracy and the computation time on seven test fuzzy sets. The results show that the proposed method provides more accurate results with shorter computation time than EKMIP.     

Hierarchical structure and applications of fuzzy logical systems

This paper focuses on hierarchical structures of formulas in fuzzy logical systems. Basic concepts and hierarchical structures of generalized tautologies based on a class of fuzzy logical systems are discussed. The class of fuzzy logical systems contains the monoidal t-norm based system and its several important schematic extensions: the ?ukasiewicz logical system, the Gödel logical system, the product logical system and the nilpotent minimum logical system. Furthermore, hierarchical structures of generalized tautologies are applied to discuss the transformation situation of tautological degrees during the procedure of fuzzy reasoning.     

The simplest protoalgebraic logic

The logic is the sentential logic defined in the language with just implication → by the axiom of reflexivity or identity “” and the rule of Modus Ponens “from φ and to infer ψ”. The theorems of this logic are exactly all formulas of the form . We argue that this is the simplest protoalgebraic logic, and that in it every set of assumptions encodes in itself not only all its consequences but also their proofs. In this paper we study this logic from the point of view of abstract algebraic logic, and in particular we use it as a relatively natural counterexample to settle some open problems in this theory. It appears that this logic has almost no properties: it is neither equivalential nor weakly algebraizable; it does not have an algebraic semantics; it does not satisfy any form of the Deduction Theorem, other than the most general parameterized and local one that all protoalgebraic logics satisfy; it is not filter‐distributive; and so on. It satisfies some forms of the interpolation property but in a rather trivial way. Very few things are known about its algebraic counterpart, save that its intrinsic variety is the class of all algebras of the similarity type.     

A bi‐level neural‐based fuzzy classification approach for credit scoring problems

The credit scoring is a risk evaluation task considered as a critical decision for financial institutions in order to avoid wrong decision that may result in huge amount of losses. Classification models are one of the most widely used groups of data mining approaches that greatly help decision makers and managers to reduce their credit risk of granting credits to customers instead of intuitive experience or portfolio management. Accuracy is one of the most important criteria in order to choose a credit‐scoring model; and hence, the researches directed at improving upon the effectiveness of credit scoring models have never been stopped. In this article, a hybrid binary classification model, namely FMLP, is proposed for credit scoring, based on the basic concepts of fuzzy logic and artificial neural networks (ANNs). In the proposed model, instead of crisp weights and biases, used in traditional multilayer perceptrons (MLPs), fuzzy numbers are used in order to better model of the uncertainties and complexities in financial data sets. Empirical results of three well‐known benchmark credit data sets indicate that hybrid proposed model outperforms its component and also other those classification models such as support vector machines (SVMs), K‐nearest neighbor (KNN), quadratic discriminant analysis (QDA), and linear discriminant analysis (LDA). Therefore, it can be concluded that the proposed model can be an appropriate alternative tool for financial binary classification problems, especially in high uncertainty conditions. © 2013 Wiley Periodicals, Inc. Complexity 18: 46–57, 2013     

Taguchi based fuzzy logic optimization of multiple quality characteristics in laser cutting of Duralumin sheet

Capability of laser cutting mainly depends on optical and thermal properties of work material. Highly reflective and thermally conductive Duralumin sheets are difficult-to-laser-cut. Application of Duralumin sheets in aeronautic and automotive industries due to its high strength to weight ratio demand narrow and complex cuts with high geometrical accuracy. The present paper experimentally investigates the laser cutting of Duralumin sheet with the aim to improve geometrical accuracy by simultaneously minimizing the kerf width and kerf deviations at top and bottom sides. A hybrid approach, obtained by combining robust parameter design methodology and Fuzzy logic theory has been applied to compute the fuzzy multi-response performance index. This performance index is further used for multi-objective optimization. The predicted optimum results have been verified by performing the confirmation tests. The confirmation tests show considerable reduction in kerf deviations at top and bottom sides.     

Deterministic implementations of fermionic quantum SWAP and Fredkin gates for spin qubits based on charge detection

We propose a scheme to implement fermionic quantum SWAP and Fredkin gates for spin qubits with the aid of charge detection. The scheme is deterministic without the need of qubit–qubit interaction, and the proposed setups consist of simple polarizing beam splitters, single-spin rotations, and charge detectors. Compared with linear optics quantum computation, this charge-measurement-based qubit scheme greatly enhances the success probability for im- plementing quantum SWAP and Fredkin gates and greatly simplifies the experimental realization of scalable quantum computers with noninteracting electrons.     

A unified charge-based model for SOI MOSFETs applicable from intrinsic to heavily doped channel

A unified charge-based model for fully depleted silicon-on-insulator (SOI) metal–oxide semiconductor field-effect transistors (MOSFETs) is presented. The proposed model is accurate and applicable from intrinsic to heavily doped channels with various structure parameters. The framework starts from the one-dimensional Poisson–Boltzmann equa- tion, and based on the full depletion approximation, an accurate inversion charge density equation is obtained. With the inversion charge density solution, the unified drain current expression is derived, and a unified terminal charge and intrinsic capacitance model is also derived in the quasi-static case. The validity and accuracy of the presented analytic model is proved by numerical simulations.     

Effect of O-vacancy defects on the Schottky barrier heights in Ni/SiO2 and Ni/HfO2 interfaces

We perform first-principles density functional calculations to study the electronic structure of Ni/HfO₂ and Ni/SiO₂ interfaces and the effect of O-vacancy (V_O) defects on the Schottky barrier height and the effective work function. We generate two interface models in which Ni is placed on O-terminated HfO₂ (1 0 0) and α-quartz (1 0 0) surfaces. As the concentration of V_O defects at the interface increases, the p-type Schottky barrier height tends to increase in the Ni/HfO₂ interface, due to the reduction of interface dipoles, whereas it is less affected in the Ni/SiO₂ interface.     

二类1错误矩阵方程增优置换变换求解及其在城市交通管理中的应用研究

消错学的错误矩阵可表达错误逻辑里所定义的分解、相似、增加、置换、毁灭、单位变换等转化词,针对其中的置换变换,构建了二类1错误矩阵方程增优置换变换错误矩阵方程,并讨论了该类错误矩阵方程的求解.用交通管理问题对错误矩阵进行了举例,并构建相应的错误矩阵方程,利用上述的求解方法,对二类1方程置换变换进行了求解.     

基于模糊决策模型的高速公路环境风险评价

本文构建了非常规突发事件下的高速公路环境风险评价的目标体系,将模糊逻辑与多目标决策、层次分析法相结合,提出一种基于模糊多目标决策模型。它与传统的多目标决策模型相比,将输入参量转化为语言变量后,获得一个集专家知识、系统变量间关系为基础的优势得分排序规则,可对不确定环境下的多目标及其子目标进行决策评价。通过设计一个高速公路路段环境评价的算例,并对其目标及子目标进行敏感性分析,验证这种决策方法在评价高速公路环境风险上的科学性。