Relative negations in non-commutative fuzzy structures

In this paper we investigate the properties of the relative negations in non-commutative residuated lattices and their applications. We define the notion of a relative involutive FL-algebra and we generalize to relative negations some results proved for involutive pseudo-BCK algebras. The relative locally finite IFL-algebra is defined and it is proved that an interval algebra of a relative locally finite divisible IFL-algebra is relative involutive. Starting from the observation that in the definition of states, the standard MV-algebra structure of [0, 1] intervenes, there were introduced the states on bounded pseudo-BCK algebras, pseudo-hoops and residuated lattices with values in the same kind of structures and they were studied under the name of generalized states. For the case of commutative residuated lattices the generalized states were studied in the sense of relative negation. We define and study the relative generalized states on non-commutative residuated lattices. One of the main results consists of proving that every order-preserving generalized Bosbach state is a relative generalized Rie?an state. Some conditions are given for a relative generalized Rie?an state to be a generalized Bosbach state. Finally, we develop a concept of states on IFL-algebras.     

Hybrid generalized Bosbach and Rie c̆ an states on non-commutative residuated lattices

Generalized Bosbach and Rie c? an states, which are useful for the development of an algebraic theory of probabilistic models for commutative or non-commutative fuzzy logics, have been investigated in the literature. In this paper, a new way arising from generalizing residuated lattice-based filters from commutative case to non-commutative one is applied to introduce new notions of generalized Bosbach and Rie c? an states, which are called hybrid ones, on non-commutative residuated lattices is provided, and the relationships between hybrid generalized states and those existing ones are studied, examples show that they are different. In particular, two problems from L.C. Ciungu, G. Georgescu, and C. Mure, “Generalized Bosbach States: Part I” (Archive for Mathematical Logic 52 (2013):335–376) are solved, and properties of hybrid generalized states, which are similar to those on commutative residuated lattices, are obtained without the condition “strong”.     

The radical of a perfect residuated structure

In this paper we extend some properties of the radical of an MTL-algebra to the non-commutative case of a more general residuated structure, namely the FL_w-algebra. For the particular case of pseudo-MTL algebras, some specific results are presented. We introduce the notion of a local additive measure on a perfect pseudo-MTL algebra and we prove that, with some additional conditions, every local additive measure can be extended to a Rie?an state; a necessary and sufficient condition is given for such an extension to be a Bosbach state.     

Relationships between generalized Bosbach states and <Emphasis Type="Italic">L</Emphasis>-filters on residuated lattices

Generalized Bosbach states and filters on residuated lattices have been extensively studied in the literature. In this paper, relationships between generalized Bosbach states and residuated-lattice-valued filters, also called L-filters, on residuated lattices are investigated. Particularly, type I and type II L-filters and their subclasses are defined, and some their properties are obtained. Then relationships between special types of L-filters and the generalized Bosbach states are considered where generalized Bosbach states are characterized by some type I or type II L-filters with additional conditions. Associated with these relationships, new subclasses of generalized Bosbach states such as implicative type IV, V, VI states, fantastic type IV states and Boolean type IV states are introduced, and the relationships between various types of generalized Bosbach states are investigated in detail. In particular, the existence of several generalized Bosbach states is provided and, as application, some typical subclasses of residuated lattices such as Rl-monoids, Heyting algebras and Boolean algebras are characterized by these generalized Bosbach states.     

NMG-代数中同态核的结构刻画

逻辑代数上的Bosbach态与Riečan态是经典概率论中Kolmogorov公理的两种不同方式的多值化推广,也是概率计量逻辑中语义计量化方法的代数公理化,是非经典数理逻辑领域中的重要研究分支.现已证明具有Glivenko性质的逻辑代数上的Bosbach态与Riečan态等价,并且逻辑代数的Glivenko性质是研究态算子的构造和存在性的重要工具,因而是态理论中的研究热点之一.研究了NMG-代数基于核算子的Glivenko性质,证明NMG-代数具有核基Glivenko性质的充要条件是该核算子是从此NMG-代数到其像集代数的同态,并给出NMG-代数中同态核的结构刻画.这里,NMG-代数是刻画序和三角模<（[0,1/2,T_NM]）,（[1/2,1,T_M]）>的逻辑系统NMG的语义逻辑代数.     

Representation theorem for probabilities on IFS-events

Rie?an gave in Rie?an (2004) [9] an axiomatic characterization of a probability on IFS-events and proved in Rie?an (2006) [10] a representation theorem for it. In Ren?ová [9], Ren?ová introduced the notions of additive φ-probability and strongly additive φ-probability and gave a representation theorem for strongly additive φ-probabilities.In this paper we give a generalization of the axiomatic characterization given by Rie?an in Rie?an (2006) [10]; from this, the representation theorem for strongly additive φ-probabilities will follow.     

Bosbach states on fuzzy structures

Pseudo-BL algebras are non-commutative fuzzy structures which generalize BL-algebras and pseudo-MV algebras. In this paper we study the states on a pseudo-BL algebra. This concept is obtained by using the Bosbach condition for each of the two implications of a pseudo BL-algebra. We also propose a notion of conditional state for BL-algebras.The author would like to thank Laureiu Leutean for his valuable suggestions in obtaining the final version of the paper.     

States on semi-divisible residuated lattices

Given a residuated lattice L, we prove that the subset MV(L) of complement elements x ^* of L generates an MV-algebra if, and only if L is semi-divisible. Riečan states on a semi-divisible residuated lattice L, and Riečan states on MV(L) are essentially the very same thing. The same holds for Bosbach states as far as L is divisible. There are semi-divisible residuated lattices that do not have Bosbach states. These results were obtained when the authors visited Academy of Science, Czech Republic, Institute of Comp. Sciences in Autumn 2006.     

States on finite linearly ordered IMTL-algebras

The aim of this paper is to study states on finite linearly ordered IMTL-algebras. We prove that Bosbach states, Riečan states and state-morphisms are equivalent on linearly ordered IMTL-algebras. Furthermore, we investigate the existence of states on finite linearly ordered IMTL-algebra and prove that if LL is locally finite, then LL has a state if and only if LL is an MV-algebra, and that if LL is peculiar and H(L)è{0,1}H(L)\cup\{0,1\} is a subalgebra of LL, then LL has a state if and only if ord(n)=|H(L)|+1ord(n)=|H(L)|+1, where H(L)={x ? L|ord(x) < ￥, ord(?x) < ￥}, n=maxH(L)H(L)=\{x\in L|ord(x)<\infty, ord(\neg x)<\infty\}, n=\max H(L).     

延迟离散Hopfield网络的动态特征分析

神经网络的稳定性被认为是神经网络各种应用的基础．主要利用网络的状态转移方程和能量函数来研究带有延迟项的离散Hopfield神经网络动力学行为．给出了延迟离散Hopfield神经网络收敛于周期小于等于2的极限环的一些充分条件．给出了延迟网络收敛于周期为2和4的特殊极限环的一些充分条件．同时，得到了网络不存在任何稳定点的一些必要条件．所获结果不仅推广了一些已有的结论，而且为网络的应用提供了一定的理论基础．     

关于离散系统的有限拍协方差控制器

在随机控制问题中，性能指林常常表示为系统状态协方差的形式．本文将讨论如下问题．即设计线性反馈控制器，使系统的状态协方差在有限拍内达到其稳态值，同时该稳态值达到预先指定值．本文讨论了这类反馈控制器的存在条件及设计方法，并给出了直接的设计步骤．     

Controlled finite automata

This paper discusses finite automata regulated by control languages over their states and transition rules. It proves that under both regulations, regular-controlled finite automata and context-free-controlled finite automata characterize the family of regular languages and the family of context-free languages, respectively. It also establishes conditions under which any state-controlled finite automaton can be turned into an equivalent transition-controlled finite automaton and vice versa. The paper also demonstrates a close relation between these automata and programmed grammars. Indeed, it proves that finite automata controlled by languages generated by propagating programmed grammars with appearance checking are computationally complete. In fact, it demonstrates that this computational completeness holds even in terms of these automata with a reduced number of states.     

Distributed finite-time consensus tracking for nonlinear multi-agent systems with a time-varying reference state

This paper investigates the consensus tracking problem for nonlinear multi-agent systems with a time-varying reference state. The consensus reference is taken as a virtual leader, whose output is only its position information that is available to only a subset of a group of followers. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position of its neighbours. In this paper, the consensus tracking problem is respectively considered under fixed and switching communication topologies. Some corresponding sufficient conditions are obtained to guarantee the states of followers can converge to the state of the virtual leader in finite time. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Simulations are presented to illustrate the theoretical analysis.     

Intervals in generalized effect algebras

A significant property of a generalized effect algebra is that its every interval with inherited partial sum is an effect algebra. We show that in some sense the converse is also true. More precisely, we prove that a set with zero element is a generalized effect algebra if and only if all its intervals are effect algebras. We investigate inheritance of some properties from intervals to generalized effect algebras, e.g., the Riesz decomposition property, compatibility of every pair of elements, dense embedding into a complete effect algebra, to be a sub-(generalized) effect algebra, to be lattice ordered and others. The response to the Open Problem from Rie?anová and Zajac (2013) for generalized effect algebras and their sub-generalized effect algebras is given.     

线性有限自动机的UIO序列及其生成算法

对线性有限自动机的UIO序列进行了讨论,得到了线性有限自动机的任意一状态有某一长度的UIO序列的充要条件,得到了线性有限自动机的(所有)状态有UIO序列的的充要条件,还给出了有UIO序列的线性有限自动机的状态的最短UIO序列长度的上界,最后给出了判断线性有限自动机的所有状态有无UIO序列以及有求其UIO序列的两个算法.     

Asymptotic properties of empirical estimates for parameters of markov sequences

This article considers conditions under which the criterion function of a Markov process with a unique minimum point can be approximated by its empirical estimate. Theorems on the convergence of an empirical function to the original one in some probabilistic sense are established for both finite and compact sets of states of the Markov process.     

Detectability for Nondeterministic Discrete Event Systems and Its Applications in Medical Diagnosis

In this paper, we extend our previous results on detectability to nondeterministic discrete event systems. Many practical systems are nondeterministic, especially those in biomedicine. Disease models of patients are usually nondeterministic because hardly anything is deterministic in biological systems. The goal is to determine or estimate the current and subsequent states of a system based on a sequence of observations when the initial state of the system is unknown. We say that a system is detectable if one can determine its state after observing some outputs. The observation includes partial event observation and/ or partial state observation. We define four types of detectabilities： strong detectability, （weak） detectability, strong periodic detectability, and （weak） periodic detectability. We derive necessary and sufficient conditions for these detectabilities. These conditions can be checked by constructing an observer, which models the estimation of states under different observation. Furthermore, we apply the results to medical diagnosis by considering a realistic example of diagnosing whether a patient suffers from one of the following five similar diseases ： （ 1 ） rheumatoid arthritis, （2） rheumatic arthritis, （ 3 ） systemic lupus eruthematosus, （4） bony ankylosis, or （ 5 ） spondylitis ankylopoietica.     

Design and analysis of discrete-time robust Kalman filters

In this paper, the problem of finite and infinite horizon robust Kalman filtering for uncertain discrete-time systems is studied. The system under consideration is subject to time-varying norm-bounded parameter uncertainty in both the state and output matrices. The problem addressed is the design of linear filters having an error variance with an optimized guaranteed upper bound for any allowed uncertainty. A novel technique is developed for robust filter design. This technique gives necessary and sufficient conditions to the design of robust quadratic filters over finite and infinite horizon in terms of a pair of parameterized Riccati equations. Feasibility and convergence properties of the robust quadratic filters are also analyzed.     

基于状态反馈的一类非线性系统动态输出反馈镇定

针对一类具有线性不可测量状态的非线性系统,基于状态反馈稳定控制器,利用不变流形和滑模变结构控制技术设计了动态输出反馈镇定控制器.这类控制器的结构类似于系统的状态反馈稳定控制器,在较简单的假定条件下,能够保证被控系统的状态得到渐近镇定.仿真算例表明该动态输出反馈控制器具有较强的镇定能力.