A fuzzy logic system based on Schweizer-Sklar t-norm

In recent years, the basic research of fuzzy logic and fuzzy reasoning is growing ac- tively day by day, such as the basic logic system BL proposed by Hajek[1]; fuzzy logic system MTL proposed by Esteva and Godo[2]; fuzzy reasoning, implication operators …     

The completeness and applications of the formal system ℒ<Superscript>*</Superscript>

Since the formal deductive system ℒ^* was built up in 1997, in has played important roles in the theoretical and applied research of fuzzy logic and fuzzy reasoning. But, up to now, the completeness problem of the system ℒ^* is still an open problem. In this paper, the properties and structure ofR ₀ algebras are further studied, and it is shown that every tautology on theR ₀ interval [0,1] is also a tautology on anyR ₀ algebra. Furthermore, based on the particular structure of ℒ^*-Lindenbaum algebra, the completeness and strong completeness of the system ℒ^* are proved. Some applications of the system ℒ^* in fuzzy reasoning are also discussed, and the obtained results and examples show that the system ℒ^* is suprior to some other important fuzzy logic systems.     

Unified forms of fully implicational restriction methods for fuzzy reasoning

The goal of this paper is to extend the scope of previously proposed “fully implicational restriction methods” for fuzzy reasoning, and provide a unified form of these methods which can employ diverse implications. By means of the residual implications generated by left-continuous t-norms, we obtain the supremum of triple I (the abbreviation of triple implications) restriction solutions for fuzzy modus ponens and the supremum of multiple I restriction solutions for general fuzzy reasoning respectively. Furthermore, we obtain the infimum of triple I restriction solutions and the supremum of triple I^* restriction solutions for fuzzy modus tolens. Finally, the optimal (i.e., the largest or smallest, depending on context) restriction solutions of both basic and general reasoning problems are derived for four specific residual implications.     

A Hierarchical Extension of the <Emphasis Type="Italic">D</Emphasis><Superscript>*</Superscript> Algorithm

In this paper a contribution to the practice of path planning using a new hierarchical extension of the D^* algorithm is introduced. A hierarchical graph is stratified into several abstraction levels and used to model environments for path planning. The hierarchical D^* algorithm uses a down-top strategy and a set of pre-calculated trajectories in order to improve performance. This allows optimality and specially lower computational time. It is experimentally proved how hierarchical search algorithms and on-line path planning algorithms based on topological abstractions can be combined successfully.     

Robustness of fuzzy reasoning via logically equivalence measure

In this paper, we discuss robustness of fuzzy reasoning. After proposing the definition of perturbation of fuzzy sets based on some logic-oriented equivalence measure, we present robustness results for various fuzzy logic connectives, fuzzy implication operators, inference rules and fuzzy reasoning machines, and discuss the relations between the robustness of fuzzy reasoning and that of fuzzy conjunction and implication operators. The robustness results are presented in terms of δ-equalities of fuzzy sets based on some logic-oriented equivalence measure, and the maximum of δ (which ensures the corresponding δ-equality holds) is derived.     

P2-Packing问题参数算法的改进

P₂-Packing问题是一个典型的NP难问题.目前这个问题的最好结果是时间复杂度为O^*(2^5.301k)的参数算法,其核的大小为15k.通过对P₂-packing问题的结构作进一步分析,提出了改进的核心化算法,得到大小为7k的核,并在此基础上提出了一种时间复杂度为O^*(2^4.142k)的参数算法,大幅度改进了目前文献中的最好结果.     

一类具有3种否定的模糊模态命题逻辑

对不同否定知识的认知、区分、表达、推理及计算是模糊知识研究处理的一个基础。具有矛盾否定、对立否定和中介否定的模糊命题逻辑形式系统FLCOM是一种能够完整描述模糊知识中的不同否定及其关系与规律的理论。基于FLCOM和中介模态命题逻辑MK,提出一类具有3种否定的模糊模态命题逻辑MKCOM及其扩充系统MTCOM,MS₄COM和MS₅COM;讨论了MKCOM的语义和语法解释,并证明了MKCOM的可靠性定理和完备性定理。     

Extensions of fuzzy hyperideals in <Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">V</Emphasis></Subscript>-semigroups

The object of the present paper is the investigation and study of (fuzzy) hyperideals in H _v - semigroups. Regular equivalence relations play in H _v - semigroup theory a role analogous to congruences in semigroup theory, so we introduce fuzzy regular equivalence relations on H _v -semigroups and then we study fuzzy Rees regular relations on H _v -semigroups. Using this ideas, we establish a relation between fuzzy hyperideal of an H _v -semigroup H and fuzzy hyperideal of a quotient H _v -semigroup of H. Some characterizations of them are then shown.      

A New view of the approximations in H v -groups

Let H is an H _v -group and the set of all finite products of elements of H. The relation β^* is the smallest equivalence relation on H such that the quotient H/ β^* is a group. The relation β^* is transitive closure of the relation β, where β is defined as follows: x β y if and only if for some . Based on the relation β, we define a neighborhood system for each element of H, and we presents a general framework for the study of approximations in H _v -groups. In construction approach, a pair of lower and upper approximation operators is defined. The connections between H _v -groups and approximation operators are examined.     

K: A heuristic search algorithm for finding the k shortest paths

We present a directed search algorithm, called K^?, for finding the k shortest paths between a designated pair of vertices in a given directed weighted graph. K^? has two advantages compared to current k-shortest-paths algorithms. First, K^? operates on-the-fly, which means that it does not require the graph to be explicitly available and stored in main memory. Portions of the graph will be generated as needed. Second, K^? can be guided using heuristic functions. We prove the correctness of K^? and determine its asymptotic worst-case complexity when using a consistent heuristic to be the same as the state of the art, , with respect to both runtime and space, where n is the number of vertices and m is the number of edges of the graph. We present an experimental evaluation of K^? by applying it to route planning problems as well as counterexample generation for stochastic model checking. The experimental results illustrate that due to the use of heuristic, on-the-fly search K^? can use less time and memory compared to the most efficient k-shortest-paths algorithms known so far.     

基于DPSO-AO*算法系统测试序列优化问题研究

为了使复杂装备信息处理系统在进行故障定位过程中耗时最少、成本最低,建立了系统测试序列优化问题的数学模型。基于DPSO-AO^*算法的改进,得到信息处理系统的最优测试策略决策树,根据信息处理系统的相关矩阵,按故障概率,随机生成故障,采用相应的测试序列进行测试,最后利用累计测试费用进行比较,从而证明了改进的DPSO-AO^*算法正确有效。     

分数阶微分的CIE L*a*b*颜色空间边缘检测

由于分数阶微积分在细节加强处理方面具有良好的性能,其在边缘检测中的应用正在逐渐增多.目前用分数阶微积分进行边缘检测的研究中大多在RGB空间中进行,但由于RGB颜色空间中亮度信息和色度信息不能相互分离,在其中进行边缘提取不能综合得到亮度边缘和色度边缘,所以分数阶微积分在其他亮度信息和色度信息分开的颜色空间中的应用研究具有一定的理论意义和实际价值.为了综合利用图像的颜色信息,在CIE L*a*b*颜色空间中利用分数阶微分进行边缘检测.相比于直接在RGB颜色空间中得到的边缘,本文方法提取到的图像边缘更符合人眼的视觉感知,边缘的连续性以及抗干扰性也更好.通过与其他经典算法的对比分析表明,本文方法存在明显的优势.     

Very and more or less in non-commutative fuzzy logic

In this paper we consider fuzzy subsets of a universe as L-fuzzy subsets instead of [ 0, 1 ]-valued, where L is a complete lattice. We enrich the lattice L by adding some suitable operations to make it into a pseudo-BL algebra. Since BL algebras are main frameworks of fuzzy logic, we propose to consider the non-commutative BL-algebras which are more natural for modeling the fuzzy notions. Based on reasoning with in non-commutative fuzzy logic we model the linguistic modifiers such as very and more or less and give an appropriate membership function for each one by taking into account the context of the given fuzzy notion by means of resemblance L-fuzzy relations.     

Continuous K-Nearest Neighbor Query for Moving Objects with Uncertain Velocity

One of the most important queries in spatio-temporal databases that aim at managing moving objects efficiently is the continuous K-nearest neighbor (CKNN) query. A CKNN query is to retrieve the K-nearest neighbors (KNNs) of a moving user at each time instant within a user-given time interval [t _s , t _e ]. In this paper, we investigate how to process a CKNN query efficiently. Different from the previous related works, our work relieves the past assumption, that an object moves with a fixed velocity, by allowing that the velocity of the object can vary within a known range. Due to the introduction of this uncertainty on the velocity of each object, processing a CKNN query becomes much more complicated. We will discuss the complications incurred by this uncertainty and propose a cost-effective P² KNN algorithm to find the objects that could be the KNNs at each time instant within the given query time interval. Besides, a probability-based model is designed to quantify the possibility of each object being one of the KNNs. Comprehensive experiments demonstrate the efficiency and the effectiveness of the proposed approach.

New result on chromaticity of K4-homeomorphic graphs

A K₄-homeomorphic graph or simply K₄-homeomorph, denoted by K₄(a, b, c, d, e, f), is the graph obtained when the six edges of a complete graph with four vertices (K₄) are subdivided into a, b, c, d, e, f segments, respectively. Each subdivided edge is called a path and its length is the number of resulting segments. The result in this paper completes the study on the chromaticity of K₄-homeomorphs with exactly two paths of length 2.     

Decentralised direct adaptive fuzzy control for a class of large-scale nonaffine nonlinear systems and application to AHS

A novel decentralised direct adaptive fuzzy controller design is presented for a class of large-scale nonaffine uncertain nonlinear systems in this article. By integrating a fuzzy logic system and H _∞ tracking technique, the designed controller is able to adaptively compensate for interconnections and disturbances with unknown bounds, but none of the control and adaptation laws contains a sign function so that control chattering can be shunned. The closed-loop large-scale system is guaranteed to be asymptotically stable and obtain good H _∞ tracking performance. The control approach developed is applied to the following control problem of a string of vehicles within an automated highway system (AHS) and simulation results verify its validity.     

Optimal (N,T)-policy for M/G/1 system with cost structures

In this paper, the optimal (N,T)-policy for M/G/1 system with cost structure is studied. The system operates only intermittently. It is shut down when no customers are present. A fixed set-up cost of K>0 is incurred each time the system is reopened. Also, a holding cost of h>0 per unit time is incurred for each customer present. The (N,T)-policy studied for this system is as follows: the system reactivates as soon as N customers are present or the waiting time of the leading customer reaches a predefined time T (see A.S. Alfa, I. Frigui, Eur. J. Oper. Res. 88 (1996) 599-613; Y.N. Doganata, in: E. Arikan (Ed.), Communication, Control, and Signal Processing, 1990, pp. 1663–1669). Later on, as a comparison, the start of the timer count is relaxed as follows: the system reactivates as soon as N customers are present or the time units after the end of the last busy period reaches a predefined time T. For both cases, the explicit optimal policy (N^*,T^*) for minimizing the long-run average cost per unit time are obtained. As extreme cases, we include the simple optimal policies for N-and T-polices. Several counter-intuitive results are obtained about the optimal T-policies for both types of models.     

Applying fuzzy arithmetic to the system dynamics for the customer–producer–employment model

This paper presents a system dynamics analysis based on the application of fuzzy arithmetic. Traditional crisp system dynamics observe that some variables/parameters may belong to the uncertain factors. It is necessary to extend the system dynamics to treat also the vague variables/parameters. The evaluation of fuzzy system dynamics may provide the decision-maker information regarding the system's behavior uncertainties. In this paper, the customer–producer–employment model is examined with the fuzzy system dynamics in two types of fuzzy arithmetic, α-cut fuzzy arithmetic and T_ω weakest t-norm operator. Symmetrical and nonsymmetrical triangular fuzzy number (TFN), varied amount of fuzzy inputs’ fuzziness, and length of the system time delay are examined with useful results provided. Particularly, it is revealed that (1) both types of fuzzy arithmetic can provide the steady-state analysis of the system's variables as their counterpart, the crisp arithmetic analysis. (2) The α-cut arithmetic realizes the fuzziness of the model interactive variables fuzzier than that of the T_ω fuzzy arithmetic due to the accumulating phenomenon of fuzziness of the α-cut arithmetic. The fuzzier the inputs, the higher the level and/or oscillation of the cyclically steady or stable pattern of the stability of these variables exhibit with the α-cut arithmetic. (3) The T_ω arithmetic gives a smaller fuzziness and defuzzified values due to the concept that it takes only the maximal fuzziness encountered and calculated in the operation. In this case, the T_ω arithmetic provides more stable (or conversely less sensitive) results to the amount of fuzziness and nonsymmetricity (fuzziness) of input.     

高密集度AGV快递包裹分拣系统的路径规划

基于自动引导小车（AGV）的快递包裹自动分拣系统是智能物流的研究热点,路径规划是其关键问题之一.在快递包裹分拣系统中,AGV具有高密集性和车辆数量较大的特点,这种情况极易造成AGV拥堵,使得整个系统的性能降低.针对此问题本文提出可避免拥挤的CAA^*（Congestion-avoidable A^*）算法,该算法以A^*算法为基础,引入动态属性节点,建立动态环境模型,对各个节点可能发生的拥挤情况进行预测,判断是否存在潜在的拥挤节点,在路径规划过程中绕过潜在的拥堵节点,避免发生拥堵现象.实验结果表明,本文所提的CAA^*路径规划方法在具有高密集度和较大规模的AGV场景中,能有效避免拥堵,从而提高场地AGV的密集度和系统的分拣效率.对实际应用场地的仿真表明,本文的算法比传统的A^*算法AGV密集度提高了28.57%,系统分拣效率提高了24.29%.     

A fuzzy vector valued KNN-algorithm for automatic outlier detection

The K nearest neighbors approach is a viable technique in time series analysis when dealing with ill-conditioned and possibly chaotic processes. Such problems are frequently encountered in, e.g., finance and production economics. More often than not, the observed processes are distorted by nonnormal disturbances, incomplete measurements, etc. that undermine the identification, estimation and performance of multivariate techniques. If outliers can be duly recognized, many crisp statistical techniques may perform adequately as such. Geno-mathematical programming provides a connection between statistical time series theory and fuzzy regression models that may be utilized e.g., in the detection of outliers. In this paper we propose a fuzzy distance measure for detecting outliers via geno-mathematical parametrization. Fuzzy KNN is connected as a linkable library to the genetic hybrid algorithm (GHA) of the author, in order to facilitate the determination of the LR-type fuzzy number for automatic outlier detection in time series data. We demonstrate that GHA[Fuzzy KNN] provides a platform for automatically detecting outliers in both simulated and real world data.