Unified full implication algorithms of fuzzy reasoning

This paper discusses the full implication inference of fuzzy reasoning. For all residuated implications induced by left continuous t-norms, unified α-triple I algorithms are constructed to generalize the known results. As the corollaries of the main results of this paper, some special algorithms can be easily derived based on four important residuated implications. These algorithms would be beneficial to applications of fuzzy reasoning. Based on properties of residuated implications, the proofs of the many conclusions are greatly simplified.     

Compositions of invariant fuzzy implications

We examine sup-min compositions in a finite family of fuzzy implications. Since the composition of invariant fuzzy implications is an invariant function, then we get a kind of `multiplication table' for such implications. A multistage proof of such table is presented. As a result we obtain examples of finite semigroups of fuzzy implications.     

Non-standard cut classification of fuzzy sets

Several important non-standard cut sets of lattice-valued fuzzy sets are investigated. These are strong cuts, “not less” and “neither less nor equal” cuts. In each case it is proved that collection of all cuts of any lattice-valued fuzzy set form a complete lattice under inclusion. Decomposition theorem (representation by cuts) is proved for “neither less nor equal” cuts. Necessary and sufficient conditions under which two lattice-valued fuzzy sets with the same domain have equal families of corresponding cut sets are given.     

The pasting constructions of lattice ordered effect algebras

The aim of this paper is to present some ways of constructing a lattice ordered effect algebra from the given family of MV-algebras. The loop lemma of lattice ordered effect algebras is proved. Then the definitions of Greechie diagrams of effect algebras are given. All these results have generalized those of orthomodular lattices. As applications of loop lemma and Greechie diagrams, some lattice ordered effect algebras without states are presented.     

Pseudocomplemented lattice effect algebras and existence of states

We prove that in every pseudocomplemented atomic lattice effect algebra the subset of all pseudocomplements is a Boolean algebra including the set of sharp elements as a subalgebra. As an application, we show families of effect algebras for which the existence of a pseudocomplementation implies the existence of states. These states can be obtained by smearing of states existing on the Boolean algebra of sharp elements.     

Some types of filters in BL algebras

In this paper we introduce some types of filters in a BL algebra A, and we state and prove some theorems which determine the relationship between these notions and other filters of a BL algebra, and by some examples we show that these notions are different. Also we consider some relations between these filters and quotient algebras that are constructed via these filters.     

Lack of associative filters in lattice implication algebras

Jun et al. (Bull Korean Math Soc 35(1):53–61, 1998) introduced the notion of associative filters in lattice implication algebra and studied some of its properties. In this paper, we show that there is no associative filter in lattice implication algebra.     

A fuzzy soft flood alarm model

A wide range of hydrological analyses for flood, water resources, water quality, ecological studies, etc., require reliable quantification of rainfall inputs. This work illustrates a fuzzy analysis that has the capability to simulate the unknown relations between a set of meteorological and hydrological parameters. A fuzzy approach to flood alarm prediction based on the fuzzy soft set theory is applied to five selected sites of Kerala, India to predict potential flood.     

Isomorphism theorems on generalized effect algebras based on atoms

A well-known fact is that every generalized effect algebra can be uniquely extended to an effect algebra in which it becomes a sub-generalized effect algebra and simultaneously a proper order ideal, the set-theoretic complement of which is its dual poset. We show that two non-isomorphic generalized effect algebras (even finite ones) may have isomorphic effect algebraic extensions. For Archimedean atomic lattice effect algebras we prove “Isomorphism theorem based on atoms”. As an application we obtain necessary and sufficient conditions for isomorphism of two prelattice Archimedean atomic generalized effect algebras with common (or isomorphic) effect algebraic extensions.     

?ukasiewicz transform and its application to compression and reconstruction of digital images

We define the ?ukasiewicz transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an MV-algebra. Then we describe the “?ukasiewicz Transform Based” (?TB) algorithm for image processing, demonstrating its applicability.     

On effect algebras of fuzzy sets

We introduce the category IE of effect algebras of fuzzy sets and sequentially continuous effect homomorphisms and describe its fundamental properties. We show that IE and the category ID of D-posets of fuzzy sets are isomorphic, hence the constructions and properties of ID related to applications to probability theory are valid for the corresponding effect algebras. We describe basic properties of categorical coproducts in ID and dually of categorical products in the corresponding category MID of measurable spaces. We end with remarks on fuzzy probability notions. Supported by VEGA Grant 1/2002/05.     

Redefined fuzzy Hv-submodules and many valued implications

This paper considers a relationship between fuzzy sets and algebraic hyperstructures. A generalization of ideas presented by Davvaz [B. Davvaz, Fuzzy H_v-submodules, Fuzzy Sets Syst. 117 (2001) 477-484] and Bhakat and Das [S.K. Bhakat, P. Das, (∈, ∈ ∨ q)-fuzzy subgroup, Fuzzy Sets Syst. 80 (1996) 359-368], is presented. In fact, the main purpose of this paper is to introduce and study a new sort of fuzzy H_v-submodule of an H_v-module called (∈, ∈ ∨ q)-fuzzy H_v-submodules. These fuzzy H_v-submodules are characterized by their level H_v-submodules. The concept of a fuzzy H_v-submodule with thresholds is introduced, and some interesting properties are investigated.     

Continuous approximations of product implication in MV-algebras with product

Recently, MV-algebras with product have been investigated from different points of view. In particular, in [EGM01], a variety resulting from the combination of MV-algebras and product algebras (see [H98]) has been introduced. The elements of this variety are called ŁΠ-algebras. Even though the language of ŁΠ-algebras is strong enough to describe the main properties of product and of ukasiewicz connectives on [0,1], the discontinuity of product implication introduces some problems in the applications, because a small error in the data may cause a relevant error in the output. In this paper we try to overcome this difficulty, substituting the product implication by a continuous approximation of it. We investigate the resulting algebras, called ŁΠ_q -algebras, and we show that these algebras constitute a quasivariety which is generated by the class of all ŁΠ _q -algebras whose lattice reduct is the unit interval [0,1] with the usual order.     

Fuzzy h-ideals of hemirings

A characterization of an h-hemiregular hemiring in terms of a fuzzy h-ideal is provided. Some properties of prime fuzzy h-ideals of h-hemiregular hemirings are investigated. It is proved that a fuzzy subset ζ of a hemiring S is a prime fuzzy left (right) h-ideal of S if and only if ζ is two-valued, ζ(0) = 1, and the set of all x in S such that ζ(x) = 1 is a prime (left) right h-ideal of S. Finally, the similar properties for maximal fuzzy left (right) h-ideals of hemirings are considered.     

λ-Statistical limit points of the sequences of fuzzy numbers

Aytar has introduced the concepts of statistical limit and cluster points of a sequence of fuzzy numbers based on the definitions given in Fridy’s study for sequences of real numbers. In this paper, we define λ-statistical limit and λ-statistical cluster points of sequences of fuzzy numbers and discuss the relations among the sets of ordinary limit points, λ-statistical limit points and λ-statistical cluster points of sequences of fuzzy numbers.     

Some remarks on the lattice of fuzzy intervals

In this paper we study the connections between three related concepts which have appeared in the fuzzy literature: fuzzy intervals, fuzzy numbers and fuzzy interval numbers (FIN’s). We show that these three concepts are very closely related. We propose a new definition which encompasses the three previous ones and proceeds to study the properties ensuing from this definition. Given a reference lattice (X, ?), we define fuzzy intervals to be the fuzzy sets such that their p-cuts are closed intervals of (X, ?). We show that, given a complete lattice (X, ?), the collection of its fuzzy intervals is a complete lattice. Furthermore we show that, if (X, ?) is completely distributive, then the lattice of its fuzzy intervals is distributive. Finally we introduce a new inclusion measure, which can be used to quantify the degree in which a fuzzy interval is contained in another, an approach which is particularly valuable in engineering applications.     

Geometric modeling of spatial constraints: objectives, methods and solid-modeling requirements

Robust Product Lifecycle Management (PLM) technology requires availability of informationally- complete models for all parts of a design-project including spatial constraints. This is the subject of the present investigation, leading to a new model for spatial constraints, the ``virtual solid', which generalizes a similar concept used by Sapidis and Theodosiou to model ``required free-spaces' in plants [14]. The present research focuses on the solid-modeling aspects of the virtual-solid methodology, and derives new solid-modeling problems (related to object definition and to object processing), whose robust treatment is a prerequisite for developing efficient models for complex spatial constraints.     

基于分变量模糊蕴涵关系的无规则模糊逻辑系统的自适应控制应用

常用的基于模糊if-then规则的模糊逻辑系统在进行控制设计应用时常会遇到规则爆炸问题,为此,提出了一种新的无规则模糊逻辑系统。首先利用从属于系统各分变量论域上开覆盖的单位分解,将模糊知识库中的专家模糊语言值信息进行整合,得到相应的分变量模糊蕴涵关系,再由模糊推理及解模糊化得到系统输出;然后,针对一类非线性不确定系统,先利用伸缩器和饱和器构造出扩展的无规则模糊逻辑系统,再设计被控系统的自适应稳定控制器;最后通过仿真算例验证了该方法的有效性。这种方法的优越性在于新的模糊逻辑系统的构造与自适应律的设计是分离的,在线估计的参数数目明显减少,有效地解决了规则爆炸问题。     

基于ATT7022B的实时分段三相电度表

本文以实现在超低负荷和正常负荷两种情况都能精确计量为目标,提出了实时分段计量的电能表设计方案.本设计从负荷信号检测端就采取了按负荷的额度进行分段的措施,通过切换控制,将检测到的不同负荷额度信号,基于ATTT022B计量芯片的处理,进行不同量程的计算,进而进行多功能电表所要求的输出处理.实验结果表明,该设计已实现了全量程的精度均衡和精确计量.     

基于AT89S52的CAN通信接口设计

随着人们对总线各方面要求的不断提高，总线上的系统数量越来越多，随之产生诸如电路复杂性增加、可靠性下降、生产成本增加等问题。为解决上述问题文中提出了一种低成本的CAN总线通信接口的设计方案。在器件选型上采用了ATMEL的典型芯片AT89S52作为主控单片机，分别从硬件电路设计和软件初始化、发送、接收设计分析，给出了部分C语言设计代码，以CAN2．0B协议来执行，既实现了应有的网络控制功能，又降低了系统的开发、生产和服务成本，具有较高的实用性。