本刊英文版Vol．22(2006),No．4论文摘要

<正>Interval Valued Intuitionistic (S, T)-fuzzy Hv-submodules Jian Ming ZHAN W. A. DUDEK Abstract On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy Hv-submodules of an     

MTL-代数的区间值$(\in,\in \vee q)$-模糊滤子

The concepts of interval valued （∈,∈ ∨q）-fuzzy Boolean, MV - and G- filters in a MTL-algebra are introduced. The properties of these generalized fuzzy filters are studied and in particular, the relationships between these fuzzy filters in an MTL-algebra are investigated.     

GENERALIZED FUZZY FILTERS OF BL-ALGEBRAS

The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered.In fact,this is a generalization of quasi-coincidence of a fuzzy point With a fuzzy set.By using this new idea,the notion of interval valued(∈,∈∨q)-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras,is defined,and related properties are investigated.In particular,the concept of a fuzzy subgroup with thresholds is extended to the concept of an interval valued fuzzy filter with thresholds in BL-algebras.     

半群的模糊内理想

Abstract The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is a generalization of the quasi-coincidence of a fuzzy point in a fuzzy set. With this new concept, the interval valued （∈, ∈ Vq）-fuzzy interior ideal in semigroups is introduced. In fact, this kind of new fuzzy interior ideals is a generalization of fuzzy interior ideals in semigroups. In this paper, this kind of fuzzy interior ideals and related properties will be investigated. Moreover, the concept of a fuzzy subgroup with threshold is extended to the concept of an interval valued fuzzy interior ideal with threshold in semigroups.     

Interval Valued (∈,∈ ∨q)-Fuzzy Filters of MTL-Algebras

The concepts of interval valued (∈,∈ ∨q)-fuzzy Boolean, MV - and G- filters in a MTL-algebra are introduced. The properties of these generalized fuzzy filters are studied and in particular, the relationships between these fuzzy filters in an MTL-algebra are investigated.     

A New View on Fuzzy Hypermodules

We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy     

Generalized fuzzy ideals of near-rings

The concept of（∈,∈∨q）-fuzzy subnear-rings（ideals） of a near-ring is introduced and some of its related properties are investigated.In particular,the relationships among ordinary fuzzy subnear-rings（ideals）,（∈,∈∨ q）-fuzzy subnear-rings（ideals） and（∈,∈∨q）-fuzzy subnear-rings（ideals） of near-rings are described.Finally,some characterization of [μ]t is given by means of（∈,∈∨ q）-fuzzy ideals.     

Fuzzy dot ideals and fuzzy dot H-ideals of BCH-algebras

The notions of fuzzy dot ideals and fuzzy dot H-ideals in BCH-algebras are introduced, several appropriate examples are provided, and their some properties are investigated. The relations among fuzzy ideal, fuzzy H-ideal, fuzzy dot ideal and fuzzy dot H-ideals in BCH- algebras are discussed, several equivalent depictions of fuzzy dot ideal are obtained. How to deal with the homomorphic image and inverse image of fuzzy dot ideals （fuzzy dot H-ideals） are studied. The relations between a fuzzy dot ideal （fuzzy dot H-ideal） in BCH-algebras and a fuzzy dot ideal （fuzzy dot H-ideal） in the product algebra of BCH-algebras are given.     

(α,β)-fuzzy Subalgebras of Q-algebras

In this note by two relations belonging to (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets,the notion of (α,β)-fuzzy Q-algebras,the level Q-subalgebra is introduced where α,β are any two of {∈,q,∈∨q,∈∧q} with α≠∈∧q.Then we state and prove some theorems which determine the relationship between these notions and Q-subalgebras.The images and inverse images of (α,β)-fuzzy Q-subalgebras are defined,and how the homomorphic images and inverse images of (α,β)-fuzzy Q-subalgebra becomes (α,β)-fuzzy Q-algebras are studied.     

Proportionally modular diophantine inequalities and their multiplicity

Let I be an interval of positive rational numbers. Then the set S （I） = T ∩ N, where T is the submonoid of （Q0＋, ＋） generated by T, is a numerical semigroup. These numerical semigroups are called proportionally modular and can be characterized as the set of integer solutions of a Diophantine inequality of the form ax rood b 〈 cx. In this paper we are interested in the study of the maximal intervals I subject to the condition that S （I） has a given multiplicity. We also characterize the numerical semigroups associated with these maximal intervals.     

格蕴涵代数的区间值$(\in, \in\vee\,q)$-模糊$LI$-理想格

In the present paper, the interval-valued (∈,∈∨q)-fuzzy LI-ideal theory in lattice implication algebras is further studied. Some new properties of interval-valued (∈,∈∨q)-fuzzy LI-ideals are given. Representation theorem of interval-valued (∈,∈∨q)-fuzzy LI-ideal which is generated by an interval-valued fuzzy set is established. It is proved that the set consisting of all interval-valued (∈,∈∨q)-fuzzy LI-ideals in a lattice implication algebra, under the partial order ?, forms a complete distributive lattice.     

On Weighted Possibilistic Mean,Variance and Correlation of Interval-valued Fuzzy Numbers

In this paper, the concept of weighted possibilistic mean of interval- valued fuzzy number is first introduced. Further, the notions of weighted possibilistic variance, covariance and correlation of interval-valued fuzzy numbers are presented. Meantime, some important properties of them and relationships between them are studied.     

Redefined generalized fuzzy ideals of near-rings

With a new idea, we redefine generalized fuzzy subnear-rings(ideals) of a near- ring and investigate some of its related properties. Some new characterizations are given. In particular, we introduce the concepts of strong prime(or semiprime) (∈,∈∨q)-fuzzy ideals of near-rings, and discuss the relationship between strong prime(or semiprime) (∈,∈∨q)-fuzzy ideals and prime(or semiprime) (∈,∈∨q)-fuzzy ideals of near-rings.     

Lattice of Interval-Valued (∈,∈∨q)-Fuzzy LI-Ideals in Lattice Implication Algebras

In the present paper, the interval-valued (∈,∈∨q)-fuzzy LI-ideal theory in lattice implication algebras is further studied. Some new properties of interval-valued (∈,∈∨q)-fuzzy LI-ideals are given. Representation theorem of interval-valued (∈,∈∨q)-fuzzy LI-ideal which is generated by an interval-valued fuzzy set is established. It is proved that the set consisting of all interval-valued (∈,∈∨q)-fuzzy LI-ideals in a lattice implication algebra, under the partial order ?, forms a complete distributive lattice.     

Second Order Nonlinear Evolution Inclusions Ⅰ： Existence and Relaxation Results

This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x（t）. In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 （T, H）. Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 （T, H） to the solutions of the original convex problem （strong relaxation）. An example of a nonlinear hyperbolic optimal control problem is also discussed.     

Geodesic discs in Teichmiiller space

Let T(S) be the Teichmuller space of a Riemann surface S. By definition, a geodesic disc in T(S) is the image of an isometric embedding of the Poincare disc into T(S). It is shown in this paper that for any non-Strebel point τ∈T(S), there are infinitely many aeodesic discs containina [0] and τ.     

α-FUZZY PAIRWISE RETRACT OF L-VALUED PAIRWISE STRATIFICATION SPACES

The notion of a fuzzy retract was introduced by Rodabaugh (1981). The notion of a fuzzy pairwise retract was introduced in 2001. Some weak forms and some strong forms of α-continuous mappings were introduced in 1988 and 1997. The authors extend some of these forms to the L-fuzzy bitopological setting and construct various α-fuzzy pairwise retracts. The concept of weakly induced spaces in the case L = [0,1] was introduced by Martin (1980). Liu and Luo (1987) generalized this notion to the case that L is an arbitrary F-lattice and introduced the notion of induced L-fts. Several results are obtained, especially, for L-valued pairwise stratification spaces.     

Single-Valued Neutrosophic Lie Algebras

A single-valued neutrosophic (SVN) set is a powerful general formal framework that generalizes the concept of fuzzy set and intuitionistic fuzzy set. In SVN set, indeterminacy is quantified explicitly, and truth membership, indeterminacy membership, and falsity membership are independent. In this paper, we apply the notion of SVN sets to Lie algebras. We develop the concepts of SVN Lie subalgebras and SVN Lie ideals. We describe some interesting results of SVN Lie ideals.     

On Rough Intuitionistic Fuzzy Ideals（Filters） in Lattices

In this paper, we introduce a new algebraic structure, called a rough intuitionistic fuzzy ideal（filter） which is a generalized intuitionistic fuzzy ideal（filter） of a lattice and study some related properties of such ideals（filters）.     

双极值模糊集在半环上的应用

On the basis of concepts of bipolar fuzzy sets, we establish a new framework of bipolar fuzzy subsemirings（resp., ideals） which is a generalization of traditional fuzzy subsemirings（resp., ideals） in semirings. The concepts of bipolar fuzzy subsemirings（resp., ideals） are introduced and related properties are investigated by means of positive t-cut, negative s-cut and equivalence relation. Particularly, the notion of a normal bipolar fuzzy ideal is given, and some basic properties are studied in this paper.