Fuzzy hyperlattices

In this paper, we introduce the notion of fuzzy hyperlattices and establish connections between fuzzy hyperlattices and hyperlattices. Then we discuss the relations between the weak homomorphism of fuzzy hyperlattices and the weak homomorphism of corresponding hyperlattices. Moreover, we define and analyze the hypercongruence on hyperlattices and the fuzzy (strong) hypercongruence on fuzzy hyperlattices. And we study the interrelation between the (fuzzy) hypercongruence on (fuzzy) hyperlattices and the homomorphism of (fuzzy) hyperlattices. Also, a relation between the fuzzy hypercongruence on fuzzy hyperlattices and the hypercongruence on corresponding hyperlattices is obtained. Finally, we apply the hypercongruence and the fuzzy strong hypercongruence to construct quotient structures of hyperlattices and fuzzy hyperlattices, respectively.     

Fuzzy hyperrings (Hv-rings) based on fuzzy universal sets

The aim of this paper is to define and study the concept of a fuzzy hyperring, which depends on the concept of a fuzzy universal set. A correspondence relation between a fuzzy hyperring based on a fuzzy universal set and both ordinary and fuzzy hyperideal in the sense of Davvaz is obtained.     

The category FGrp of fuzzy groups is not equivalent to the category Grp of classical groups

In this paper, the concept of strong homomorphism of fuzzy group in the sense of [⁴] is given. The fundamental homomorphism theorem of fuzzy group, in the sense of strong homomorphism, is also obtained. We built a category FGrp of fuzzy groups and strong homomorphism and show that category FGrp and the category Grp of group and homomorphism are not equivalent. These discussions show that fuzzy group is different from classical group.     

Normal fuzzy hyperideals in hypernear-rings

Applying the concept of fuzzy sets to hypernear-rings, Davvaz introduced the notion of a fuzzy hyperideal as early as 1999, and it has been studied by several authors. In this paper, we introduce the notion of fuzzy hyperideals in hypernear-rings and investigate some related properties. Also, we characterize maximal fuzzy hyperideals and show that every maximal fuzzy hyperideal of a hypernear-ring is completely normal.     

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.      

格的模糊同态

研究模糊同态,自然离不开模糊映射,群与环的模糊同态分别利用了不同的模糊映射进行讨论。利用经典集间的模糊映射,引入了格的模糊同态和模糊弱同态概念,给出了模糊同态与模糊弱同态下模糊子格（模糊理想）的对应关系,并由模糊同态得到了格的理想,建立了格的同构映射,基于模糊同态所确定的映射等价刻画了模糊子格的弱（满）同态。     

Equiprime, 3-prime and c-prime fuzzy ideals of nearrings

In this paper, we present the notions of equiprime fuzzy ideal, 3-prime fuzzy ideal and c-prime fuzzy ideal of a nearring. We characterize these fuzzy ideals using level subsets and fuzzy points. If f: N → M is an onto nearring homomorphism, we show that the map defines a one-to-one correspondence between the set of all f-invariant (alternatively with sup property) equiprime (3-prime and c-prime, respectively) fuzzy ideals of N and the set of all equiprime (3-prime and c-prime, respectively) fuzzy ideals of M. Finally, we define fuzzy cosets determined by generalized fuzzy ideals; obtain fundamental results and isomorphism theorems.     

On the structure of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in commutative rings

This paper is a continuation of ideas presented by Davvaz [Roughness in rings, Inform. Sci., 164 (2004) 147-163; Roughness based on fuzzy ideals, Inform. Sci., 176 (2006) 2417-2437]. We introduce the notions of rough prime (primary) ideals and rough fuzzy prime (primary) ideals in a ring, and give some properties of such ideals. Also, we discuss the relations between the upper and lower rough prime (primary) ideals and the upper and lower approximations of their homomorphism images.     

赋范格H蕴涵代数和模糊格H蕴涵代数

在范数的条件下扩充了格H蕴涵代数的概念,即赋范格H蕴涵代数,并讨论一些性质。然后将模糊集合论运用于赋范格H蕴涵代数,给出了模糊赋范格H蕴涵代数的定义,得到了一些基本性质。通过使用两个赋范格H蕴涵代数之间的映射定义了赋范格H蕴涵代数同态,且得到了一些性质。最后得到了在赋范格H蕴涵代数中的数列对于蕴涵距离是有界的结论。     

群上的模糊软同余

为了进一步研究模糊软集理论,通过将软集与模糊同余结合,给出了模糊软同余的定义,并在一定程度上推广了模糊软集。研究了群上的模糊软同余的相关性质。建立了群上的模糊软同余与正规模糊软群之间的联系,给出了软模糊同态定理。     

双极值模糊（反）软子群

在双极值模糊软集理论的基础上,给出了双极值模糊（反）软子群的概念,讨论了它们的一些相关性质及等价刻画。提出了双极值模糊软映射下双极值模糊软集的像与原像的概念,并研究了双极值模糊软同态下双极值模糊（反）软子群的同态像与原像的初等性质。     

确定型模糊多重集有限自动机的极小化

主要研究确定型模糊多重集有限自动机的状态极小化问题。给出了模糊多重集有限自动机的同余和同态概念,并利用同余和同态关系研究了确定型模糊多重集有限自动机的极小化问题。进一步从确定型模糊多重集有限自动机自身出发,构造出极小模糊多重集有限自动机,并给出了极小化的算法。     

粗糙集与直觉模糊特殊集

粗集理论和直觉模糊特殊集理论都是近年来发展起来的一种有效的信息处理理论,尤其在不确定信息处理中各有优势。本文首先讨论了直觉模糊特殊集及其算子的一些性质,并给出了其海明距离的定义和计算。同时研究了粗糙近似空间上一类粗代数结构与直觉模糊特殊集的同态关系。     

直觉模糊同步机与最小化

提出了具有输入和输出功能的直觉模糊同步机的概念,研究了直觉模糊同步机直觉容许关系、等价关系、同态的若干性质。在直觉模糊同步机同构的基础上,得到了极小化直觉模糊同步机。     

坡代数的区间值模糊理想

模糊子代数是模糊代数的一个重要研究内容。为了进一步了解坡代数的模糊理想的特性,在坡代数中引入了区间值模糊理想概念。讨论了坡代数的区间值模糊理想的相关性质。证明了坡代数的区间值模糊理想的交,直积以及同态像也是区间值模糊理想。     

剩余格上的模糊软滤子

Molodtsov引入的软集理论,可作为通用的数学工具去处理不确定性问题。给出了剩余格上的模糊软滤子,对它们的性质进行了研究,此外,定义了剩余格上的模糊软滤子间的模糊软同态和模糊软同构,给出了剩余格上的模糊软滤子的同构像定理和同态逆像定理。     

近环上的模糊软理想和反模糊软理想

Molodtsov引入的软集理论,可作为通用的数学工具去处理不确定性问题。给出了近环上的模糊软理想和反模糊软理想的概念,对它们的性质进行了研究,进一步,定义了近环上的模糊软理想和反模糊软理想间的模糊软同态和模糊软同构,给出了近环上的模糊软理想和反模糊软理想的同构像定理和同态逆像定理。     

模糊BCK-代数及其模糊左(右)简理想

将Dib的模糊空间和模糊二元运算的概念引入BCK-代数中,给出了研究模糊BCK-代数的一个新方法。提出了模糊子代数、模糊左(右)简理想和模糊同态的概念,初步建立了新的模糊BCK-代数理论。结果表明,经典的 BCK-代数之模糊子代数、模糊左右简理想都是新理论的特例,因而这种新方法提供了发展模糊BCK-代数理论的一个有力工具。     

Node connectivity and arc connectivity of a fuzzy graph

The fuzzy graph approach is more powerful in cluster analysis than the usual graph - theoretic approach due to its ability to handle the strengths of arcs effectively. The concept of node-strength sequence is introduced and is studied in a complete fuzzy graph. Two new connectivity parameters in fuzzy graphs namely, fuzzy node connectivity (κ) and fuzzy arc connectivity (κ^′) are introduced and obtained the fuzzy analogue of Whitney’s theorem. Fuzzy node cut, fuzzy arc cut and fuzzy bond are defined. Fuzzy bond is a special type of a fuzzy bridge. It is proved that at least one of the end nodes of a fuzzy bond is a fuzzy cutnode. It is shown that κ=κ^′ for a fuzzy tree and it is the minimum of the strengths of its strong arcs. The relationships of the new parameters with already existing vertex and edge connectivity parameters are studied and is shown that the value of all these parameters are equal in a compete fuzzy graph. Also a new clustering technique based on fuzzy arc connectivity is introduced.     

Rough Sets Model Based on Random Fuzzy Sets and Fuzzy Logic Operators

As knowledge block in knowledge base is fuzzy and obtained randomly, we propose a random fuzzy rough set model based on random fuzzy sets and fuzzy logic operators. We give some properties of the random fuzzy rough set. We investigate the relationship between fuzzy measures defined by lower approximation and upper approximation of fuzzy set and fuzzy probability measures.