The Journal of Fuzzy Mathematics
Volume 20, Number 4, December 2012
CONTENT
DETAILS
On Several Types of Graded Continuity in l-topological Spaces
Sadik Bayhan
Department of Mathematics Faculty of Sciences and Arts,Mehmet Akif Ersoy University, 15030-Ort¨¹l¨¹ Burdur/Turkey.E-mail: bayhan@mehmetakif.edu.tr
Abstract:The purpose of this paper is to introduce some weaker forms of graded continuity in L-topological spaces on the basis of a fixed quadruple M=(L,D,*), where (L,f), A?and *, respectively, denote a complete lattice and binary operations on L?satisfying some further axioms, was presented by Hohle and Sostak.
Study of Some Aspects of Mixed d-pre Fuzzy Topological Spaces
N. R. Das
Department of Mathematics, Gauhati University Guwahati 781014, Assam, India
Jonali Sharma
Laban Assamese Girls' Secondary School, Laban Shillong 793004, Meghalaya, India.E-mail:jonalisharma2007@rediffmail.com
Abstract:The study of mixed topology originated from the work of Polish mathematicians Alexiewicz and Semadini. N. R. Das and P.C. Baishya have constructed fuzzy mixed topology and then studied various properties of this topology. Anjana Bhattacharyya of University of Calcutta has defined fuzzy d-pre-q-nbd of a fuzzy point and fuzzy d-preclosure of a fuzzy set.
This paper deals with the introduction and study of a mixed d-pre fuzzy topological space.? The work of N. R. Das and P. C. Baishya is used and at the same time combined with the work of Anjana Bhattacharyya to construct this mixed d-pre fuzzy topological space. This topological space is constructed from two different topologies using fuzzy d-pre-q-nbd of a fuzzy point with respect to one topology and fuzzy d-preclosure of a fuzzy set with respect to the another topology.Then it is proved to satisfy the four conditions of a fuzzy topological space. Under certain conditions, some relations are established between the two topologies used and their corresponding mixed topology. ?Relation between the product of two mixed d-pre fuzzy topologies and the mixed d-pre fuzzy topology of the product topologies is established.Some results of fuzzy continuity are proved in the newly constructed mixed d-pre fuzzy topological space. Fascinated by the work on mixed fuzzy topological space, attempts are also made to study separation axioms and also open and closed maps in mixed d-pre fuzzy topological space. It is hoped that these results will help to explore the mixed fuzzy topological space with its applications to justify that such a study is really fruitful.
Fuzzy Congruence Relations on Lattice Implication Algebras
Yi Liu
Intelligent Control Development Center, Southwest Jiaotong University, Chengdu Sichuan 610031, P. R. China College of Mathematics and Information Science, Neijiang Normal University, Neijiang Sichuan 641000, P. R. China.E-mail:liuyiy1@126.com
Jun Liu
School of Computing and Mathematics, Faculty of Computing and Engineering, University of Ulster (Jordanstown Campus), Shore Road, Newtownabbey, Co Antrim, BT370QB, Northern Ireland.E-mail: j.liu@ulster.ac.uk
Yang Xu
Intelligent Control Development Center, Southwest Jiaotong University,Chengdu Sichuan 610031, P. R. China.E-mail: xuyang@home.swjtu.edu.cn
Abstract:The notion of fuzzy congruence relations on lattice implication algebras is proposed and properties of fuzzy congruence relations are discussed. Secondly, equivalence characterization of fuzzy congruence relation are obtained, and, showed the fact that the fuzzy congruence is a generalization of congruence on lattice implication algebras. Thirdly, we prove that the set FF(+) of all fuzzy filter is isomorphic to the set FC(+) of all fuzzy congruence relations. Finally, the quotient lattice implication algebras which determined by fuzzy congruence relation is studied and homomorphism theorem is obtained.
T-locality Rings
Khaled A. Hashem
Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt.E-mail: Khaledahashem@yahoo.com
Abstract:
In this paper, we introduce the concept of T-locality rings, where T-stands for any continuous triangular norm. we give the necessary and sufficient conditions for a T-locality ring structure and a T-locality system to be compatible. The notion of bounded fuzzy set is introduced in T-locality rings and some results in this context are provided.
On Fuzzy Weakly g-open and g-closed Functions
J. Bhuvaneswari
Department of Computer Applications, Rajalakshmi Engineering College,Thandalam, Chennai-602105, TamilNadu, India.E-mail: sai_jbhuvana@yahoo.co.in
N. Rajesh
Department of Mathematics, Rajah Serfoji govt. College,Thanjavur-613005, Tamilnadu, India.E-mail: nrajesh_topology@yahoo.co.in
Y. B. Jun
Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, KoreaE-mai: skywine@gmail.com
Abstract:In this paper, we introduce and characterize fuzzy weakly g-open(resp. fuzzy weakly g-closed) functions between fuzzy topological spaces and also study these functions in relation to some other types of already known functions.
Generalized Fuzzy S-irresolute Mappings in Fuzzy Topological Spaces
S. E. Abbas
Department of Mathematics, Faculty of Science, Jazan University, Saudi Arabia.E-mail: sabbas73@yahoo.com
I. M. Taha
Department of Mathematics, Faculty of Science, Sohag University, Egypt.E-mail: imtaha2010@yahoo.com
Abstract: In this paper, we introduce and study the concepts of r-generalized fuzzy strongly semi-closed sets and generalized fuzzy strongly semi-closure of 1in Sostak¡¯s fuzzy topological spaces. Generalized fuzzy strongly semi-continuity, generalized fuzzy S-irresolute and generalized fuzzy semi-S-irresolute mappings are introduced and the relationship between these mappings are investigated. Moreover, we investigates some properties of them. The separation axioms of r-fuzzy strongly semi-closed sets and separation axioms of r-generalized fuzzy strongly semi-closed sets are introduced and studied.? Also, some applications are introduced.
Characterizations of Some Fuzzy Separation Axioms
S. E. Abbas
Department of Mathematics, Faculth of Science, Jazan University, Saudi Arabia.E-mail: sabbas73@yahoo.com
I. M. Taha
Department of Mathematics, Faculth of Science, Sohag University, Egypt.E-mail: imtaha2010@yahoo.com
Abstract:The aim of this paper is to introduce and characterize some topological separation axioms in terms of quasi-coincidence, q-closure and d-closure operators as initiated in [8] in fuzzy setting. Also, we introduce and characterize fuzzy weakly q-closed functions between fuzzy topological spaces and also study these functions in relation to some other types of already known functions.
Weaker Forms of Fuzzy Contra-continuity in Fuzzy Topological Spaces
S. E. Abbas
Department of Mathematics, Faculth of Science, Jazan University, Saudi Arabia.E-mail: sabbas73@yahoo.com
I. M. Taha
Department of Mathematics, Faculth of Science, Sohag University, Egypt.E-mail: imtaha2010@yahoo.com
Abstract:In this paper, we introduce the concepts of fuzzy contra-continuity, fuzzy almost contra-continuity, fuzzy contra m-continuity, fuzzy almost contra m-continuity, fuzzy contra semi-continuity and generalized fuzzy contra continuity in fuzzy topological spaces in Sostak sense. The relationship between these mappings are investigated and we investigate some properties of them. Separation and regularity axioms in fuzzy topological subspaces are defined and studied.
Fixed Points and Common Fixed Points in a-fuzzy Pseudo-ordered Sets
Abdelkader Stouti
Center for Doctoral Studies: Sciences and Techniques, Laboratory of Mathematics and Applications, Faculty of Sciences and Techniques, University Sultan Moulay Slimane, P. O. Box 523, 23000 Beni-Mellal, MOROCCO.E-mail: stouti@yahoo.com
Lemnaouar Zedam
Laboratory of Pure and Applied Mathematics, M¡¯sila University,P. O. Box 166 Ichbilia, M¡¯sila 28105, ALGERIA.E-mail: L.zedam@yahoo.fr
Abstract:In this paper, we first introduce the notions of a-fuzzy pseudo-order and a-fuzzy trellis. Secondly, we establish the existence of the greatest and the least fixed points of a-fuzzy monotone maps defined on a nonempty a-fuzzy pseudo-ordered set.? Furthermore, we prove that the set of all fixed points of two classes of a-fuzzy monotone maps defined on a nonempty complete a-fuzzy trellis is also a nonempty complete a-fuzzy trellis. As consequences, we obtain an a-fuzzy version of a Skala¡¯s results and we establish that the set of all common fixed points of finite commutative families of ra-fuzzy monotone maps defined on of two classes of nonempty ra-fuzzy compete trellises is also a nonempty ra-fuzzy compete trellis.
On (1,m)-fuzzy Prime Ideals of Semirings
P. Dheena and G. Mohanraaj
Department of Mathematics, Annamalia University, Annamalainagar-608002, India.
E-mail: dheenap@yahoo.com and gmohanraaj@gmail.com
Abstract:In this paper we introduce the concept of (1,m)-fuzzy subsemiring and (1,m)-fuzzy ideals of a semiring which can be regarded as a generalization of fuzzy subsemiring and fuzzy ideals. We introduce the notion of (1,m)-fuzzy prime ideals and find the relationship with other prime ideals.? We characterize semi-regular rings with (1,m)-fuzzy ideals.
Lattice Valued Double Fuzzy Ideal Structure
S. E. Abbas
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt.
A. H. Zakari
Department of Mathematics, Girl¡¯s Education College, Jazan University, Jazan 1178, Saudi Arabia
AbstractIn this paper, the concepts of lattice valued double fuzzy ideal and double fuzzy idealbase are introduced and studied. We study the images and preimages of double fuzzy idealbase induced by functions. Also, we obtain some characterizations of I-map and I-preserving map by using the notion of double fuzzy idealbase. In particular, we prove the existence of product double fuzzy ideals.
Belief Aggregation in Fuzzy Framework
Ismat Beg and Asma Khalid
Department of Mathematics, and Centre for Advanced Studies in Mathematics,Lahore University of Management Sciences, Lahore-54792, Pakistan.E-mail: ibeg@lums.edu.pk
Abstract:We explore how belief aggregation in the fuzzy framework can be molded into an optimization problem which helps avoid paradoxical outcomes without the fear of indecision. We further illustrate that depending on the choice of t-norm and fuzzyimplication, we can find aggregation functions that produce collectively rational outcome without compromising on systematicity.
A Note on Intuitionistic Fuzzy Interior Ideals in Ordeered Semigroups
P. Dheena and G. Mohanraj
Department of Mathematics, Annamalai University, Annamalainagar-608 002, India.E-mail: dheenap@yahoo.com, gmohanraaj@gmail.com
Abstract:In this note we remark that Theorem 3.10 given by Ezhilarasi et al [1] appears to be wrong. We give counter example for Theorem 3.10. However, We get rid of this problem by altering condition of the proposed theorem Theorem 3.10 by Ezhilarasi et al [1].
Extension Operations of Normal Interval Valued Fuzzy Sets Induced by s-norm
Xiao-ping Li
School of Management, Tianjin Normal University, Tianjin 300387, China.Email: lxpmath@126.com
Gang Sun
Marine Engineering College, Dalian Maritime Universiyt, Dalian 116026, China.E-mail:
sungang@yahoo.com.cn
Abstract:In this paper, firstly, we introduce a s-norm operator on the space of normal interval valued fuzzy sets, define the s-norm extension operations, and point out that this kind of operations still constitute s-norm on the space of normal interval valued fuzzy sets. And then, some basic properties of extension operations are showed. Furthermore, on the basis of this, a class of special interval valued fuzzy numbers are discussed in detail. All of three results will be applied extensively to interval analysis, fuzzy pattern recognition as well as decision analysis.
On Fuzzy Pairwise Semi Pre Regular Space and Fuzzy Pairwise Semi Pre Normal Space
Anjan Mukherjee
Department of Mathematics, Tripura University, Suryamaninagar, Agartala-799130, Tripura, India.E-mail: anjan2002_m@yahoo.co.in
Jhilly Choudhury
E-mail: jhilly_c@rediffmaiil.com
Abstract: The purpose of this paper is to introduce and study the concept of fuzzy pairwise semi pre regular space and fuzzy pair wise semi pre normal space using (ti,tj)-fuzzy semi pre open sets. Some characterization theorems and basic properties of these concepts are to be discussed.
Lattice Valued Double Fuzzy Quasi-uniform Spaces
S. E. Abbas
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt.
A. H. Zakari
Department of Mathematics, Girl¡¯s Education College, Jazan University, Jazan 1178, Saudi Arabia
Abstract:In this paper, the concept of lattice valued double fuzzy quasi-uniform spaces is introduced. We study the images and preimages of double fuzzy quasi-uniform base induced by functions. Also, we obtain some characterizations of U-map and U-preserving map by using the notion of double fuzzy quasi-uniform base. In particular, we prove the existence of product double fuzzy uniformity.
Generalized Intuitionistic Fuzzy Contra Continuous
E. Roja, M. K. Uma and R. Dhavaseelan
Department of Mathematics, Sri Saradha College for Women, Salem-16, Tamil Nadu, India.E-mail: dhavaseelan.r@gmail.com
Abstract:In this paper the concept of generalized intuitionistic fuzzy contra continuous function, strongly generalized intuitionistic fuzzy contra continuous function and generalized intuitionistic fuzzy contra irresolute are studied. The concepts of generalized intuitionistic fuzzy S-closed and strongly generalized intuitionistic fuzzy S-closed are studied. The concepts of generalized intuitionistic fuzzy compact spaces and generalized intuitionistic fuzzy almostcompact spaces are established. The concepts of generalized intuitionistic fuzzy filter and intuitionistic fuzzy C-convergent are established. Some interesting properties are investigated besides giving several examples.
a-group Semantic Resolution Method Based on Lattice-valued Propositional Logic System LP(X)
Xiaomei Zhong and Yang Xu
School of Matheamtics, Southwest Jiaotong University, Chengdu, 610031
E-mail: zhongxm@126.com,xuyang@home.swjtu.edu.cn
Abstract:On the basis of a-group resolution principle, an a-group resolution automated reasoning method for lattice-valued prepositional logic system LP(X)based on lattice implication algebra is proposed in the present paper. Firstly, a-group semantic resolution method is established in LP(X), as well as its soundness and condition completeness. Secondly, a-group semantic resolution in lattice-valued propositional logic (Ln'L2)P(X) is equivalently transformed into that in lattice-valued propositional logic LnP(X) under certain conditions. Finally, as product lattice implication algebra Ln'L2 and linguistic truth-valued lattice implication algebra LV(n'2)?have the same structure, the conclusion that a-group semantic resolution in linguistic truth-valued lattice-valued propositional logic LV(n'2) is equivalent to that in lattice-valued propositional logic LVnP(X) is also obtained.
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