The Journal of Fuzzy Mathematics
Volume 22, Number 2, June 2014
CONTENT
DETAILS
Some More Results on Bipolar Fuzzy Sets and Bipolar Fuzzy Intersection Graphs
Sovan Samanta and Madhumangal Pal
Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University, Midnapore-721 102, India.
E-mail address:ssamantavu@gmail.com , mmpalvu@gmail.com
Abstract: In this paper, some basic concepts of bipolar fuzzy set, cut level set of bipolar fuzzy set, truncations of bipolar fuzzy set and bipolar fuzzy intersection graphs are defined.? It is shown that any bipolar fuzzy graph can be expressed as the bipolar fuzzy intersection graphs of some bipolar fuzzy sets.
Keywords: Bipolar fuzzy graphs, bipolar fuzzy intersection graphs, cut level sets, truncations
On Fuzzy garma-compact Spaces
N. Gowrisankar
70/232 6B, Kollupettai Street, M, Chavady, Thanjavur-613001, Tamilnadu, India.
E-mail address:gowrisankartnj@gmail.com
N. Rajesh
Department of Mathematics, Rajah Serfoji Govt. College, Thanjavur-613005, Tamilnadu, India.
E-mail address:nrajesh-topology@yahoo.com
V. Vijayabharathi
Department of Mathematics, National Institute of Technology, Tiruchi-rapppali, Tamilnadu, India
E-mail address:vijayabharathi_v@yahoo.com
Abstract: In this paper, we introduce and study a new type of compact space called -compact space in L-topological spaces by means of garma-open L-sets and their inequality.? This form of garma-compactness is a good generalization and has many characterizations when L?is completely distributive De Morgan algebra
Keywords and phrases:
L-topology, garma-open L-set, Compactness, garma-compactness.
Connectedness and Disconnectedness in Soft Fuzzy Quasi Uniform Topological Space with Reference to Soft Fuzzy Quasi Uniform B Open Set
D. Vidhya, E. Roja and M. K. Uma
Department of Mathematics Sri Sarada College for Women, Salem-16 Tamilnadu, India
E-mail:vidhya.d85@gmail.com
Abstract:
The concepts of soft fuzzy connectedness and soft fuzzy disconnectedness are introduced by using soft fuzzy quasi uniform B open sets. Several properties and characterizations of such spaces are discussed.
Keywords and phrases:
Soft fuzzy quasi uniform B connectedness, soft fuzzy quasi uniform super B connectedness, soft fuzzy quasi uniform strongly B connectedness, soft fuzzy quasi uniform BCi connectedness (resp. disconnectedness) (i = S,M), soft fuzzy quasi uniform extremally B disconnectedness, soft fuzzy quasi uniform totally B disconnectedness.
On Some Recent g#-a-closed Fuzzy Sets, Fuzzy g#-a-closed Mappings and Fuzzy g#-a-homeomorphism in Fuzzy Topological Spaces
Sadanand. N. Patil
Senior Scientist Assistant Professor and H.O.D. Department of Mathematics, KLS's VDRIT, Haliyal, 581329. (UK).(Karnataka-India).
E-mail:patilsadu@gmail.com sada_np@rediffmail.com
Abstarct:
In this paper, the class of g#-a-closed fuzzy sets are introduced.? This class is property placed in between the class of g*-closed fuzzy sets and the class of ag-closed fuzzy sets in fuzzy topological spaces. Further, the concept of fuzzy g#-a-continuous, fuzzy g#-a-irresolute mappings, fuzzy g#-a-closed maps, fuzzy g#-a-open maps and fuzzy g#-a-homeomorphism in fuzzy topological spaces are also introduced, studied and some of their properties are obtained
Keywords and phrases:
g#-a-closed fuzzy sets, fg#-a-continuous, fg#-a-irresolute, fg#-a-open, fg#-a-closed mappings and fg#-a-homeomorphism.
On Phi-closed Fuzzy Sets and Fuzzy Phi-irresolute Maps in Fuzzy Topological Spaces
Sadanand. N. Patil
Senior Scientist Assistant Professor and H.O.D. Department of Mathematics, KLS's VDRIT, Haliyal, 581329. (UK).(Karnataka-India).
E-mail: patilsadu@gmail.com sada_np@rediffmail.com
Abstarct:
In this paper, the class of Phi-closed fuzzy sets are introduced.? This class properly fits between the class of closed fuzzy sets and the class of gs-closed fuzzy sets in fuzzy topological spaces.Further, the concept of fuzzy Phi-continuous, fuzzy Phi-irresolute mappings, fuzzy Phi-closed maps, fuzzy Phi-open maps and fuzzy Phi-homeomorphism in fuzzy topological spaces are also introduced, studied and some of their properties are obtained.
Keyword and phrases: Phi-closed fuzzy sets, fPhi-continuous, fPhi-irresolute, fPhi-open, fPhi-closed mappings and fPhi-homeomorphism.
On Fuzzy g-continuous Maps and Fuzzy g-homeomorphisms in Fuzzy Topological Spaces
Sadanand. N. Patil
Senior Scientist Assistant Professor and H.O.D. Department of Mathematics, KLS's VDRIT, Haliyal, 581329. (UK).(Karnataka-India).
E-mail: patilsadu@gmail.com sada_np@rediffmail.com
Abstract:
The aim of this paper is to introduce a new class of fuzzy sets, namely g-closed fuzzy sets for fuzzy topological spaces. g-closed fuzzy sets, which are lies in between the class of closed fuzzy sets, semi-closed fuzzy sets and g-closed fuzzy sets. In this paper, we study many basic properties of g-closed fuzzy sets together with the relationships of these fuzzy sets with some other fuzzy sets. We introduce two new separation properties, namely fuzzy-Tgspaces and fuzzy-gT spaces.Further, the concept of fuzzy g-continuous, fuzzy g-irresolute mappings, fuzzy g-closed maps, fuzzy g-open maps and fuzzy g-homeomorphism in fuzzy topological spaces are also introduced, studied and some of there properties are obtained.
Keywords and phrases: g-closed fuzzy sets, fuzzy-Tg spaces and fuzzy-gT spaces, fg-continuous, fg-irresolute, fg-open, fg-closed mappings and fg-homeomorphism.
On Some New Mappings in Fuzzy Topological Spaces
Sadanand. N. Patil
Senior Scientist Assistant Professor and H.O.D. Department of Mathematics, KLS's VDRIT, Haliyal, 581329. (UK).(Karnataka-India).
E-mail: patilsadu@gmail.com sada_np@rediffmail.com
Abstract:
In this paper, the class of delta*gs-closed fuzzy sets are introduced.? This class properly fits between the class of semi-closed fuzzy sets and the class of -closed fuzzy sets in fuzzy topological spaces. Further, the concept of fuzzy delta*gs-continuous, fuzzy delta*gs-irresolute mappings, fuzzy deltags-closed maps, fuzzy delta*gs-open maps and fuzzy delta*gs-homeomorphism in fuzzy topological spaces are also introduced, studied and some of their properties are obtained.
Keywords and phrases:
delta*gs-closed fuzzy sets, -continuous, -irresolute, -open, -closed mappings and -homeomorphism.
On Some Stronger Forms -fuzzy Open Maps and -homeomorphism Mappings in Fuzzy Topological Spaces
Sadanand. N. Patil
Senior Scientist Assistant Professor and H.O.D. Department of Mathematics, KLS's VDRIT, Haliyal, 581329. (UK).(Karnataka-India).
E-mail: patilsadu@gmail.com sada_np@rediffmail.com
Abstract:
The aim of this paper is to introduce a new class of fuzzy sets, namely *u-closed fuzzy sets for fuzzy topological spaces.? This class if a super class of closed of fuzzy closed fuzzy sets.? We introduce and study new space namely fuzzy -spaces and uTu*-spaces. Further, the concept of fuzzy *u-continuous, fuzzy *u-irresolute mappings, fuzzy *u-closed maps, fuzzy *u-open maps and fuzzy *u-homeomorphism in fuzzy topological spaces are also introduced, studied and some of there properties are obtained.
Keywords and phrases:
*u-closed fuzzy sets, f*u-continuous, f*u-irresolute, f*u-open, f*u-closed mappings and f*u-homeomorphism
On Some Advances in Stronger Forms of Fuzzy g*-semi-continuous Functions in Fuzzy Topological Spaces
Sadanand. N. Patil
Senior Scientist Assistant Professor and H.O.D. Department of Mathematics, KLS's VDRIT, Haliyal, 581329. (UK).(Karnataka-India).
E-mail: patilsadu@gmail.com sada_np@rediffmail.com
Abstract: In this paper, the class of g*?semi-closed fuzzy sets are introduced.? This class properly fits between the class of semi-closed fuzzy sets and the class of sg-closed fuzzy sets in fuzzy topological spaces. Further, the concept of the stronger forms of fuzzy g*s-continuous functions namely strongly fuzzy g*s-continuous, perfectly fuzzy g*s-continuous and completely fuzzy g*s-continuous have been introduced, studied and some of their properties are obtained.
Keywords and phrases :
Fuzzy g*s-continuous functions, strongly fuzzy g*s-continuous, perfectly fuzzy g*s-continuous and completely fuzzy g*s-continuous
On *gs-open Fuzzy Sets and Fuzzy *gs-irresolute Mappings in Fuzzy Topological Spaces
Sadanand. N. Patil
Senior Scientist Assistant Professor and H.O.D. Department of Mathematics, KLS's VDRIT, Haliyal, 581329. (UK).(Karnataka-India).
E-mail: patilsadu@gmail.com sada_np@rediffmail.com
Abstract: The aim of this paper is not introduce a new class of fuzzy sets, namely *gs-closed fuzzy sets for fuzzy topological spaces.? This class is obtained by generalizing g-open fuzzy sets via-g-open fuzzy sets.? This new class is properly placed between the class of g*-closed fuzzy sets and the class of g-closed fuzzy sets.? We also introduce and study fuzzy -spaces. Further, the concept of fuzzy *gs-continuous, fuzzy *gs-irresolute mappings, fuzzy *gs-closed maps, fuzzy *gs-open maps and fed and some of there properties are obtained.
Keywords and phrases:
*gs-closed fuzzy sets, f*gs-co
uzzy *gs-homeomorphism in fuzzy topological spaces are also introduced, studintinuous, f*gs-irresolute, f*gs-open, f*gs-closed mappings and f*gs-homeomorphism.
Connectedness and Disconnectedness in An Intuitionistic Fuzzy Centred Ditopological Texure Space
R. Narmada Devi, G. K. Revathi and M. K. Uma
Department of Mathematics Sri Sarada College for Women, Salem-636016 Tamilnadu, India
E-mail:narmadadevi23@gmail.com gk_revathi@yahoo.com
Abstract:
In this paper, the concept of intuitionistic fuzzy centred system is introduced.? The concept of an intuitionistic fuzzy centred texture space and intuitionistic fuzzy centred texture connectedness are introduced.? Some interesting properties of intuitionistic fuzzy centred texture connectedness are discussed.? Also, the characterizations of intuitionistic fuzzy centred ditopological texture space are discussed and some interesting properties of intuitionistic fuzzy cnetred product ditopological texture space are studied.
Keywords:
Intuitionistic fuzzy centred system, intuitionistic fuzzy centred texture space, intuitionistic fuzzy centred texture connectedness, intuitionistic fuzzy centred ditopological texture space, intuitionistic fuzzy centred product ditopological texture space.
Fuzzy Weakly Pre-irresolute Functions
N. Gowrisankar
70/232, Kollupetti Street, M. Chavady, Thanjavur 613001, Tamildu, India
E-mail:gowrisankartnj@gmail.com
N. Rajesh
Department of Mathematics, Rajah Serfoji Govt. College, Thanjavur-613005, Tamilnadu, India.
E-mail:nrajesh_topology@yahoo.com
Abstract:
In this paper, we have introduce and study a new type of fuzzy irresolute functions, called fuzzy weakly pre-irresolute functions by using fuzzy preopen sets.
Keywords and phrases: Fuzzy topology, fuzzy preopen sets, fuzzy pre-irresolute functions
-contractive Mixed Monotone Mappings in Coupled Fixed Point Consideration on Intuitionistic Fuzzy Metric Spaces with Application to Integral Equations
Bhavana deshpande
Department of Mathematics Govt. P. G. Arts and Science College Ratlam(MP), India
Pin:457001
E-mail:bhavnadeshpande@yahoo.com
Sushil Sharma
Department of Mathematics Govt. P. G. Arts and Science College Ratlam(MP), India
E-mail:sksharma2005@yahoo.com
Amrish Handa
Department of Mathematics Govt. P. G. Arts and Science College Ratlam(MP), India
E-mail:amrishhanda83@gmail.com
Abstract:
We establish coupled fixed point theorems for -contractive mixed monotone mappings on partially ordered non-Archimedean intuitionistic fuzzy metric spaces.? As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation.? We also give an example to validate our result.
Keywords and phrases:
Non-Archimedean intuitionistic fuzzy metric space, Mixed monotone mappings, Coupled fixed point, Contractive condition, Integral equation.
On Double Fuzzy Topological Spaces
M. A. Hebeshi and I. M. Taha
Department of Mathematics, Faculty of Science, Sohng University, Egypt
E-mail:imtaha2010@yahoo.com
Abstract:
In this paper, we introduce fuzzy upper and fuzzy lower generalized continuous, generalized irresolute, semi-generalized continuous and generalized semi-continuous multifunctions.? Also, several characterizations and properties of these multifunctions along with their mutual relationships are established in double fuzzy topological spaces
Keywords and phrases:
Double (intuitionistic) fuzzy topology, fuzzy multifunction, upper and lower generalized continuous, generalized irresolute, semi-generalized continuous and generalized semi-continuous.
Group Soft Topology
Sk. Nazmul
Govt. College of Education, Burdwan Kazirhat, Lakurdi, Burdwan-713102, West Bengal, India.
E-mail:sk.nazmul_math@yahoo.com
S. K. Samanta
Department of Mathematics, Visva-Bharati Santiniketan-731235, West Bengal, India
E-mail:syamal_123@yahoo.com
Abstract:
In the present paper, a notion of group soft topology is introduced and some of its important ?properties are studied.? Also some definitions and results on soft sets and soft topologies are established.
Keywords:
Soft sets, soft groups, topological groups, soft topology, soft topological groups, group soft topology.
Automated Medical Diagnosis: A Method Using Neutrosophic Sets
Athar Kharal
National University of Sciences and Technology(NUST), H-12, Islamabad, Pakistan
E-mail:atharkharal@gmail.com
Abstract:
Sanchez¡¯s method of medical diagnosis has been extended into neutrosophic paradigme; a generalization of fuzzy sets.? The method allows to specify and handle the association, indeterminacy and non-association of a symptom to both, the patient and the disease.? Two neutrosophic compositions of relations and three different selection indices have been presented and applied through an illustrative example.
Keywords:
Automated Diagnosis; Sanchez¡¯s method; Neutrosophic set; Fuzzy Reasoning.
Fuzzy Ultrametrics Based on Idempotent Probability Measures
Changqing Li and Zhongqiang Yang
Department of Mathematics, Shantou University, Shantou, Guangdong, 515063, China P. R
E-mail address:helen_smile0320@163.com(C.Li) zqyang@stu.edu.cn(Z. Yang)
Abstract:
In the paper, we construct a fuzzy ultrametric space based on idempotent probability measures (IPM), and study its completeness.? We also investigate nonexpanding maps in the fuzzy ultrametric spaces based on IPM.? Furthermore, we prove that the set of IPM with finite compact support is dense in this fuzzy ultrametric space.? At last, we show that a compact fuzzy ultrametric space is isometric to the fuzzy ultrametric space based on IPM.
Keyword: Idempotent probability measure; Fuzzy ultrametric space; Support; Nonexpanding map
Convergence of Maxgeneralized Mean-mingeneralized Mean Powers of Intuitionistic Fuzzy Matrices
Rajkumar Pradhan and Madhumangal Pal
Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar university, Midnapore-721102, India.
E-mail: math.rajkumar@gmail.com mmpalvu@gmail.com
Abstract:
Intuitionistic fuzzy relations on finite universes can be represent by intuitioinistic fuzzy matrices and the limiting behavior of the power matrices depends on the algebraic operation employed on the matrices.? In this paper, the power of intuitionistic fuzzy matrices with maxgeneralized mean-mingeneralized mean operation have been studied.? Here it is shown that the power of intuitionistic fuzzy matrices with the said operations are always convergent.? The convergence of powers for an intuitionistic fuzzy matrix with convex combination of max-min and maxarithmetic mean-minarithmetric mean are also dicussed here.
Keywords:
Intuitionistic fuzzy number, intuitionistic fuzzy matrix, intuitionistic fuzzy graph, convergence of intuitionistic fuzzy matrix, convex combination.
Redundancy of Set of Clauses in Propositional Logic
Shihui Tang and Yang Xu
School of Mathematics, Southwest Jiaotong University, Sichuan, Chengdu 610031, China
E-mail:tangshihui2007@163.com xuyang@home.swjtu.edu.cn
Abstract:
Detection and elimination of redundant classes from prepositional formulas in Conjunctive Normal Form (CNF) is a fundamental problem with numerous application domains, including AI, and has been the subject of extensive research.? In this paper, we mainly studied the redundancy of clause and literal in the prepositional logic formula.? According to the characteristics of the redundant clauses, the clause can be divided into three categories: irredundant clauses, relatively redundant clauses and absolute redundant clauses.? Some equivalent descriptions of three types of clauses for a particular set of clauses were given respectively, and irredundant equivalent subsets of any set of clause were discussed.? In addition, an approach of identification of redundant literal was presented.? At last, an equivalent condition of the redundancy clause was obtained by using the concept of satisfiability.? These results serve as the theoretical foundation of a new method for judging the redundancy of set of clauses.
Keywords:
Relatively redundant clauses, Absolute redundant clauses, Redundancy literal, Irredundant equivalent subset, Satisfiability.
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