The Journal of Fuzzy Mathematics
Volume 21, Number 1, December 2013
CONTENT
DETAILS
Some Properties of Generalized Ultrametric Spaces
Shaban Sedghi
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
E-mail address: sedghi_gh@yahoo.com
Nabi Shobe
Department of Mathematics, Islamic Azad university, Science and Research Branch, 1477893855 Tehran, Iran
E-mail address: nabi_shobe@yahoo.com
S. Firouzian
Payame Noor University Iran
E-mail address: siamfirouzian@pnu.ac.ir
Abstract:
In this paper, we generalize the concept of ultrametric spaces, which is called T-metric space and give some properties of it.? Also, we prove a common fixed point theorem for two mappings under the condition of R-weakly commuting in complete T-metric spaces.? A lot of fixed point theorem on ordinary metric and ultrametric space are special case of our main result, since every ordinary metric and ultrametric space is also T-metric space.
Key words and phrases:
T-metric space, contractive mapping, fixed point.
Fuzzy Topological Groups
SK. Nazmul
Govt. College of Education, Burdwan, Kazirhat, Lakurdi, Burdwan-713102, West Bengal, India
E-mail: sk.nazmul_math@yahoo.in
H. Hazra
Department of Mathematics, Bolpur College, Bolpur, Birbhum-731204, West Bengal, India
E-mail: h.hazra2010@gmail.com
S. K. Samanta
Department of Mathematics, Visva-Bharati, Santiniketan-731235, West Bengal, India
E-mail: syamal_123@yahoo.co.in
Abstract:
In this paper Lowen type gradation of openness (LGO), Lowen type subspace gradation of openness (LSGO), Gradation Presserving map (gp-map) in LGO?and LSGO are defined and their properties are studied.? The definitions of the fuzzy topological groups with respect to LGO?and LSGO?are given and some of their properties are studied.
Keywords:
Fuzzy sets, fuzzy groups, topological groups, fuzzy topological spaces, gradation of openness, gradation preserving map, fuzzy topological groups.
New Separation Axioms in Smooth Fuzzy Topology
N. Gowrisankar
70/232 6B, Kollupettai Street, M. Chavady, Thanjavur-613001, Tamil-Nadu, India
E-mail: gowrisankartnj@gmail.com
N. Rajesh
Department of Mathematics, Rajah Serfoji Govt. College, Thanjavur 613005, Tamilnadu, India.
E-mail: nrajesh_topology@yahoo.co.in
Abstract:
In this paper we have introduce and study the concepts of fuzzy W-T(i=0,1,2,1/2)?spaces, fuzzy W-normal spaces and fuzzy W-regular spaces in the sence of Sostak [5].
Key words and phrases:
Smooth fuzzy Topology, fuzzy W-open set.
On P-closed Fuzzy Topological Spaces
N. Gowrisankar
70/232 6B, Kollupettai street, M. Chavady, Thanjavur-613001, Tamil-Nadu, 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.co.in
Abstract:
In this paper the concept of pre-W-e-open sets and making use of this concept we give characterization of P-closed fuzzy topological spaces.
Key words and phrases:
Fuzzy topology, Fuzzy pre-W-e-open set.
Bounded Linear Operators in Generating Spaces of Quasi-norm Family
G. Rano, T. Bag?and S. K. Samanta
Department of Mathematics, Visva-Bharati Santiniketan 731235, INDIA
E-mail: tarapadavb@gmail.com
Abstract:
Following the concept of generating spaces of quasi-norm family, introduced by Xiao and Zhu, we redefine it and introduce the idea of continuity and boundedness of linear operators in such spaces.? Quasi-norm family of bounded linear operators is deduced.? Concept of dual space for quasi-norm family is developed.
Key words:
Quasi-norm, Generating space, Bounded linear operator.
On Quadratic Membership Functions in Solving Assignment Problem under Fuzzy Environment
D. Stephen Dinagar
Department of Mathematics, T. B. M. L. College, Porayar-609307, TamilNadu, India
E-mail: dsdina@rediffimail.com
K. Palanivel
School of Advanced Sciences, VIT University, Vellore-632014, TamilNadu, India
E-mail: drkpalanivel@gmail.com
Abstract:
In this article, a bell shaped fuzzy number called piece wise quadratic fuzzy number (PQFN) whose membership function is quadratic in nature is used.? New arithmetic operations of the fuzzy number are also utilized.? Fuzzy Hungarian method is proposed to find the optimal solution in terms of fuzzy numbers and verified its solution in the nature of quadratic membership functions.? A relevant numerical example is also included.
Keywords:
Fuzzy Constraints, Fuzzy Numbers, Piece Wise Quadratic Fuzzy Membership
Functions, Fuzzy Hungarian Method.
Solving A Travelling Salesman Problemin Fuzzy Environment
D. Stephen Dinagar
PG & Research Department of Mathematics, T. B. M. L. College, Porayar-609307, TamilNadu, India
E-mail: dsdina@rediffmail.com
K. Palanivel
School of Advanced Sciences-Mathematics, VIT University, Vellore-632014, TamilNadu, India
E-mail: drkpalanivel@gmail.com
Abstract:
Travelling salesman problem (TSP) is one of the challenging real-life problems, attracting researchers of many fields including artificial intelligence, operations research and algorithm design and analysis.? The problem has been well studied till now under different heading has been solved with different approaches including genetic algorithms and linear programming, Linear programming is designed to deal with crisp parameters, but information about real life systems is often available in the form of vague descriptions.? Fuzzy methods are designed to handle vague terms, and are most suited to finding optimal solutions to problems with vague parameters.? In this paper, we are solving a TSP with the help of trapezoidal membership functions and its arithmetic operations.? Solving procedure have been applied from the way of fuzzy assignment problem [9,10].? The optimal solution in terms of fuzzy numbers and verified its solution in the nature of fuzzy membership functions.? The fuzzified version of the problem has been discussed with the aid of a numerical example.
Keywords:
Fuzzy Numbers, Trapezoidal Fuzzy Numbers, Fuzzy Assignment Problem, Fuzzy Travelling Salesman problem.
Common Fixed Point for Fuzzy Mappings Using Generalized Altering Distance Function in Ordered Metric Spaces
Hemant Kumar Nashine
Department of Mathematics, Disha Institute of Management and Technology, Satya Vihar, Vidhansabha-Chandrakhuri Marg, Mandir Hassaud, Raipur-492101 (Chhattisgarh), India.
E-mail: dkhknashine@rediffmail.com, nashine_09@rediffmail.com
Ismat Beg
University of central Punjab, Lahore-54770, Pakistan.
E-mail: ibeg@lums.edu.pk
Abstract:
We study common fixed point for a pair of fuzzy mappings satisfying a contractive condition which involves generalized altering distance functions in three variables in complete metric spaces endowed with order.? As application, we present a fuzzy fixed point result for mappings satisfying a contraction of integral type.
Keywords:
Generalized altering distance function; fuzzy mapping; fixed point; partially ordered set.
On Some Applications of Intuitionistic Fuzzy G-a-locally Closed Sets
R. Narmada Devi, E. Roja and M. K. Uma
Department of Matheamtics, Sri Sarada College for Women, Salem, Tamil Nadu, India.
E-mail: narmadadevi23@gmail.com
Abstract:
This paper is devoted to the study of new class of sets called an intuitionistic fuzzy G-a-locally closed sets.? The concepts of an intuitionistic fuzzy G-a-locally closed set, intuitionisitc fuzzy G-a-local spaces, intuitionistic fuzzy G-a-local border, intuitionistic fuzzy G-a-local frontier and intuitionistic fuzzy G-a-lcoal exterior are introduced and interesting properties are established.? In this connection, interrelations are discussed.? Examples are provided where necessary.
Keywords:
Intuitionistic fuzzy G-a-locally closed set, intuitionistic fuzzy G-a-local spaces, intuitionistic fuzzy G-a-local border, intuitionistic fuzzy G-a-local frontier and intuitionistic fuzzy G-a-localexterior.
A New Type of Fuzzy Topological Groups
N. Rajesh
Department of Mathematics, Rajah Serfoji Govt, College, Thanjavur-613005, Tamilnadu, India.
E-mail: nrajesh_topology@yahoo.co.in
V. Vijayabharathi
Research Scholar, Department of Mathematics, Rajah Serfoji Govt. College,Thanjavur-613005,Tamilnadu, India.
Abstract:
In this paper, we consider fuzzy topological group and g-fuzzy topological group.? We prove some results about the connection between these two concepts.
Key words and phrases:
Fuzzy topological group, Quotient fuzzy topological group, g-fuzzy topological group.
Study of Fuzzy q-preopen Sets and Its Related Topics
N. R. Das
Deptt.of Mathematics, Gauhati University Guwahati 781014, Assam, India
Jonali Sharma
Laban Assames Girls¡¯ Secondary School, Laban Shillong 793004, Meghalaya, India
E-mail: jonalisharma2007@rediffmail.com
Abstract:
In this paper we have introduced fuzzy q-preopen sets and studied its relation with fuzzy d-preopen sets.? Then we have introduced two new continuity structures--almost continuity and q-almost continuity in fuzzy structure.? We have then tried to study their various properties and also to relate them with d-almost continuous and d-almost continuous functions in fuzzy settings.
Keywords:
Fuzzy q-preopen sets, fuzzy d-preopen sets, fuzzy d-almost continuity, fuzzy d-almost continuity, fuzzy q-almost continuity and fuzzy q-almost continuity.
Non-normal Triangular Fuzzy Numbers, Its Operations, Inequalities and Optimization Techniques
Mijanur Rahaman Seikh?and Madhumangal Pal
Department of Applied Mathematics with Oceanology and Computer Progarmming, Vidyasagar University, Midnapore-721 102, India
E-mail: ?mrseikh@ymail.com, ?mmpalvu@gmail.com
Prasun Kumar Nayak
Bankura Christian College, Bankura, 722 101, India,
E-mail: nayak_prasum@rediffmail.com
Abstract:
The new concept of generalized fuzzy numbers is proposed and treated in this paper by removing the ¡°normality¡± on the definition of fuzzy numbers.? We introduce the notion of isosceles triangle fuzzy number.? We also discuss about the algebra of this fuzzy numbers.? Ranking of fuzzy numbers play an important role in decision making.? Though it is difficult to rank between fuzzy numbers like crisp.? In this paper we got some inequality relations to obviate this problem.? A new concept ranking index, is defined and employed to describe this method.? Some relevant numerical examples are also included.
Keywords:
Non-normal triangular fuzzy number, Ranking index, Nearest interval number.
Fuzzy a-preirresolute Functions
S. E. Abbas
Math. Department, Faculty of Science, Jazan University, Saudi Arabia
E. El-Sanousy and A. A. Hussien
Department Mathematics, Faculty of Science, Sohag University, Egypt
Abstract:
In this paper, we introduce the concepts of fuzzy a-preirresolute function and strongly fuzzy a-preirresolute function on fuzzy topological spaces in ?ostak sense.? Some of their characteristic properties are considered.? Also, we investigate the relationship between these classes of functions.
Key words and phrases:
Fuzzy a-preirresolute functions and strongly fuzzy a-preirresolute functions.
Generalized M-fuzzy Metric Spaces
A. Singadurai?and G. Pushpalakshmi
T. D. M. N. S. College, T. Kallikulam627117, Tamil nadu, India
E-mail: singadurai_59@yahoo.co.in
Abstract:
The purpose of this paper is to introduce generalized M-fuzzy metric space and study some of its topological properties and some fixed point theorems.
Keywords:
Generalized M-fuzzy metric space, Contraction mapping.
On Filters of Lattice Implication Product Algebra L1,L2
Li Zhao and Yang Xu
College of Mathematics, Southwest Jiaotong University, Chengdu 610031, China
E-mail: yuyehuaixiang@163.com,? E-mail: xuyang@home.swjtu.edu.cn
Shuwei Chen
School of Computing and Mathematics, University of Ulster at Jordanstown, UK, BT370QB.
E-mail: chensw915@gmail.com
Abstract:
This paper investigates the relationships between a kind of filters (including implicative filters, proper filters, prime filters, ultra-filters, obstinate filters, I-filters, involution filters and weak filters) of lattice implication product algebra L1,L2?and that of L1?and L2, then the study is extended to L1,L2,...,Ln? These kinds of filters are discussed in finite Lukasiewicz chain Lm?and the corresponding conclusions in Lm,Ln?are given.
Keywords:
Lattice implication algebra, Lattice implication product algebra, Finite Lukasiewicz chain, Filter
On Fuzzy g-continuous Multifunctions
N. Gowrisankar
70/232 6B, Kollupettai street, M. Chavady, Thanjavur-613001, Tamilnadu, India.
E-mail: gowrisankartnj@gmail.com
N. Rajesh
Department of Mathematics, Rajah Serfoji Govt. College, Thanjavur-613005, Tamilnadu, India.
E-mail: nrajesh_topology@yahoo.co.in
V. Vijayabharathi
Department of Mathematics, National Institute of Technology, Tiruchirappalli, Tamilnadu, India.
Abstract:
In this paper we use fuzzy g-open sets in order to obtain certain characterizations and properties of upper (lower) fuzzy g-continuous multifucntions.
Key words and phrases:
Fuzzy g-open, fuzzy g-continuous, fuzzy multifunction.
A Study on Constrained Fuzzy Games
T. Porchelvi
PG Department of Mathematics, Magna College of Engineering, Chennai, TamilNadu, India
E-mail: selvi4685@yahoo.com
D. Stephen Dinagar
PG & Research Department of Mathematics, T. B. M. L. College, Porayar-609307, TamiNadu, India
E-mail: dsdina@rediffmail.com
Abstract:
In this article the concept of constrained fuzzy games is discussed and a method to solve such games is given.? Some important theorems are also given.? The simplex method is used to find the fuzzy value of the constrained fuzzy game.? Relevant numerical examples are also included.
Keywords:
Fuzzy sets, Fuzzy numbers, Trapezoidal fuzzy numbers, Constrained fuzzy games.
Necessary and Sufficient Conditions for The Representation of A Max-T-transitive Fuzzy Preference by A Utility Function on An Uncountable Set
Louis Aime Fono
Departement de Mathematiques et Informatique, Faculte des Sciences Universite de Douala, B. P. 24157 Douala, Cameroun
E-mail: lfono2000@yahoo.fr
Maurice Salles
University of Caen-France, CREM (UMR-CNRS 6211) MSRH F-14032, Caen, cedex, France. August 25, 2011
Abstract:
Fono and Andjiga [8] established necessary and sufficient conditions under which a given max-T-transitive fuzzy binary relation is representable by a utility function on a countable universe (set of alternatives).
In this paper, we study the uncountable case.? Specifically, we show that in an uncountable universe, these conditions are necessary but not sufficient.? We introduce the condition of ¡°separability of a fuzzy binary relation¡± and show that this new condition and the previous ones (those obtained in the countable case) are necessary and sufficient for the representation of a given max-T-transitive fuzzy binary relation by a utility function on an uncountable universe.
Keywords:
Fuzzy binary relation; utility function; uncountable universe; fuzzy separability; max-T-transitivity.
On Soft Complex Sets and Soft Complex Numbers
Sujoy Das
Department of Mathematics, Bidhan Chandra College, Asansol-4, W. B., India
S. K. Samanta
Department of Mathematics, Visva Bharati, Santiniketan-731235, W. B. India
Abstract:
Combining the recent revised definition of fuzzy numbers proposed by Dubios and Prade [6] and the idea of Soft set introduced by Molodtsov [12], we introduce, in this paper, a definition of soft complex set and soft complex number and study some basic properties of soft complex sets and soft complex numbers.? An attempt is made to develop differentiation and integration of soft functions.
Keywords:
Soft set, soft real number, soft complex number, soft function, soft limit of soft function, fuzzy numbers, fuzzy set.
Intuitionistic Fuzzy Mathematical Morphological Approach in Image Processing
Sharmistha Bhattacharya
E-mail: halder_731@rediffmail.com
Atikul Islam
Dept. of Mathematics Tripura University, Suryamaninagar, India
E-mail: atik.math@yahoo.com
Abstract:
Mathematical Morphology is geometric approach in image processing and analysis with a strong mathematical flavour.? Originally it was developed as a powerful tool for shape analysis in binary and, later grayscale images.? Fuzzy Mathematical Morphology aims to extend the binary morphological operators to gray scale image.? In this paper our main aim is to introduce IF Mathematical Morphological operators in image processing and to study their various properties in image processing.? Also some applications of IF Mathematical Morphology in image processing are shown with the help of examples.
Keywords:
IF sets, Image processing, Structuring element, IF mathematical morphological operators.
Fuzzy Programming with Nonlinear Membership Function for Multiobjective Solid Transportation Problem with Chance Constraints
A. K. Bit
Department of Mathematics, Faculty of Civil Engineering, College of Military Engineering, Pune-411031 (M. S.), India
E-mail: amalkbit@yahoo.com
Abstract:
A method for solving a multiobjective solid (three-dimensional) transportation problem with chance constraints has been presented.? After converting the proposed model to a deterministic model, fuzzy programming with nonlinear membership function is used to find the solution.? Assuming the demand, availability and conveyance capacity are normal random variables the methodology has been presented.? In some cases assuming the demand as log-normal or uniform random variable, methodology also has been presented.? The method leads to efficient solutions as well as the best compromise solution.? An example is included to illustrate the methodology.? Fuzzy programming with nonlinear membership function is compared to fuzzy programming with linear membership function with an example.
Keywords:
Multi criteria decision making, stochastic solid transportation problem, chance constraints, fuzzy programming, efficient solution, compromise solution, membership function.
T-fuzzy N-subgroups and T-fuzzy Ideals of N-groups
L. K. Barthakur
Department of Mathematics, Morigaon College, Morigaon, Assam, India
G. K. Barthakur
Department of Mathematics, G. K. B. College, Morigaon, Assam, India
H. K. Saikia
Department of Matheamtics, Gauhati University, Guwahati-781014 India
E-mail: hsaikia@yahoo.com
Abstract:
Our attempt is to extend the notion of fuzzyN-subgroups and fuzzy ideals of nearing group E?to T-fuzzy N-subgroups and T-fuzzy ideals.? In this paper we investigate various properties of these fuzzy substructures.
Key words:
Near-ring, N-group, T-fuzzy N-subgroup, T-fuzzy normal subgroup, T-fuzzy ideal. |