The Journal of Fuzzy Mathematics
Volume 18, Number 4, December 2010
CONTENT
DETAILS
Fuzzy Partition and Fuzzy Algebraic Partition of Fuzzy Subsets
Asok Kumar Ray
Department of Mathematics, Dibrugarh University, Dibrugarh-786004, Assam, INDIA
E-mail: akraydu@sify.com
Abstract:
In this paper, we introduce the concepts of fuzzy partition of a fuzzy subset and the fuzzy algebraic partition of a fuzzy subset.
Keyword:
Fuzzy Partition, Fuzzy Algebraic Partition, Proximity Relation, Similarity Relation.
On Fuzzy Faintly Semi-continuous Functions
G. Palani Chetty
Department of Mathematics, I. R. T. Polytechnic College, Krishnagiri-635108, Tamilnadu, India
G. Balasubramanian
Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai-600005, India.
Abstract:
The aim of this paper is to introduce a new generalization of fuzzy faintly continuous functions called fuzzy faintly semi-continuous functions and also we have introduced and studied weakly fuzzy semi-continuous functions. Several characterizations of fuzzy faintly semi-continuous functions are given and some interesting properties of the abovefunctions are discussed.
Keyword:
Fuzzy faintly semi-continuous functions, fuzzy -open functions, fuzzy semi-compact, fuzzy -compact, fuzzy space, weakly fuzzy semi-continuous functions, some what fuzzy faintly semi-continuous functions.
Ishikawa Type Perturbed Iterative Algorithm for Generalized Variational-like Inclusions for Fuzzy Mappings
Rais Ahmad
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
E-mail: raisain@lycos.com
Abstract:
In this paper, we study a new class of generalized variational-like inclusions for fuzzy mappings. We have established an equivalence of generalized variational-like inclusions for fuzzy mappings with some fixed point problems and develop Ishikawa type perturbed iterative algorithm for this class of generalized variational-like inclusions by using the definitions of multivalued relaxed Lipschitz and relaxed monotone operators. Convergence criteria is also discussed. Some examples are given.
Keyword:
Variational-like inclusions, Algorithm, Fuzzy mapping, Relaxed Lipschitz operator, Relaxed monotone operator.
Fuzzy-valued Variable and Regression Equation
Srabani Sarkar
Department of Mathematics, Vivekanada College for Women Barisa, Kolkata-700008, India
E-mail: srabani_sarkar@rediffmail.com
Madhumangal Pal
Department of Applied Mathematics with Oceanology and Computer Programming. Vidyasagar University, Midnapore-721102, India.
E-mail: mmpalvu@gmail.com
Abstract:
Every fuzzy set is concept as well as context dependent. In other words every fuzzy set is a variable. When a fuzzy set can be represented (in meaning) in terms of other fuzzy sets, it is called a fuzzy-valued variable. In this paper we introduce the concept of fuzzy-valued variable and the difference between fuzzy random variable and the newly introduced fuzzy-valued variable is explained.
This paper also deals with regression equation related to fuzzy-valued variable.
In classical statistics regression equations are considered to be a kind of relation between two variables so that if the value of one variable is known, using the equations, corresponding value of the other variable can be found out.
In fuzzy mathematics too, two fuzzy variables should be related by some general relation, which can be termed as fuzzy regression.
In the existing literatures, fuzzy regression equations are defined to relate fuzzy sets through crisp coefficients. This paper presents and approach to relate fuzzy-valued variables through regression equation with fuzzy regression coefficients. Though the classical least-square approach is used here, conceptually it is more generalized than the usual approach of fuzzy regression.
Representation of T-fuzzy Finite Distributive Lattices by means of T-fuzzy Priestley Spaces
Abdelaziz Amroune
Department of Mathematics, M¡¯slis University, P. O. Box 166 M¡¯Sila 28000, Algeria
E-mail: aamrounedz@yahoo.fr
Abstract:
The purpose of this paper is to show that the dual category of finite T-fuzzy Priestley spaces.
Keyword:
T-fuzzy ordered relation, Fuzzy ordered sets, Fuzzy lattices, Fuzzy Priestley spaces, Homomorphism of fuzzy lattice, Homomorphism of fuzzy Priestley spaces.
Convergence Class of Generalized Fuzzy Filters
K. K. Mondal
Department of Mathematics, Kurseong College, Kurseong-734203, West Bengal, INDIA
S. K. Samanta
Department of Mathematics, Visva Bharati, Santiniketan-731235, West Bengal, INDIA
E-mail: syamal_123@yahoo.co.in
Abstract:
In this paper, some results on convergence of generalized fuzzy filters are derived in L-fuzzy topological spaces and characteristic properties of two types of convergence classes are studied.
Keyword:
Fuzzy belongingness, fuzzy quasi-coincidence, gradation of openness, gradation of neighborhoodness, L-fuzzy topological spaces, g-filters.
Study of Some Aspects of Fuzzy H-continuum
N. R. Das
Department of Mathematics, Gauhati University Guwahati 781014, Assam, India
Brojen Das
Department of Mathematics, M. C. College, Barpeta, Assam, India
E-mail: brojen.das@rediffmail.com
Abstract:
This paper deals with the study of the behavior of H-continuum in fuzzy topological spaces. The study of H-continuum in general topology was introduced by S. Ganguy and T. Bandopadhyay in the year 1991. For H-continuum we have considered H-closedness (or H-set) and -connectedness instead of compactness and connectedness respectively. In this paper several properties of H-continuum are established in fuzzy setting. Our endeavor will continue to explore more results in this direction.
Keyword:
-cluster point, -closure, H-set, H-closed, -separation, product related.
On Some New Type of Summable and Statistically Convergence Difference Sequences of Fuzzy Numbers
Hemen Dutta
Department of Mathematics, A. D. P. College, Nageaon-782002, Assam, INDIA
E-mail: hemen_dutta08@rediffmail.com
Abstract:
In this article we introduce and study the concepts of -strongly -summable and -statistical -convergence of sequence of fuzzy numbers. Further we extend these notions to -strongly -summable and -statistical -convergence of sequence of fuzzy numbers and prove that the space of ¡-strongly ¡-summable sequences are Banach spaces for ¡.
Keyword:
Sequence of fuzzy numbers; Difference sequence space; Statistical convergence; Summability.
Intuitionistic Fuzzy Set Connected Mappings
S. S. Thakur
Department of Applied Mathematics, Government Engineering College, Jabalpur (M.P.) 482011 India.
Email:samajh_singh@rediffmail.com
Mahima Thakur
Department of Applied Mathematics, Government Engineering College, Jabalpur(M.P.) 482011 India.
Email:mahimavtlakue@gmail.com
Abstract:
The aim of this paper is to introduce and discuss the concepts of intuitionistic fuzzy connectedness between intuitionistic fuzzy sets and intuitionistic fuzzy set connected mappings in intuitionistic fuzzy topological spaces.
Keyword:
Intuitionistic fuzzy sets, Intuitionistic fuzzy topology, Intuitionistic fuzzy closed sets, Intuitionistic fuzzy open sets, intuitionistic fuzzy connectedness between intuitionistic fuzzy sets and Intuitionistic fuzzy set connected mappings.
Fuzzy Reflexive Spaces
T. Bag and S. K. Samanta
Department of Mathematics, Visva-Bharati Santiniketan-731235 West Benegal, INDIA
Email:syamal_123@yahoo.co.in
Abstract:
In this paper a definition of fuzzy reflexive space is given and some properties of such spaces are studied. A concept of fuzzy uniform normal structure is introduced in a fuzzy normed linear space and some results on reflexivity of a fuzzy normed linear space are derived from this structure.
Keyword:
Fuzzy reflexive space, fuzzy uniform normal structure.
On Fuzzy n-normed Spaces
Renu Chugh and Sushma
Department of Mathematics, M.D. University, Rohtak-124001 INDIA
Email:lathersushma@yahoo.com
Abstract:
The aim of this paper is first to give a simple way to derive fuzzy -norm from fuzzy n-norm and then prove that any fuzzy n -normed linear space is an fuzzy -normed linear space. We also establish some results regarding convergence and completeness in the fuzzy n -normed linear spaces and use these results to prove a fixed point theorem in fuzzy n -Banach spaces.
Keyword:
Convergence, completeness, fuzzy ¡-normed space, fixed point, ¡-normed linear spaces
Application of Fuzzy Decision Making to Smoking Problem
Yoshiki Uemura
Fac. Of Education, Mie University
Abstract:
We often fall into a state of waver. For instance, smokers know that smoking harms their health in the head. However they feel that they desire to smoke in order to compuse themselves at heart. If they are struck by illnesses with pneumonia or lung cancer (observations), there gradually occurs a waver whether they should give up smoking or not. We can describe the modeling of this case in the process that two states of nature in the head and at heart, however one is buried and then gradually restored by observations, move into two conflicting states of nature. Hence, we can interpret that 1 of the second row and the second column becomes a fuzzy number by placing a transitive matrix from 1 to 2 into a unit matrix, if we assume that the occurrence probability of the other is zero although only one emerges in appearance at an initial stage in this paper, we determine a state of waver in a fuzzy event using this fuzzy transitive matrix. Furthermore we propose a fuzzy decision making rule in keeping with the theory of maximum expected utility using the probability of a fuzzy event, under the premises that a decision maker will set a distribution of preliminarily probability, a multi-attribute utility function and importance a t two states of nature. We also often fall into silence as well as a state of waver. After that we make a decision through confusion in most cases. In silence, cool mind runs parallel with warm heart. Traversing over them, it comes about that a fuzzy event which is called ¡°waver¡±. In other words, two states of nature move conflicted and are covered in a fuzzy event. In confusion, we consider that states of nature which move conflicted not only invert but also transform warm heart into dry mind. Thus, we can derive a fuzzy function at present from fuzzifying a transitive matrix from silence to confusion, absorbing noise, and taking an expectation between this membership[ function and a multi-attribute utility function. It shows that we can calculate an expected utility by using both probability of a fuzzy event and subjective importance of decision maker for two states of nature, we can obtain an optimum action based on a theory of maximum expected utility.
Keyword:
Fuzzy event, bays decision rule, fuzzy observation , smoking problem.
Fuzzy Complete Weakly -irresolute Functions
N. Gowrisankar
70/232£¬Kollupetti Street, M. Chavady, Thanjavur-613001, Tamil Nadu, India
E-mail: gowrisankartnj@gmail.com
Abstract:
In this paper, fuzzy -closed sets are used to define and investigate a new class of fuctions called fuzzy compeletely weakly -irresolute. Relationships between the new class and other classes of functions are established.
Keyword:
Fuzzy topology, fuzzy -open sets, fuzzy -irresolute functions.
On Fuzzy Contra--continuity
N. Gowrisankar
70/232£¬Kollupetti Street, M. Chavady, Thanjavur-613001, Tamil Nadu, India
E-mail: gowrisankartnj@gmail.com
Abstract:
In this paper, fuzzy -open sets and -closed sets are used to define and investigete a new class of functions in the fuzzy topological space. Relationships between this new class and other classes of functions are established.
Keyword:
Fuzzy Contra--continuous functions, fuzzy -closed space, fuzzy graphs.
Fuzzy Totally -continuous Functions
N. Gowrisankar
913
70/232£¬Kollupetti Street, M. Chavady, Thanjavur-613001, Tamil Nadu, India
E-mail: gowrisankartnj@gmail.com
Abstract:
In this paper, fuzzy -open sets and -closed sets are used to define and investigete a new class of functions called fuzzy totally -continuous functions. Relationships between the new class and other classes of function are established.
Keyword:
Fuzzy topological spaces, fuzzy -open set, fuzzy -closed set, fuzzy totally -continuity.
Separation Axioms of R-generalized Fuzzy ideal Closed Sets
M. Zahran
Department of mathematics, Faculty of science, Taibgh University, K. S. A. Egypt
S. E. Abbas
Department of mathematics, Faculty of science, Soheg University, Soheg 82524, Egypt
S. A. Abd El-Baki
Department of mathematics, Faculty of science, Assiut University, Assiut 71524, Egypt
Y. M. Saber
Department of mathematics, Faculty of science, Al-Azhar University, Assiut 71524, Egypt
Abstract:
In this paper, we difine concepts where and where . In Sostak fuzzy topological spaces. We investigate some properties of them. Also, we introduce and study, -generalized fuzzy -regular and -generalized fuzzy -normal. Moreover, we investigate the relationships between these classes of functions.
Keyword:
, , -generalized fuzzy -regular, -generalized fuzzy -normal.
On Anti Fuzzy Ideals of BCK-algebras
B. L. Meng
Department of Basic Courses, Xian University of Science and Technology, Xian 710054. P. R. China
E-mail: mengbl_100@yahoo.com
M. Akram
Punjab University College of Information Technology. University of the Punjab, Old Campus. P. O . Box 54000, Labhore, Pakistan.
E-mail: m.akram@pucit.edu.pk
Abstract:
In this paper we given an equivalent condition of anti fuzzy ideals of BCK-algebras and obtain some interesting properties. In particular, we give a procedure for generating and anti fuzzy ideal by a fuzzy subset of BCK-algebra. Finally we give characterizations of Noetherian BCK-algebras by anti fuzzy ideals.
Keyword:
BCK-algebra, fuzzy ideal, anti fuzzy ideal, level subset, Noetherian BCK-algebras
Fuzzy Banach Algebra with Felbin Type Fuzzy Norm
Ramkrishna Thakur and S. K. Samanta
Department of Mathematics, Visva Bharati, Santiniketan-731235, West Bengal, INDIA
E-mail: syamal_123@yahoo.co.in
Abstract:
In this paper a definition of fuzzy Banach Algebra with Felbin type fuzzy norm is given. Some results involving the relation between fuzzy Banach algebra and a family of crisp Banach algebras have been obtained. It is shown that the space of fuzzy bounded linear operators on a fuzzy normed linear space form a fuzzy Banach algebra.
Keyword:
Fuzzy norms, fuzzy normed algebra, fuzzy Banach Algebra, fuzzy bounded linear opertator.
The Fuzzy Abridged Life Table
Kangkana Sarmah Baruah, Aparna Dutta and Hemanta K. Baruah
Department of Statistics, Gauhati University, Gauhati-781014, Assam, India
Abstract:
An abridged life table yields nearly the same information as a complete life table and it has the advantages of being much shorter and involving fewer calculations. In this article, fuzzification of the abridged life table has been taken into consideration. We have studied the effect of fuzziness on number of deaths, person years generated in age interval, total person years lived by survivors and life expectancy. The findings have been discussed with one practical example.
Keyword:
cut, membership function, fuzzy abridged life table.
Fuzzy Topological Algebra on Function Space
Tazid Ali
Department of Mathematics, Dibrugarh University Dibrugarh-786004, Assam, India
E-mail: tazidali@yahoo.com
Abstract:
In this paper we have introduced the notion of fuzzy topological algebra and investigated some its properties. Then we have constructed fuzzy topological algebra on function space.
Keyword:
Fuzzy topological algebra, Function space.
Ordered Intuitionistic Fuzzy Soft Sets
Sunny Joseph Kalayathankal
Department of Mathematics, K. E. College, Mannanam Kottayam-686561, Kerala, India
E-mail: sunnyjose2000@yahoo.com
G. Suresh
Department of Mathematics, University of Kerala,Kariavattom Thiruvananthapuram-695581, Kerala, India
P. B. Vinodkumar
Department of Mathematics, Rajagiri School of Engineering, Technology Kakkanad, Cochin-682039, Kerala, India
Abstract:
In this paper we difine ordered intuitionistic fuzzy soft sets and establish some results on them.
Keyword:
Soft set, Fuzzy soft set, Intuitionistic fuzzy soft set.
A Characterization of Blocks in Fuzzy Graphs
Sunil Mathew and M. S. Sunitha
Department of Mathematics Notional Institute of Technology, Calicut-673601, India
E-mail: sm@nitc.ac.in
Department of Mathematics Notional Institute of Technology, Calicut-673601, India
E-mail: sunitha@nitc.ac.in
ST-subgroups
Arpita Das, Prasenjit Mandal and A. S. Ranadive
Department of Pure and applied mathematics, Guru Ghasidas University, Bilaspur (C. G.) Inida
E-mail: prasenjitmandal08@yahoo.com
Fuzzy Minimal Structures, Fuzzy m-regularity, Fuzzy m-normality and Fuzzy Bitopological Spaces
Anjan Mukherjee
Department of Mathematics, Tripura University, Surjyamaninagar, A gartala-799130 TRIPURA, India
E-mail: anjan2002_m@yahoo.co.in
Abstract:
The purpose of this paper is to study some more results on fuzzy minimal structures and fuzzy m-open functions. We obtain some characterizations of a function which is fuzzy m-open at a fuzzy point of the range of the function and also characterize the set of all fuzzy points at which a function is not fuzzy m-open.
The notion of -fuzzy open function is introduced and genetalize this concept in fuzzy bitopological spaces. Lastly the concepts of fuzzy m-regular space and fuzzy m-normal space are introduced and some preservation theorems of fuzzy m-regularity, fuzzy m-normality are also studied.
Keyword:
Fuzzy minimal structures, fuzzy m-open set, - -fuzzy open function, fuzzy m-continuity, fuzzy bitopological space, fuzzy m-regular space, fuzzy m-normal space. |