The Journal of Fuzzy Mathematics
Volume 22, Number 4, December 2014
CONTENT
DETAILS
Fuzzy Anti Inner Product Space and Its Properties
Parijat Sinha
Department of Mathematics, V. S. S. D. College, Kanpur
Divya Mishra and Ghanshyam Lal
Department of Mathematics, M. G. C. G. University, Satna (INDIA) E-mail: dvmishra275@gmail.com
Abstract:
The purpose of this paper is to introduce the concept of fuzzy anti inner product function in a linear space and its properties. The relative fuzzy anti norm with respect to fuzzy anti inner product is defined and parallelogram law and polarization identity has been proved.
Key words:
Fuzzy anti inner product space, ¦Á-anti norm, Parallelogram law.
Fuzzy Farthest Points in The Space of Fuzzy Continuous Functions
Alireza Kamel Mirmostafaee
Department of Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran E-mail: mirmostafaei@ferdowsi.um.ac.ir
Abstract: Let (X,N) be a fuzzy normed space and A be a fuzzy bounded subset of X. We define a notion for the space of continuous functions from a compact space X to a fuzzy normed space (Y,N) . We will show that in this space, every set with fuzzy unique farthest point property is singleton.
Key words and phrases:
Fuzzy normed spaces, space of fuzzy continuous functions, fuzzy remotal set.
A Fixed Point Theorem on ¦Å-chainable Generalized Fuzzy Metric Space
A. Deb Ray and Mita Das
Department of Mathematics West Bengal State University Barasat,
North 24 Paraganas Kolkata-700126, INDIA E-mail: atasi@hotmail.com, mitadas1295@gmail.com
Abstract:
Two special type of subclasses of generalized fuzzy metric spaces (in short, ), named as ¦Å-chainable and ¦Å-chainable generalized fuzzy metric spaces, for each are introduced in this paper. It is shown by examples that an ¦Å-chainable is not necessarily a fuzzy metric space and a need not be ¦Å-chainable. Besides, the class of all ¦Å-chainable spaces are strictly contained in the class of all -chainable spaces. A fixed point theorem for a typical class of functions, termed as fuzzy (¦Å,l) -uniform local contraction has been established in (¦Å,l)-chainable spaces.
Key words: Generalized fuzzy metric space (GFMS), T-orbitally complete GFMS,¦Å-chainable GFMS, fuzzy (¦Å,l)-uniform local contraction.
On Homotopy and Contractibility in Vague Fuzzy Digital Structure Spaces
R. Narmada Devi, E. Roja and M. K. Uma
Department of Mathematics, Sri Sarada College for Women, Salem, Tamil Nadu, India.E-mail:narmadadevi23@gmail.com
Abstract:
In this paper, the concepts of vague fuzzy digital structure homotopy and vague fuzzy digital structure contractible spaces are introduced. Some interesting properties are discussed.
Key words:
Vague fuzzy digital structure continuous functions, vague fuzzy digital structure homotopy, vague fuzzy digital structure contractile spaces, vague fuzzy digital structure retraction functions and vague fuzzy digital structure weak functions.
Representation of Locally m-convex Intuitionistic Fuzzy Topological Algebras
S. Padmapriya, M. K. Uma and E. Roja
Department of Mathematics, Sri Sarada College for Women, Salem, Tamil Nadu, India.E-mail:priyasathi17@gmail.com
Abstract:
The purpose of this paper is to introduce the concepts of intuitionistic fuzzy topological algebras, idempotent, absolutely convex, absolutely m-convex, locally m-convex intuitionistic fuzzy topological algebras, intuitionistic fuzzy Hausdorff spaces, intuitionistic fuzzy normed* algebras, intuitionitic fuzzy norm*, intuitionistic fuzzy normed* algebra with identity, intuitionistic fuzzy normed* topology, intuitionistic fuzzy topological groups are introduced and studied. Some interesting properties are also discussed. In this paper, our purpose is to introduce a particular kind of an intuitionistic fuzzy normed* algebra, viz. intuitionistic fuzzy normed* algebras, and to use an intuitionistic fuzzy normed* algebras to represent locally -convex intuitionistic fuzzy topological algebras.
Key words:
Intuitionistic fuzzy topological algebra, idemotent, absovlutely convex, absolutely m-convex, local m-convex intuitionistic fuzzy topological algebra, intuitionistic fuzzy Hausdorff space, intuitionistic fuzzy normed* algebra, intuitionistic fuzzy norm*, intuitionistic fuzzy normed* algebra with identity, intuitionistic fuzyz normed* topology, intuitionistic fuzzy topological group.
Soft Fuzzy Overlapping Families via Dimension Theory
D. Vidhya, E. Roja and M. K. Uma
Department of Mathematics Sri Sarada College for Women, Salem-16 Tamil Nadu, India.E-mail:vidhya.d85@gmail.com
Abstract:
In this paper the concept of overlapping families of soft fuzzy sets and the order of a family of soft fuzzy sets leading to a coherent theory of covering dimension in soft fuzzy topological spaces are introduced and studied. In this connection, the concept of soft fuzzy semicrisp space is introduced which provides a suitable framework for the study of soft fuzzy dimension function in the soft fuzzy setting.
Key words:
Soft fuzzy overlapping, soft fuzzy order, soft fuzzy dimension function, soft fuzzy semicrisp space.
Introducing Soft Statistical Measures
Ranjit Biswas
Department of Computer Science, Jamia Hamdard University, Hamdard Nagar, New Delhi-110062, INDIA.E-mail: ranjitbiswas@yahoo.com
Abstract:
In the subject area of Statistics, population can be divided into two categories: R-population and NR-population. If a population is of real number data (n-dimensional) then it is of category ¡®R-population¡¯, and if a population does not fall into the category of ¡®R-population¡¯ then it is of the category ¡®NR-population¡¯. Thus a ¡®NR-population¡¯ could be a collection of the type of data viz. collection of 10 sounds (blows) from a bus horn, collection of a large number of handwritten characters of the English character ¡°A¡±, collection of 250 paints of beautiful ¡®Tajmahal¡¯ by 250 number of under-10 aged children, etc. The various classical measures in statistics, even in particular the three fundamental measures: mean (arithmetic mean), median and mode, in their present format of respective definitions, are undefined measures for NR-population data. But there are a lot of significant analysis, survey, estimations, conclusions, etc. being carried out by the analysts/statisticians for various important objectives over such type of NR-populations in real life. The failure of these classical measures to play any role over NR-populations has been a hidden truth so far to the statisticians or analysts. The ¡°NR-statistics¡± is a new direction in statistics initiated in [14] by formulating a number of new statistical measures, new theories, and new results for both kind of populations (the classical R-populations and the newly introduced NR-populations). Thus the subject ¡®statistics¡¯ can be meaningfully divided into two: R-statistics (the existing statistics popularly known as ¡®mathematical statistics¡¯) and NR-statistics. It is claimed that the ¡®Theory of NR-statistics¡¯ will play fundamental important roles in many areas of engineering, technology, statistics, mathematics, management science, medical science, social science, etc. to list a few only out of many; and will widen the present universe of working-domains of the statisticians, analysts and the scientists, will open a new gate for huge and rigorous research in future.
Key words:R-population, NR-population, R-statistics, NR-statistics, m-mapping, m1-mapping, plot function, metric measures, linear measures, region measures, nucleus, coefficient of homogeneity, coefficient of heterogeneity.
On Some Operations on Bounded Fuzzy Lattices
Ivan Mezzomo
Department of Mathematical Sciences, Technology and Humanities-DCETH Rural Federal University of Semi-Arid-UFERSA 59.515-000, Angicos, Rio Grande do Norte, Brazil.E-mail: imezzomo@ufersa.edu.br
Benjamin Bedregal and Regivan H. N. Santiago
Department of Informatics and Applied Mathematics-DIMAp Federal University of Rio Grande do Norte-UFRN 59.072-970, Natal, Rio Grande do Norte, Brazil.E-mail: bedregal@dimap.ufrn.br and regivan@dimap.ufrn.br
Renata H. S. Reiser
Center of Tecnological Development-CDT, Federal University of Pelotas-UFPel, Pelotas, Rio Grande do Sul, Brazil 96010-610.E-mail: reiser@inf.ufpel.edu.br
Abstract:
We consider the notion of fuzzy lattice introduced by Chon (Korean J. Math 17 (2009), No.4, 361-374), and define the operations of product, collapsed sum, lifting, opposite, interval and intuitionist on bounded fuzzy lattice analogous to the classical theory. Finally, we prove that these operations on bounded fuzzy lattices are also bounded fuzzy lattices.
Key words: Fuzzy lattices, Operations, Product, Collapsed sum, Lifting, Opposite, Interval, intuitionist.
Multi-stage Mixed System Reliability via Random Fuzzy, Possibility and Credibility Measure
A. K. Shaw and T. K. Roy
Department of Mathematics, Bengal Engineering and Science University, Shibpur Howrah-711103, West Bengal, India. E-mail address:ashokshaw2001@yahoo.co.in
D. K. Jana
Department of Applied Science, Haldia Institute of Technology, Haldia Purba Midnapur-721657, West Bengal, India. E-mail:dipakjana@gmail.com
R. N. Yadava
Director, Environment Management and Human Welfare Council Bhopal-INDIA. Ex. Director, Advance Material Process Research Institute, (AMPRI-CSIR) Bhopal-INDIA. E-mail address:dryadava@gmail.com
Abstract: In this paper, a multi-stage mixed problem has been formulated in different environment viz. crisp, random, fuzzy and random fuzzy and solved. Here, costs and resources are random, fuzzy and random fuzzy in natures. The optimum multi-stage mixed problem is formulated as a decision making model optimizing possibilistic value at risk(pVaR) by incorporating the concept of value at risk(VaR) into possibility and necessity measure theory. The reduced deterministic constrained problem is solved using generalized reduced gradient(GRG) method (LINGO-10). Some particular models have been presented. The model is illustrated with numerical example.
Key words and phrases: Reliability, Random Fuzzy variables, Possibility, Necessity, Credibility.
Soft Fuzzy Overlapping Families via Dimension Theory
D. Vidhya, E. Roja and M. K. Uma
Department of Mathematics Sri Sarada College for Women, Salem-16 Tamil Nadu, India. E-mail:vidhya.d85@gmail.comm
Abstract: In this paper the concept of overlapping families of soft fuzzy sets and the order of a family of soft fuzzy sets leading to a coherent theory of covering dimension in soft fuzzy topological spaces are introduced and studied. In this connection, the concept of soft fuzzy semicrisp space is introduced which provides a suitable framework for the study of soft fuzzy dimension function in the soft fuzzy setting.
Key words: Soft fuzzy overlapping, soft fuzzy order, soft fuzzy dimension function, soft fuzzy semicrisp space.
Generalized Continuity in Fuzzy Ideal Topological Spaces
S. S. Thakur, Anita Singh Banafar
Department of Applied Mathematics Jabalpur Engineering College Jabalpur (M.P.)-482011 INDIA. E-mail:samajh_singh@rediffmail.com, Email: anita.banafar1@gmail.com
Shailendra Singh Thakur
Department of Computer Science and Engineering Gyan Ganga College of Technology Jabalpur (M.P.) 482001 INDIA. E-mail:ssthakurji@gmail.com
Abstract:In this paper we introduce the concepts of fuzzy Ig-continuous and fuzzy Ig -open mappings in fuzzy ideal topological spaces and obtain some of their basic properties and characterizations.
Key words: Fuzzy ideal topological spaces, fuzzy Ig -closed sets and fuzzy Ig -continuous mappings.
Disconnectedness in An Intuitionistic Fuzzy Structure Rings
R. Narmada Devi, E. Roja and M. K. Uma
Department of Mathematics, Sri Sarada College for Women, Salem, Tamil Nadu, India. Email: :narmadadevi23@gmail.com
Abstract: In this paper, the concepts of an intuitionistic fuzzy disconnected structure space and intuitionistic fuzzy extremally disconnected structure space are introduced. Some interesting properties of disconnectness and extremally disconnectedness in an intuitionistic fuzzy structure ring are studied.
Key words: Intuitionistic fuzzy interior, intuitionistic fuzzy closure, structure space, intuitionistic fuzzy disconnected structure space and intuitionistic fuzzy extremally disconnected structure space.
On Preserving Fuzzy Ig-closed Sets
S. S. Thakur
Department of Applied Mathematics Jabalpur Engineering College Jabalpur (M. P.)-482011 INDIA.E-mail: samajh_singh@rediffmail.com
Abstract: In this paper we introduce the concepts of fuzzy Ig -continuous and fuzzy Ig -open mappings in fuzzy ideal topological spaces and obtain some of their basic properties and some results on preservation of fuzzy Ig -closed sets using these mappings.
Key words: Fuzzy ideal topological spaces, fuzzy Ig-closed sets and fuzzy Ig -continuous and fuzzy Ig -closed mappings.
On Fuzzy Bi-ideal and it¡¯s Extension in G-near-rings NIA Left Operator Near-rings
N. Meenakumari and C. Parameswari
Department of Mathematics, A. P. C. Mahalaxmi College for Women, Thoothukudi-2
Abstract: The purpose of this paper is to study fuzzy bi-ideal and it¡¯s extension in a restricted type of G-near-rings via left operator near-rings.
Key words: Fuzzy bi-ideals, Left Operator near-rings and Fuzzy bi-ideal extension
A Study on IF Regular Closed mx Set
Sharmistha Bhattacharya (Halder) and Jayanti Tripathi
Department of Mathematics Tripura University, Suryamaninagar, Tripura, INDIA-799022.E-mail:halder_731@rediffmail.com
Abstract: The purpose of this paper is to study on the new concept of IF regular closed mx set in IF topological space. Some characterization theorems and properties of this newly constructed set are studied. Also it can be shown that there cannot exist two IF regular closed mx sets A and B if A¡ÉB¡Ù0, A or B. This indicates a difference between IF set and fuzzy set. Also IF completely mx continuous function etc are studied.
Key words: Intuitionistic fuzzy mx structure, IF topological space, IF supra continuous function, IF completely continuous function etc.
On Fuzzy Upper And Lower Semi-continuous Multifunctions
S. E. Abbas
Department of Mathematics, Faculty of Science, Jazan University, Saudi Arabia.
M. A. Hebeshi and I. M. Taha
Department of Mathematics, Faculty of Science, Sohag Unviersity, Egypt.E-mail:imtaha2010@yahoo.com
Abstract:
Our aim in this paper is to introduce the concepts of upper and lower inverse of a fuzzy multifunction and investigate some properties of them. Fuzzy upper and fuzzy lower semi-continuous multifunctions are introduced on fuzzy topological spaces in Sostak sense. Also, many interesting properties of fuzzy upper and fuzzy lower semi-continuous multifunctions are presented, including the composition and union of fuzzy upper and fuzzy lower semi-continuous multifucntions and the compactness preserving property of -continuous and compact-valued multifunctions.
Key words: Fuzzy topology, fuzzy multifunction, upper and lower semi-continuity, composition and stratification.
Fuzzy Scott Continuous Multifunctions and Their Fixed Points
A. F. Sayed
Mathematics Department, Al-Lith University College, Umm Al-Qura University P. O. Box 122, Al-Lith 21961, Makkah Al Mukarramah, Kingdom of Saudi Arabia.E-mail: dr.afsayed@hotmail.com
Abstract: In this paper, we introduce the concept of fuzzy Scott continuity of multifunctions on fuzzy domains, which is characterized as the definition of a fuzzy Scott continuity given in ([29], [30]) if it becomes a single-valued function. Fixed Points of fuzzy Scott continuous multifunctions and some properties are investigated.
Key words: Fuzzy domain, fuzzy Scott topology, fuzzy Scott continuous multifunction, fixed points, minimum fixed point, maximal element.
A Note on Fuzzy Soft Semi Open Sets and Fuzzy Soft Semi Continuous Functions
Ramkrishna Prasad Chakraborty and Prakash Mukherjee
Department of Mathematics, Hijli College, Hijli, Kharagpur, Paschim Medinipur-721301, West Bengal, India.E-mail: ramda2004@rediffmail.com, prakashmukherjee25@gmail.com
Pradip Kumar Gain
Department of Mathematics, Kharagpur College, Inda, Kharagpur, Paschim Medinipur-721305, West Bengal, India.E-mail: pradip_gain@rediffmail.com
Abstract: In this article semi-open and semi-closed sets on a fuzzy soft topological space are introduced and some properties have been studied. Fuzzy soft semi closure and fuzzy soft semi interior operators are also introduced and studied. Semi-continuous, semi-open, semi-clsoed and irresolute fuzzy soft functions on a fuzzy soft topological space are introduced and characterized.
Key words: Fuzzy soft function, fuzzy soft topology, fuzzy soft closure and interior, fuzzy soft continuity, fuzzy soft semi open (semi closed) sets, fuzzy soft semi closure and semi interior, fuzzy soft semi q-nbd, fuzzy soft semi continuous (semi open, semi closed) functions fuzzy soft irresolute function.
On Pairwise Connectedness and Pairwise Disconnectedness in Vague Fuzzy Digital Bi-structure Spaces
R. Narmada Devi, E. Roja and M. K. Uma
Department of Mathematics, Sri Sarada College for Women, Salem-636016 Tamil Nadu, India
E-mail: narmadadevi23@gmail.com
Abstract: In this paper, the concepts of pairwise vague fuzzy digital connected structure space, pairwise vague fuzzy digital super connected structure space, pairwise vague fuzzy digital strongly connected structure space, pairwise vague fuzzy digital extremally disconnected sstrcuture space and pairwise vague fuzzy digital totally disconnected structure space are introduced. Some interesting properties are established.
Key words: Pairwise vague fuzzy digital connected structure space, pairwise vague fuzzy digital super connected structure space, pairwise vague fuzzy digital strongly connected structure space, pairwise vague fuzzy digital extremely disconnected structure space and pairwise vague fuzzy digital totally disconnected structure space.
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