THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 21, Number 3, September 2013

CONTENT

DETAILS

Fuzzy Bioperations on Fuzzy Topological Space
N. R. Das
Department of Mathematics,Gauhati University-14,Assam,India.
E-mail address: nrd47@yahoo.co.in
B. Kalita
Department of Mathematics,Dudhnoi College,Dudhnoi,Goalpara,Assam,India.
E-mail address: kalitabidyut@yahoo.com
Abstract:
In this paper we generalized the concept of fuzzy operation [1] on fuzzy topological space to fuzzy bioperations. We defined fuzzy bioperation-open sets and fuzzy bioperation-closures. We also obtained some Properties of fuzzy bioperation-open sets and fuzzy bioperation-closures.
Keywords:
Fuzzy -open sets, fuzzy -closed sets and fuzzy -closures.

On Interval-valued Fuzzy Semiprime Ideals of A Semiring
T. K. Dutta
Department of Pure Mathematics,University of Calcutta.35,Ballygunge Circular Road,Kolkata-700019,India.
E-mail: duttatapankumar@yahoo.co.in
S. Kar and S. Purkait*
Department of Mathematics,Jadavpur University.188,Raja S.C.Mallick Road,Kolkata-700032,India.
E-mail: karsukhendu@yahoo.co.in,*sanuiitg@gmail.com
Abstract:
In this paper we introduce the notion of interval-valued fuzzy semiprime ideal of a semiring, interval-valued fuzzy completely semiprime ideal of a semiring and study some important properties of these two ideals in the context of interval-valued fuzzy algebra.
Keywords:
Semiring, Interval Number, Interval-valued Fuzzy Ideal, Interval-valued Fuzzy Semiprime Ideal, Interval-valued Fuzzy Completely Semiprime Ideal.

On Intuitionistic Fuzzy Continuity and Boundedness
Pinaki Majumdar
Department of Mathematics M.U.C Women's College,Burowan,West-Bengal.
E-mail: pmajumdar2@rediffmail.com
S. K. Samanta
Department of Mathematics,Visva-Bharati,Santiniketn,West-Bengal.
E-mail: syamal_123@yahoo.co.in
Abstract:
In this paper we introduce the notion of intuitionistic fuzzy continuous functions and its variants.? The relation between several types of intuitionistic fuzzy continuous functions is studied.? The notion of intuitionistic fuzzy boundedness has been introduced and its connection with intuitionistic fuzzy continuity has also been studied.
Keywords:
Intuitionistic fuzzy norm; intuitionistic fuzzy continuous function; weakly intuitionistic Cauchy sequence, intuitionistic fuzzy bounded linear operator.

On g# -semi-open Fuzzy Sets and Fuzzy g# -semi-irresolute Maps in Fuzzy Topological Spaces
Sadanand. N. Patil
Department of Mathematics,KLS's,Vdrit,Haliyal,581329.(UK).Karnataka,India.
E-mail address: patilsadu@gmail.com,sada_np@rediffmail.com
Abstract:
In this paper, the class of g#s -closed fuzzy sets are introduced. This class properly placed in between the class of semi-closed fuzzy sets and the class of gs -closed fuzzy sets in fuzzy topological space.
Further, the concept of fuzzy g#s -continuous, fuzzy g#s -irresolute mapping, fuzzy g#s -closed maps, fuzzy g#s -open maps and fuzzy g#s -homeomorphism in fuzzy topological spaces are also introduced, studied and some of their properties are obtained.
Key words and phrases:
g#s -closed fuzzy sets, fg#s -continuous, fg#s -irresolute, fg#s -open, fg#s -closed mappings and fg#s -homeomorphism.

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
Department of Mathematics,KLS's,VDRIT,Haliyal,581329.(UK).(Karnataka-India).
E-mail: patilsadu@gmail.com,sada_np@rediffmail.com
Abstract:
The concept of intuitionistic fuzzy regular Gd continuous function is introduced and intuitionistic fuzzy regular Gd separation axioms are discussed in this paper. Some properties of intuitionistic fuzzy regular Gd continuous function are studied. Intuitionis-tic fuzzy regular GdTi(i=1,2,3 and 4) spaces are introduced and separation axioms are investigated.
Keywords:
Intuitionistic fuzzy regular Gd continuous function and intuitionistic fuzzy regular GdTi(i=1,2,3 and 4) spaces.

On y -closed Fuzzy Sets and Fuzzy y -irresolute Maps in Fuzzy Topological Spaces
Sadanand. N. Patil
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 y -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 y -continuous, fuzzy y -irresolute mappings, fuzzy y -closed maps, fuzzy y -open maps and fuzzy y -homeomorphism in fuzzy topological spaces are also introduced, studied and some of their properties are obtained.
Key words and phrases:
y -closed fuzzy sets, fy -continuous, fy -irresolute, fy -open, fy -closed mappings and fy -homeomorphism.

On Fuzzy -continuous Maps and Fuzzy-homeomorphisms in Fuzzy Topological Spaces
Sadanand. N. Patil
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 -closed fuzzy sets for fuzzy topological spaces. -closed fuzzy sets, which are lies in between the class of closed fuzzy sets, semi-closed fuzzy sets and -closed fuzzy sets. In this paper, we study many basic properties of -closed fuzzy sets together with the relationships of these fuzzy sets with some other fuzzy sets. We introduce two new separation properties, namely fuzzy-spaces and fuzzy-spaces.
Further, the concept of fuzzy -continuous, fuzzy -irresolute mappings, fuzzy -closed maps, fuzzy -open maps and fuzzy -homeomorphism in fuzzy topological spaces are also introduced, studied and some of there properties are obtained.
Key words and phrases:
-closed fuzzy sets, fuzzy-spaces and fuzzy-spaces, -continuous, -irresolute, -open, -closed mappings and -homeomorphism.

On Some New Mappings in Fuzzy Topological Spaces
Sadanand. N. Patil
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 d-g# -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 fuzzy d-g# -continuous, fuzzy d-g# -irresolute mappings, fuzzy d-g# -closed maps, fuzzy d-g# -open maps and fuzzy d-g# -homeomorphism in fuzzy topological spaces are also introduced, studied and some of their properties are obtained.
Key words and phrases:
d-g# -closed fuzzy sets, fd-g# -continuous, fd-g# -irresolute, fd-g# -open, fd-g# -closed mappings and fd-g# -homeomorphism.

On Some Stronger Forms *m -fuzzy Open Maps and *m -homeomorphism Mappings in Fuzzy Topological Spaces
Sadanand. N. Patil
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 *m -closed fuzzy sets for fuzzy topological spaces. This class is a super class of class of the closed fuzzy sets. We introduce and study new space namely fuzzy cTm* -spaces and mTm* -spaces.
Further, the concept of fuzzy *m -continuous, fuzzy *m -irresolute mappings, fuzzy *m -closed maps, fuzzy *m -open maps and fuzzy *m -homeomorphism in fuzzy topological spaces are also introduced, studied and some of there properties are obtained.
Key words and phrases:
*m -closed fuzzy sets, f*m -continuous, f*m -irresolute, f*m -open,f*m -closed mappings and f*m -homeomorphism.

On Some Advances in Stronger Forms of Fuzzy g* -semi-continuous Functions in Fuzzy Topological Spaces
Sadanand. N. Patil
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.
Key words and phrases:
Fuzzy g*s -continuous functions, strongly fuzzy g*s -continuous, perfectly fuzzy g*s -continuous and completely fuzzy g*s -continuous.

Fuzzy Wavelets
Ismat Beg
Center for Mathematics and Statistical Sciences,Lahore School of Economic,Pakistan.
E-mail: ibeg@lums.edu.pk
Khalid Mahmood Aamir
Department of Computer Sciences,Rachna College of Engineering and Technology,Gujranwala,Pakistan.
E-mail: kmaamir@lums,edu.pk
Abstract:
A notion of fuzzy wavelets is introduced by using idea of fuzzy transforms. A detailed procedure for analysis and synthesis of functions through fuzzy wavelets is presented.
Key words and phrases:
Fuzzy wavelets, wavelets, fuzzy multiresolution analysis, fuzzy orthogonality, fuzzy convolution, fuzzy delta function

Intuitionistic Fuzzy Gd-a -locally Continuous Functions
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:
The purpose of this paper is to introduce the concepts of an intuitionistic fuzzy Gd
set and intuitionistic fuzzy Gd-a -locally closed sets. The concepts of an intuitionistic fuzzy eGd-a -locally quasi neighourhood, intuitionistic fuzzy Gd-a -local T2 space, intuitionistic fuzzy Gd-a -local urysohn space, intuitionistic fuzzy Gd-a -local connected space and intuitionistic fuzzy Gd-a -local compact space are introduced and interesting properties are established.
Keywords:
Intuitionistic fuzzy Gd set, intuitionistic fuzzy Gd-a -lcoally closed set, intuitionistic fuzzy e Gd-a -locally quasi neighbourhood, intuitionistic fuzzy Gd-a -locally continuous function, intuitionistic fuzzy Gd-a -local T2 space, intuitionistic fuzzy Gd-a -local urysohn space, intuitionistic fuzzy Gd-a -local connected space and intuitionistic fuzzy Gd-a -local compact space.

Some Results in Probabilistic Normed Space
A. Singadurai
Department of Mathematics,T.D.M.N.S.College,T.Kallikulam,India.
E-mail: singadurai_59@yahoo.co.in
A. Thenmozhi
Department of Mathematics,M.S.University Constituent College,Satankulam,India
Abstract:
The purpose of this paper is to study the basic concepts in probabilistic norm and to study the behaviors of probabilistic normed space. The topology induced by the probabilistic norm and its characters are also studied.
Keywords:
Probabilistic nor, t-norm, continuous triangle mapping.

On Fuzzy Baire Spaces
G. Thangaraj and S. Anjalmose
Department of Mathematics Thiruvalluvar University Vellore-632115,Tamilnadu,India
Abstract:
In this paper the concepts of fuzzy Baire spaces are introduced and characterizations of fuzzy Baire spaces are studied. Several examples are given to illustrate the concepts introduced in this paper.
Keywords:
Fuzzy nowhere dense set, fuzzy first category, fuzzy second category and fuzzy Baire spaces, Fuzzy contra-continuous and fuzzy S-contra pre-continuous functions.

Relation between Fuzzy Normed Linear Space and Generating Space of Quasi-norm Family
G. Rano, T. Bag and S. K. Samanta
Department of Mathematics,Visva-Bharati Shantiniketan-731235,INDIA.
E-mail: gobardhanr@gmail.com,tarapadavb@gmail.com syamal_123@yahoo.co.in
Abstract:
In this paper, we established two decomposition theorems. In the first theorem, we deduce generating space of quasi-norm family (G. S. Q-N. F) from a generalized Bag and Samanta type fuzzy normed linesr space. In the second theorem, from a G. S. Q-N. F, generalized Bag and Samanta type fuzzy normed linear space is derived. Lastly we show that under certain condition these two fuzzy norms are identical.
Keywords:
Fuzzy norm, Quasi-norm, Fuzzy normed linear space, Generating space, t-norm.

A Fuzzy Mathematical Model of Globalization
Annie Gowen, John N. Mordeson, Davender S. Malikand Terry D. Clark
Department of Economics,Department of Mathematics,Department of Political Science Creighton University Omaha,Nebraska 68178.
E-mail: anniegowan@creighton.edu,mordes@creighton.edu,malik@creighton.edu tclark@creighton.edu
Abstract:
The KOF index of Globalization measures the economic, social, and political dimensions of globalization. We use alternative methods to that of KOF to determine measures of the economic, social, and political dimensions of globalization
Keywords:
Globalization; Analytic Hierarchy Process; Guiasu method; Yen method; fuzzy preference modeling; outranking relations

On Soft Metric Spaces
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.
E-mail: syamal-123@yahoo.co.in,syamal.samanta@visva-bharati.ac.in
Abstract:
In this paper an idea of soft metric spaces is given and some of their properties are studied. Soft open, soft closed sets and soft closure are defined and their properties are studied. Completeness of soft metric spaces is also studied and Cantor¡¯s intersection theorem and Banach¡¯s fixed point theorem are proved in soft metric space settings.
Key words and phrases:
Soft sets, soft elements, soft metric spaces, softopen sets, softclosed sets, soft metric topology.

Some Properties of IF Semi mx Open Set
Sharmistha Bhattacharya (Halder) Jayanti Tripathi
Department of Mathematics,Tripura University,Postal code 799130,Tripura,India.
E-mail: halder_731@rediffmail.com
Abstract:
The purpose of this papers is to introduce the concept of IF semi mx open set and to study the topological properties of this set. Also the connection of this set with some other sets is studied in this paper. It may be noted that in a IF topological space generated by IF mx structure, IF semi mx open set and IF semi open sets are similar concepts. We have also introduced the concept of IF semi mx continuous function and given its characterizations.
Keywords:
Intuitionistic fuzzy mx structure, Intuitionistic fuzzy semi mx open set, intuitionistic fuzzy semi mx closed set etc.

On H-closure of Fuzzy Ideals in Hemirings
Chen Gui-ying
School of Mathematics and Science,Liaocheng University,Shandong 252059,China.
E-mail: chengquiying@126.com
Abstract:
In this paper, the concept of h-closure of a fuzzy subset in a hemiring is introduced. By this concept the relationship of the fuzzy ideals and the corresponding fuzzy h-ideals in a hemiring is given. Many important properties about the h-closure of fuzzy left ideals ( resp., fuzzy right ideals, fuzzy ideals, fuzzy bi-ideals and fuzzy generalized bi-ideals) are also investigated. Finally, by the fuzzy h-left ideals, fuzzy h-right ideals, fuzzy h-ideals, and fuzzy h-generalized bi-ideals the h-hemiregular hemirings and h-intra-hemiregular hemirings are characterized. These characterization theorems are the fuzzy version of the corresponding theorems in paper [6] and [7].
Keywords:
Hemirings, H-closure, Fuzzy h-generalized bi-ideals, H-hemregular hemrings