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THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 21, Number 4, December 2013

CONTENT

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Some Fixed Point Theorems in Fuzzy 2-metric Spaces

N. R. Das

Department of Mathematics, Gauhati University, Guwahati, 781001, Assam India.

Email: nrd47@yahoo.co.in

M. L. Saha

Department of Mathematics, Handique Girls' College, Guwahati 781001, Assam India.

Email: mintulal3@rediffinail. com

Abstract: In this paper, we have established two well-known fixed point theorems of Banach and Edelstein in fuzzy 2-metric spaces. Our results are extensions of the results of M. Grabiec [2] to fuzzy 2-metric spaces.

Key words: Fuzzy 2-metric spaces, Complete, Compact, Fixed Point.

 

A Study on Interval Valued Intuitionistic Fuzzy Sets of Type-2

Abhijit Saha* and Anjan Mukherjee**

Department of Mathematics,Tripure University ,Suryamaninagar,Agartala-799022,Tripura, India.

E-mail: * abhijit_aptech2003@yahoo.co.in **anjan2002_m@yahoo.co.in

Abstract: In this paper the concept of interval valued intuitionistic fuzzy sets of type-2 is introduced. The basic properties of these sets are presented. We then define necessary, possibility and reduction operators on these sets and establish some theorems. Also the concept of A-cut on interval valued intuitionistic fuzzy sets of type-2 is discussed.

Key words: Fuzzy sets, intuitionistic fuzzy sets, interval valued intuitionistic fuzzy sets, interval valued intuitionistic fuzzy sets of type-2, necessary, possibility and reduction operators,A-cut.

 

On Fuzzy Pairwise *-pre-continuity and It¡¯s Connection with Fuzzy Pairwise &-pre-continuity in Fuzzy Bitopological Spaces

Anjan Mukherjee* and Bishnupada Debnath**

Department of Mathematics, Tripure University , Suryamaninagar, Agartala-799022, Tripura, India.

E-mail: * anjan2002_m@yahoo.co.in and ** debnath_bishnupada@rediffinail. com

Abstract: The main aim of this paper is to introduce and investigate two new classes of functions, called fuzzy pairwise *-pre-continuity (briefly, FP&-Pre-continuity) and fuzzy pairwise &-pre-continuity (briefly,FP&-Pre-continuity) between fuzzy bitopological spaces of which first one being weaker than the later. The description of those functions is chiefly facilitated by the introduction of a generalized type of open sets, called fuzzy pairwise *-pre-open set and fuzzy pairwise &-pre-open set whose allied details are studied to some extent to ultimately achieve a list of characterizations, some basic and preservation properties of the said types of functions.Their inter-relations are also taken into consideration.

Key words:FP pre-*-cluster point,FP pre-*-open (closed) sets, FP pre-continuity, FP weakly-Pre-continuity,FP Strongly *-Pre-continuity, FP*-Pre-continuity, FP&-Pre-continuity etc.

 

Connectedness in Fuzzy Minimal Structure

S. S. Thakur

Department of Applied Mathematics, Jabalpur Engineering College,Jabalpur(M.P.)- 482001.

E-mail: samajh_singh@rediffinail. com

Abstract: A fuzzy minimal structure Fm on a non empty set X is a subfamily of fuzzy power set of X which contains the null fuzzy set 0 and whole fuzzy set 1. In the present paper we introduce and discuss the concept of fuzzy m-connectedness in fuzzy minimal structure.It is shown that the concepts of fuzzy connectedness, fuzzy semi connectedness, fuzzy pre connectedness, fuzzy&-pre connectedness, semi pre connectedness and fuzzy semi &-preconnectedness are the special case of fuzzy m-connectedness.Several known results have been generalized using this concept.

Key words: Fuzzy minimal structure, fuzzym-connectedness, , fuzzy semi connectedness, fuzzy pre connectedness, fuzzy &-pre connectedness, fuzzy semi &-preconnectedness

 

On ijS* -lower Semi Continuous Functions in A Bitopological Spaces

Subrata Bhowmik and Anjan Mukherjee*

Department of Mathematics,Tripure University ,Suryamaninagar,Tripura-799022,( India).

E-mail:subrata_bhowmik_math@rediffmail.com . E-mail: anjan2002_m@yahoo.co.in *

Abstract: The objective of this paper is to introduce fuzzy supra topological spaces indused from the ijS* lower semi continuous functions from a bitopological space (X,T1,T2) to the unit interval [0,1], where i, j belongs to {1,2} and i=/j and to study some relationships between a bitopological space and the fuzzy supra topological space induced from the bitopological space.

Key words: Bitopological spaces,ij-semi open sets in bitopological spaces, fuzzy supra topological spaces.

 

Generalized Closed Sets in Fuzzy Ideal Topological Spaces

S. S. Thakur

Department of Applied Mathematics, Jabalpur Engineering College,Jabalpur(M.P.)- 482011.

E-mail: samajh_singh@rediffinail. com

Anita Singh Banafar

Department of Applied Mathematics, Jabalpur Engineering College, Jabalpur(M.P.)- 482011.

E-mail: anita.banafarl@gmail. com

Abstract: The purpose of this paper is to extend the concepts of Ig-closed sets due to Dontchev, Ganster and Noiri [2] to fuzzy ideal topological spaces and study some of its basic properties and characterizations.

Key words: Fuzzy ideal topological spaces, fuzzy Ig-closed sets and fuzzy Ig-open sets

 

On Generalized Fuzzy Normed Spaces

Shaban Sedghi

Department of Mathematics Qaemshahr Branch, Islamic Azad University , Ghaemshah, Iran.

E-mail address : sedghi_gh@yahoo.com

Bijan Davvaz

Department of Mathematics , Islamic Azad University-Babol Branch , Iran.

E-mail address : nabi_shobe@yahoo.com

Nabi Shobe

Department of Mathematics, Yazd University ,Yazd, Iran.

E-mail : davvaz@yazduni.ac.ir

Abstract: The theory of rough set, proposed by Pawlak and the theory of fuzzy set, proposed by Zadeh are complementary generalizations of classical set theory.? In this paper concerns a relationship between rough sets, fuzzy set and fuzzy normed space. We consider a fuzzy normed space as a universal set and we assume that the knowledge about objects is restricted by a fuzzy normed spaces.? In fact, we apply the notion of fuzzy set of a fuzzy normed space for definitions of the lower and upper approximations in a fuzzy normed space.

Key words: Fuzzy normed space, compatible mappings, common fixed point.

 

Some Generalizations of Possibility and Necessity Measures

Gigi George

Department of Mathematics, Mar Thoma College for Women, Perumbavoor, Kerala-683542 S. India.

E-mail: frpraise@yahoo.com

Sunny Kuriakose

Principal, BPC College, Piravom, Kerala, S. India.

Abstract: Possibility measures were introduced by L. A. Zadeh [8] as an auxiliary tool for numerical characterization and processing of uncertainty involved in real life situations.Since then the original very simple notion of these measures viewed as functions defined on the powerset of a given universal set X to the unit interval [0,1]has been subjected to various modifications and generalizations. In this paper, some generalizations of possibility measures and their dual-necessity measures are considered and studied their properties.The domains of these measures are generalised to Boolean algebras, atomic Bollean algebras and L-fuzzy sets and co-domains to complete lattices and lattice intervals. Particular functions induced by generalized possibility distributions and satisfying the axiomatic requirements of lattice interval valued possibility and necessity measures are generated with the aid of extended fuzzy connectives and the conditions under which the measures will satisfy the natural relations are analysed.

Key words: Lattice valued possibility measure, lattice valued necessity measure, lattice interval valued possibility measure, lattice interval valued necessity measure, lattice interval valued possibility distribution.

 

Fuzzy A -continuous Mappings

Athar Kharal

National University of Sciences and Technology (NUST), Islamabad, PAKISTAN.

E-mail: atharkharal@gmail.com

B. Ahmad

Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, PAKISTAN.

E-mail: dr ba shir9@gmail.com

Abstract: Different notions of Classical Topology which are defined through A-open sets resist a straightforward fuzzification due to the fact that unlike classical counterpart the collection of fuzzy A-open sets does not make a fuzzy topology in the sense of Chang. Expecting such interesting deviations, in this paper we study the notion of fuzzy A-continuous mappings.? We first give several fundamental properties of fuzzy A-open sets. Using these results different characterizations of fuzzy A-continuous, fuzzy almost A-continuous and fuzzy semi-weakly continuous mappings have been obtained.

Key words: Fuzzy A-continuous mappings; Fuzzy A-open mappings; Fuzzy almost A-continuous mappings; Fuzzy semi-weakly continuous mappings;

 

A View on Hardly Soft Fuzzy G&preTu Open Function in Soft Fuzzy Quasi Uniform Topological Space

V. Visalakshi, M. K. Uma and E. Roja

Department of Mathematics,Sri Sarada College for Women, Salem-636016, tamil Nadu India.

E-mail: visalkumar_cbe@yahoo.co.in

Abstract: In this paper the concept of soft fuzzy quasi uniform space and the topologyTu generated by the uniformity is introduced. Soft fuzzy G&preTu open set, soft fuzzy G&preTu open, somewhat soft fuzzy G&preTu open and hardly soft fuzzy G&preTu open functions are discussed and the characterizations are established. Interrelations are discussed with counter examples.Also the concepts soft fuzzy quasi uniform Tu* spaces, soft fuzzy quasi uniform D closed space, soft fuzzy quasi uniform N* space are introduced and studied.

Key words: Soft fuzzyG&preTu open set; Soft fuzzy F#preTu closed set; Soft fuzzy G&preTu open function; Soft fuzzy quasi uniform dense; Soft fuzzy quasi uniform G&preTu dense; Somewhat soft fuzzy G&preTu open function; Hardly soft fuzzy G&preTu open function; Soft fuzzy quasi uniform Tu* space; Soft fuzzy quasi uniform connected space; Soft fuzzy G&preTu connected space; Soft fuzzy strongly G&preTu connected space; Soft fuzzy quasi uniform D closed space; Soft fuzzy quasi uniform N* space.

 

(A,B)-fuzzy Submodules with Respect to A t -norm

Saifur Rahman

Department of Mathematics, Rajiv Gandhi University, Itanagar-791112, India.

Email: saifur_ms@yahoo.co.in

Helen K. Saikia

Department of Mathematics, Gauhati University, Guwahati,-781014, India.

Email: haaikia@yahoo.co.in

Abstract: On the basis of the concept of a fuzzy point belongingness ($) or quasi-coincident (q) or belongingness and quasi-coincident ($&q) or belongingness or quasi-coincident ($ Or q), an (A,B)-fuzzy submodule with respect to a t -norm T has been defined. We characterize (A,B)-fuzzy submodules with respect to T in terms of its level sets.It is established that a fuzzy subset u of a module over a ring is a ($,$)-fuzzy submodule with respect to T if and only if u is a fuzzy submodule with respect to the t-norm T . Necessary and sufficient conditions for t-norm based (A,B)-fuzzy submodule are established. We investigate the nature of (A,B)-fuzzy submodules of a module with respect to the t-norm T in terms of t-norm based intersection.

Key words: Fuzzy Submodule, Fuzzy Submodule with respect to a t-norm T ,(A,B)-fuzzy Submodules with respect to a t-norm T.

 

Common Fixed Point Theorems for Fuzzy Mappings under(1,2)-weak Contraction Condition

H. M. Abu-Donia

Department of Mathematics, Faculty of Science, Zagazig University Zagazig Egypt

Abstract: The concept of the weak contraction was defined by Alber and Guerre-Delabriere {3} also, defined such mappings for single-valued maps on Hilbert spaces and proved the existence of fixed points. Rhoades [4] showed that most results of [3] are true forany Banach space. Popeseu [7] introduced a fixed points for(1,2)-weak contractions.The aim of this work is to generalize results proved by Popeseu (2011) [7], using two fuzzy multi-valued mappings.

Key words: Complete metric space, common fixed point, fuzzy multi-valued mappings, (1,2)-weak contraction condition.

 

On Pairwise Ordered Soft L -fuzzy BTu Extremally Disconnected Spaces

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, a new class of soft L-fuzzy quasi uniform topological space called pairwise ordered soft L-fuzzyBTu extremally disconnected spaces is introduced.? Besides providing some interesting properties and characterizations are studied. Tietze extension theorem for pairwise ordered soft L-fuzzy BTu extremally disconnected spaces is established.

Key words: Pairwise ordered soft L-fuzzyBTu extremally disconnected spaces, ordered soft L-fuzzyBTu continuous function, lower (upper) soft L-fuzzy BTu continuous function.

 

On Fuzzy Volterra Spaces

G. Thangaraj

Department of Mathematics Triruvalluvar University Vellore-632115, Tamilnadu, India

S. Soundararajan

Department of Mathematics, Islamiah College (Autonomous) Vaniyambadi-635752, Tamilnadu, INDIA

Abstract: In this paper the concepts of fuzzy Volterra spaces and fuzzy weakly Volterra spaces are introduced and characterizations of fuzzy Volterra spaces and fuzzy weakly Volterra spaces and studied. Several examples are given to illustrate the concepts introduced in this paper.

Key words: Fuzzy nowhere dense set, Fuzzy first category, Fuzzy second category fuzzy Baire, fuzzy Volterra and fuzzy weakly Volterra spaces.

 

Fuzzy Cores in Spatial Models

John N. Mordeson and Lance Nielsen

Department of Mathematics Greighton University Omaha ,Nebraska 68178,USA .

E-mail: mordes@creighton.edu, lnielsen@creighton.edu

Terry D. Clark

Department of Mathematics Political Science Greighton University Omaha ,Nebraska 68178,USA .

E-mail: tclark@creighton.edu

Abstract: We consider the effect of regular strict fuzzy preferences on several important questions in fuzzy social theory. We begin by considering the conditions under which a nonempty fuzzy maximal set and a fuzzy core exist when fuzzy strict preferences are regular. We then present the conditions under which the supports of fuzzy cores are the same for a fuzzy aggregation rule and the fuzzy simple rule and fuzzy voting rule it determines.

Key words: Fuzzy subset; fuzzy preference relation; fuzzy maximal sets; fuzzy core; fuzzy aggregation rule; partial, regular; simple rule, voting rule.

 

(R,S) -fuzzy Minimal Structures and (R,S) -fuzzy Minimal Spaces

Won Keun Min

Department of Mathematics, Kangwon National University , Chuncheon, 200-701,Korea.

S. E. Abbas

Department of Mathematics, Faculty of Science, Jazan University Saudi- Arabia.

E. El-sanowsy and A. Atef

Department of Mathematics, Faculty of Science, Sohag 82524, Egypt.

Abstract: In this paper, we introduce the concept of(R,S) -fuzzy minimal structure which is an extension of intuitionistic gradation of openness introduced by Samanta and Mondal (2002).Also, we introduce and study the concepts of (R,S) -fuzzy M continuity and several types of (R,S)-fuzzy minimal compactness on (R,S)-fuzzy minimal spaces.

Key words: Minimal structure, minimal spaces,(R,S)-fuzzy M -continuity and (R,S)-fuzzy minimal compactness

 

Some Properties of Subdifferential Convex Fuzzy Mapping

Yu-E Bao

College of Mathematics Science , Inner Mongolia University for Nationalities, Tongliao, 028043, P.R.China

E-mail: byebed@163.com

Abstract: Based on the concept of subdifferentiability, first, the subdifferentiability problem of convex fuzzy mapping are discussed and structure expression of subdifferential is given.Second, the subdifferentiability relationship between convex fuzzy mapping and it¡¯s upper/(lower) extreme function are discussed and some sufficient conditions for differentiable convex fuzzy mapping are given. Finally, P-positive homogeneity of fuzzymapping is discussed and generalized Euler formula (Euler formula) of subdifferential (differential) P-positive homogeneity fuzzy mapping are given.

Key words: Convex fuzzy mapping, Subdifferential (differential),P-positive homogeneity fuzzy mapping, Generalized Euler formula (Euler formula)

 

Double L -fuzzy C-uniform Spaces-convering Approach

S. E. Abbas and A. A. Abd-Allah

Department of Mathematics, Faculty of Science, Sohag 82524, Egypt.

Abstract: In this paper, we introduce a new double L -fuzzyC-uniformity in term of covering approach and investigate some of their properties. We study the relationships between double L -fuzzy C-uniform space and double L -fuzzy uniform space.

Key words: Fuzzy sets, double L -fuzzyC-uniformity, double L -fuzzy uniformity.

 

Supra (L,M)-fuzzy Closure Operator

S. E. Abbas

Department of Mathematics, Faculty of Science, Sohag University, Egypt.

A. A. Abd-Allah

Department of Mathematics, Faculty of Science, Jazan University, Kingdom of Saudi- Arabia.

Abstract: In this paper, we introduce and study the concept of supra (L,M)-fuzzy closure space and relationship between supra (L,M)-fuzzy topological spaces and supra (L,M)-fuzzy closure spaces. Also, the supra (L,M)-fuzzy topological space induced by (L,M)-fuzzy bitopological space is introduced. We study the relationship between supra (L,M)-fuzzy closure space and the supra (L,M)-fuzzy topological space induced by an (L,M)-fuzzy bitopological space.

Key words:Fuzzy closure operator, fuzzy supra closure operator.

 

Ordered Extremally Disconnectedness in an Ordered Intuitionistic Fuzzy Convergence Bitopological 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 we introduce the new concept of an ordered extremally disconnectedness in an ordered intuitionistic fuzzy convergence bitopological spaces. Besides giving some interesting propositions. Tietze extension theorem for pair-wise ordered intuitionistic fuzzy Tlim extremally disconnected space is established.

Key words: Ordered intuitionistic fuzzy convergence bitopological space, pairwise ordered intuitionistic fuzzy Tlim extremally disconnected spaces, orderedTlim intuitionistic fuzzy Tlim continuous function, lower (resp. upper) Tlim intuitionistic fuzzy Tlim continuous function, (i=1 or 2).

 

An Approach to Find Optimal Solution in Fuzzy Project Networks

V. Sireesha and N. Ravi Shankar

Dept. of applied mathematics, GITAM University ,Vishakhapatnam, India

Abstract: Identification of critical path is important in a project network to control time, costs and to allocate resources competently. The aim of this paper is to present a new approach to determine the critical path in a fuzzy project network based on the maximum total float of the path. The advantage of the proposed method over existing straight forward methods (Chen [12], Liang [29]) is shown by solving different combinations of project network with symmetric and asymmetric activity times. The comparisons reveal that the proposed approach is an improved method over existing methods and more efficient in finding the critical path.

Key words:Critical Path;Fuzzy PERT; Path float; Triangular Fuzzy numbers.

 

On Optimality of Multiobjective Nonlinear Generalized Disjunctive Fuzzy Fractional Programming

E. E. Ammar

Department of Mathematics and Statistic, Faculty of Science, Taif University Saudi Arabia.

E-mail : amr.saed@ymail.com

Abstract: This paper is concerned with the study of necessary and sufficient optimality conditions to convex-concave generalized multiobjective fractional disjunctive programming problems for which the decision set is the union of a family of convex sets.The Lagrangian function for such problems is defined and the Kuhn-Tucker Saddle and Stationary points are characterized. In addition, some important theorems related to the Kuhn-Tucker problem for saddle and stationary points are established.

Key words: Generalzied multiobjective fractional programming; Disjunctive programming; fuzzy parameters; Optimality.

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