THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 21, Number 2, June 2013

CONTENT

DETAILS

Multi-objective Fuzzy Probabilistic Programming Problem Involving Laplace Distribution

M.P.Biswal,S.K.Barik

department of mathematics.E-mail: suresh@math.iitkgp.ernet.in

D.Chakravarty

Department of Mining Engineering Indian Institute of Technology, Kharagpur-721302,India.E-mail:dc@mining.iitkgp.ernet.in

Abstract: The aim of the present paper is to solve a multi-objective fuzzy probabilistic programming problem where the right hand side parameters of the constraints follows Laplace distribution and the technological coefficients of the constraints and objective function coefficients are considered as fuzzy. In this paper, we introduce S-curve membership function to handle the fuzziness in the problem. Multi-objective fuzzy probabilistic programming problem is transformed into an equivalent crisp multi-objective non-linear programming problem which is solved by fuzzy programming method. One numerical example is presented to illustrate the methodology. Further a deterministic model is also established by assuming the right hand side parameters as normal random variable and the technological coefficients of the constraints and objective function coefficients as fuzzy. Then the problem is solved by fuzzy programming method. Then the result is compared with the result obtained by Laplace distribution.

Key words: Multi-objective programming problem, Probabilistic programming problem, Laplace distribution, Normal distribution, S-surve membership function, Fuzzy programming method.

Simply a-generalized Rough Types

M.Swealam and M.El Sayed

Department of Matheamtics, Faculty of Science,Tanta university, Egypt

Abstract:In this paper we investigate the approximate operations on the sets, approximate equality, approximate inclusion and definability of sets.We shall study some of their properties.

Key words: Rough sets.

On Intuitionistic Fuzzy g-compactness

N.Gowrisankar

70/232 6B,Kollupettal 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

V.Vijayabharathi

Department of mathematics,National Institute of Technology, Tiruchi-Rappalli, Tamilnadu,India.E-mail address :vijayabharathi_v@yahoo.com

Abstract: In this paper, we have introduce and study the concept of intuitionistic fuzzy g-compactness. Several preservation properties and some characterizations concerning intuitionistic fuzzy g-compactness have been obtained.

Key words and phrases:Intuitionistic fuzzy topology, Intuitionistic fuzzy g-open set, intuitionistic fuzzy g-compact space.

Order in Probability of Intuitionistic Fuzzy Random Variables

R.Helen

Department of Mathematics,Poompuhar College,Melaiyur-Tamil Nadu,S.India.E-mail:helenranjan@gmail.com

Abstract: In this paper, a new notion of order in probability of intuitionistic fuzzy random variable such as smaller order and atmost of order is introduced and properties of these orderings are established.

Key words: Intuitionistic fuzzy random variable, Intuitionistic fuzzy number and fuzzy probability.

A New Approach to Intuitionistic Fuzzy Regular Gd Separation Axioms

G.K.Revathi, E.Roja and M.K.Uma

Department of Mathematics Sri Sarada College For WomenSalem, TamiNadu, India.E-mail:gk_revathi@yahoo.co.in

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. Intuitionistic fuzzy regular GdTi (i=1,2,3 and 4)spaces are introduced and separation axioms are investigated.

Key words: Intuitionistic fuzzy regular Gd continuous function and intuitionistic fuzzy regular GdTi(i=1,2,3 and 4)spaces.

Critical Path in A Project Network Using A New Representation for Trapezoidal Fuzzy Numbers

Thangaraj Beaula

Department of Mathematics,T.B.M.L College,Porayar-609307,tele no.04364-289166

V.Vijaya

Department of Mathematics,A.V.C College,Mayiladuthurai-609001

Abstract: The methods for finding critical path where all the parameters are represented as fuzzy numbers is inadequate and cannot be extended. In this paper, a new representation of fuzzy trapezoidal numbers is proposed. Also a new method to find the critical path in networks using this new representation is proposed.

Key words:(S) Project Scheduling,(P) Project Management.

Application of Fuzzy Programming with Nonlinear Membership Function to Multiobjective 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 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 and availability 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. Two Examples are included to illustrate the methodology. Fuzzy programming with nonlinear membership function is compared to fuzzy programming with linear membership function with examples.

Key words:Multicriteria decision making, stochastic transportation problem, chance constraints, fuzzy programming, efficient solution, compromise solution, membership function.

On Soft Fuzzy B-open Sets

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:The purpose of this paper is to introduce the concepts of soft fuzzy B-open set, soft fuzzy AB-open set and weak soft fuzzy AB-open set. Besides providing some interesting properties, interrelations among the sets introduced are discussed.? The concepts of soft fuzzy B-continuity, soft fuzzy B-connected spaces, soft fuzzy B-compact spaces and soft fuzzy B-normal spaces are introduced and studied.

Key words:Soft fuzzy B-open set, soft fuzzy AB-open set, weak soft fuzzy AB-open set, soft fuzzy B-continuous function, soft fuzzy AB-continuous function, weak soft fuzzy AB-continuous function, soft fuzzy B-compact space, soft fuzzy B-connected space and soft fuzzy B-normal space.

A View on Soft Fuzzy C-continuous Function

T.Yogalakshmi,E.Roja and M.K.Uma

Department of Mathematics,Sri Sarada College for Women (Autonomous), Salem-16 Tamil Nadu,India.E-mail:YogaPrithvi_ssp@yahoo.co.in

Abstract:A new class of set, namely soft fuzzy C-open set is introduced in this paper. Some interesting properties and characterizations are established. The concepts of soft fuzzy Kernel, soft fuzzy C-kernel, soft fuzzy C-continuity, soft fuzzy C-connected, soft fuzzy C-compact and soft fuzzy C-normal spaces are introduced and studied.

Key words:Soft fuzzy C-open set, soft fuzzy C-kernel and soft fuzzy C-neighbourhood of a soft fuzzy set, soft fuzzy C-continuous function, soft fuzzy C-connected space, soft fuzzy C-compact space, soft fuzzy C-normal space.

Intuitionistic L-fuzzy Soft Sets and Intuitionistic L-fuzzy Soft Groups

SK.Nazmul

Govt.College of Education,Burdwan Kazirhat,Lakurdi,Burdwan-713102,West Bengal,India.E-mail:sk.nazmul_math@yahoo.in

S.K.Samanta

Department of Mathematics,Visva-Bharati Santiniketan-731235,West Bengal,India. E-mail:syamal_123@yahoo.co.in

Abstract:In this paper, definitions of Intuitionistic L-fuzzy soft sets and intuitionistic L-fuzzy soft groups are introduced and some of their properties are studied.

Key words:Soft sets, soft groups, fuzzy soft sets, fuzzy soft groups, intuitionistic fuzzy set, intuitionistic L-fuzzy set, intuitionsitic L-fuzzy subgroups, intuitionistic L-fuzzy soft sets, intuitionsitic L-fuzzy soft groups.

Fuzzy Probabilistic Linear Programming Problems with Fuzzy Log-normal Random Variables

S.Acharya

School of Applied Sciences(Mathematics),KIIT University, Bhubaneswar, India.E-mail:sacharyafma@kiit.ac.in, srikumar.kpg@gmail.com,Call:+91-8763215721

M.P.Biswal

Department of Mathematics,IIT Kharagpur,Kharagpur,India.E-mail: mpbiswal@maths.iitkgp.ernet.in,Call:+91-3222-283642

S.Nanda

Prof of Eminece and Research Chair,KIIT University, Bhubaneswar,India.E-mail: snanda@kiit.ac.in,Call:+91-674-2378577

Abstract:In a typical managerial decision making problem both randomness and fuzziness are involved. The aim of the paper is to present a solution procedure for a fuzzy probabilistic programming problem involving both fuzziness and randomness. In this problem, we consider independent log-normally distributed fuzzy random variables. Using a-cut principle, the fuzziness of the problem is removed. Then the probabilistic problem is converted to a deterministic problem.? Standard mathematical programming procedure is applied to solve the deterministic problem. Illustrative numerical examples are presented in support of the proposed methodology.

Key words:Fuzzy random variables, Fuzzy probabilistic programming,Fuzzy log-normal random variable,Non-linear programming.

Distributive Lattice over Intuitionistic Fuzzy Matrices

Amal Kumar Adak and Madhumangal Pal

Department of Applied Mathematics with Oceanology and Computer Programming£¬Vidyasagar University,Midnapore-721102,India.E-mail: mmpalvu@gmail.com

Monoranjan Bhowmik

Department of Mathematics,V.T.T College,Midnapore,Paschim Medinipur-721101, India.E-mail:mbvttc@gmail.com

Abstract:In this paper, the concept of lattice over intuitionistic fuzzy matrices (IFMs)are introduced and have shown that the set of IFMs forms a distributive lattice. Some algebraic properties of intuitionistic fuzzy matrices (IFMs) over distributive lattice are presented. Also, some characteristics of intuit ionistic fuzzy nilpotent matrices (IFNMs) over distributive lattice are discussed. Finally, the reduction of (IFMs) over distributive lattice are given with some properties.

Key words:Intuitionistic fuzzy matrices, distributive lattice of intuitionsitic fuzzy matrix, intuitionistic fuzzy nilpotent matrices.

Occasionally Weakly Biased Maps on Fuzzy Metric Spaces for Common Fixed Point Consideration

Bhavana Deshpande

Department of Mathematics Govt.Arts and Science P.G College, Ratlam-457001 (M.P.) India.E-mail:bhavnadeshpande26@gmail.com

Suresh Chouhan

Department of Mathematics Govt.Girls College,Ratlam-457001 (M.P.) India.E-mail: s.chouhan31@gmail.com

Abstract:In this paper, we define weakly biased and occasionally weakly biased maps in the settings of fuzzy metric spaces. We prove common fixed point theorems by using occasionally weakly biased maps in fuzzy metric space. We also proved a common fixed point theorem for occasionally weakly biased maps satisfying an implicit relation in fuzzy metric spaces. The maps involved in our theorems are not continuous and the space is noncomplete.? We improve, generalize and fuzzify many known results.

Key words and phrases:Common fixed point, coincidence point, occasionally weakly biased mappings, fuzzy metric spaces.

A Fuzzy Mathematical Model of Political Stability

Michael B.Gibilisco

Department of Political Science.E-mail:michaelgibilisco@creighton.edu

John N.Mordeson

Department of Mathematics(Creighton University Omaha,Nebraska 68178 USA).E-mail:mordes@creighton.edu

D.S.Malik

Department of Mathematics(Creighton University Omaha,Nebraska 68178 USA).E-mail:malik@creighton.edu

Terry D.Clark

Department of Political Science.E-mail:tclark@creighton.edu

Abstract:The purpose of this paper is to propose a weighted average approach to measure the political stability of countries. Our measure builds on intuitionistic fuzzy sets to study the counterintuitive behavior occurring in social systems and makes use of the analytic hierarchy process, the Guiasu method, and the Yen method. We conclude by using our measure to rank 75 countries with respect to political stability.

Key words:Political stability; AHP method, Guiasu method, Yen method; counterintuitive behavior, intuitionistic sets.

Product of L-modules and Exact Sequences of L-homomorphisms over Rings

Nazek A.Al-Essa

Math Department,Faculty of Sciences,Princess Noura University, Riyadh,Saudi Arabia.E-mail:nazekaa@yahoo.com

Abstract: The concept of exact sequences is an important area in the module theory.?In this paper we introduce the concepts of product and coproduct of L-modules as objects of a category of L-modules. We introduce also the concept of semiexact series, sequences, exact sequences, and split exact sequences of LR-homomorphisms, (LR-homomorphisms or L-homomorphisms over rings are used in this work interchangeable) it means that we introduce the structure of exact sequenceof L-modules by means of L-sets on mappings and homomorphisms.Then we study some of their properties.We conclude that the exact sequence¹«Ê½is isomorphic to the exact sequence¹«Ê½ if they satisfy some conditions in the category.

Key words:L-modules, Product and coproduct of L-modules, Exact seqeucnes of L-modules, Split exact sequence of L-modules, Category theory.

On Pairwise Separation Axioms in Fuzzifying Bitopology

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

V. Vijayabharathi

Department of Mathematics,National Institute of Technology, Tiruchi-Rappalli, Tamilnadu,India.E-mail:vijayabharathi_v@yahoo. com

Abstract:In this paper we have introduce and study the concepts of fuzzifying pairwise separation axioms in fuzzifying bitopological spaces.

Key words:Lukasiewicz logc, fuzzifying bitopology, fuzzifying pair-wise a-open sets.

Common Fixed Point for Mappings on Nonconvex Domain in Fuzzy Normed Spaces

Ismat Beg and Mujahid Abbas

Lahore University of Management Sciences,54792-Lahore, PAKISTAN.E-mail: IBEG@LUMS.EDU.PK;MUJAHID@LUMS.EDU.PK

Abstract:Sufficient conditions for existence of common fixed point for weakly compatible mappings satisfying nonexpansive type conditions on fuzzy normed spaces are obtained. The special feature of our results is relaxation of the convexity condition on domain of mappings which is key assumption in the several comparable results in the existing literature.

Key words:Fuzzy normed space; fixed point; fuzzy nonexpansive mapping; fuzzy R-weakly commuting mappings.

On Some Stronger Forms of Strongly Fuzzy #gs-continuous, Perfectly Fuzzy #gs-continuous and Completely Fuzzy #gs-continuous Functions

Sadanand.N.Patil

Senior Scientist,Assistant Professor and H.O.D,Department of Mathemtics, KLS¡®s, VDRIT,Haliyal,581329.(UK).(Karnataka-India).

E-mail: patilsadu@gmail.com, sada_np@rediffmail.com

S.R.Sadugol

Dept.of E&E,B.L.D.E A¡¯s Dr.PG Halakatti engineering College, Bijapur-586103 (Karnataka-India).E-mail:srsadugol@gmail.com

Abstract:In this paper, now the stronger forms of fuzzy #gs-continuous functions namely strongly fuzzy #gs-continuous, perfectly fuzzy #gs-continuous and completely fuzzy #gs-continuous functions have been introduced and studied. And some of their properties are obtained.

Key words and phrases:Strongly fuzzy #gs-continuous, perfectly fuzzy #gs-continuous and completely fuzzy #gs-continuous functions.

On Some Stronger Forms of Strongly Fuzzy #g-continuous, Perfectly Fuzzy #g-continuous and Completely Fuzzy #g-continuous Functions

Sadanand.N.Patil

Senior Scientist,Assistant Professor and H.O.D,Department of Mathemtics, KLS¡®s,VDRIT,Haliyal,581329.(UK).(Karnataka-India).

E-mail: patilsadu@gmail.com, sada_np@rediffmail.com

S.R.Sadugol

Dept.of E&E,B.L.D.E A¡¯s Dr.PG Halakatti engineering College, Bijapur-586103 (Karnataka-India).E-mail:srsadugol@gmail.com

Abstract:In this paper, now the stronger forms of fuzzy #g-continuous functions namely strongly fuzzy #g-continuous, perfectly fuzzy #g-continuous and completely fuzzy #g-continuous functions have been introduced and studied.? And some of their properties are obtained.

Key words and phrases:Strongly fuzzy #g-continuous, perfectly fuzzy #g-continuous and completely fuzzy #g-continuous functions.

Study on T-fuzzy LI-ideal of Lattice Implication Algebras

Xiqing Long

School of Maths,YiBin University,YiBin 644000,China

Yang Xu

Department of Mathematics,Southwest Jiaotong University, Chengdu 610031, China

Abstract:In this paper, the notion of the L-fuzzy LI-ideal is proposed in the lattice implication algebra.The necessary and sufficient conditions for a fuzzy set m is a T-fuzzy LI-ideal were presented.

Key words:Lattice implication algebras, fuzzy LI-ideals, T-fuzzy LI-ideal.