THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 20, Number 2, June 2012

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Multi-objective Economic Order Quantity Model under A Constraint:A Geometric Programming Approach

Sahidul Islam

Department of Mathematics, Gushkara Mahavidyalaya, Gushkara, Burdwan, W. B., India. E-mail: sahidull@yahoo.ca

Abstract: In this paper , we have formulated a multi-objective economic quantity model under a limited total purchasing and holding cost constraint. Here, we have discussed multiobjective geometric programming problem based on global criterion method.. The different objective functions are combined to a single objective function by global criterion method. Geometric programming technique is used to derive the optimal solutions for different preferences on objective functions. Finally, the solution procedure is illustrated by a numerical example.

Key words: Global Crirerion method; hybrid method; set-up cost; Multi-objective; inventory.

On common Fixed Point Theorem in Intuitionistic Fuzzy Metric Spaces

Sushil Sharma

Department of Mathematics, Madhav Science College, Vjjain-456010, India. E-mail: sksharma2005@yahoo.com

Prashant Tilwankar

Department of Mathematics, Shri Vaishnav Institute of Managment, Indore-452009, India. E-mail: prashant_tilwankar@yahoo.com

Abstract: In this paper we improve and intuitionistic fuzzify the results of Cho and we characterize the conditions for discontinuous mappings of noncomplete intuitionistic fuzzy metric space have a unique common fixed point in .

Key words: Intuitionistic fuzzy metric space, Weakly compatible mapping, Common fixed point.

Tow New Operations on Intuitionistic Fuzzy Soft Sets

Pabitra Kumar Maji

Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata-19, West Bengal, India. E-mail: pabitra_maji@yahoo.com

Abstract: In this paper we study the concept of intuitionistic fuzzy soft sets. We have introduced two new operations on intuitionistic fuzzy soft sets.Some properties of these operations have also been investigated.

Key words: Soft set, intuitionistic, fuzzy sets, intuitionistic, fuzzy soft sets.

A Population Projection Moel Using Fuzzy Data

Kangkana Sarmah Baruah and Hemanta K. Baruah

Department of Statistics Gauhati University, Guwahati-781014 Assam, India. Email:kangkana5@gmail.com, Email:hemanta_bh@yahoo.com

Abstract: In our work we have used the model with exponential relative growth rate derived by Chakrabarty and Baruah with fuzzy data to calculate the total population of a region in fuzzy intervals. This model is based on the assumption that the relative growth rate of the population concerned decreases exponentially over time. We will also see the effecct of fuzziness on the model with exponential relative growth rate. The fuzzy model developed will be applied to the situation prevailing in India as India is with large population.

Key words: cut, fuzzy membership function, fuzzy interval, fuzzy model with exponential growth rate.

-cut of Intuitionistic Fuzzy Metrices

S.Sriam and P.Murugadas

Mathematics Section, FEAT, Annamalai University, Annamalainagar-608002, India. Email:ssm_3096@Yahoo.co.in, Email:bodj_muruga@yahoo.com

Abstract: The concept of -cut (zero patterns) has been defined for Intuitionistic Fuzzy Matrices in which each entries are comparable ang any such IFM can be expressed as intuitionistic fuzzy linear combination of its zero patterns. Further we study relations such as reflexive, symmetry and transitive between -cut of IFM and IFM.

Key words: Intuitionistic fuzzy matrix (IFM), Intuitionistic fuzzy set(IFS), section.

Generalie Fuzzy Topological Spaces

S.E.Abbas, E.El-Sanousy, Y.H.Raghp

Department of Mathematics, Facutly of Science, Sohag University, Sohag, Eygpt.

S.Abdel-Baki

Department of Mathematics, Facutly of Science, Assuit University, Assuit, Eygpt.

Abstract: We introduce the concepts of generalized fuzzy topological spaces, generalized fuzzy neighborhood systems, in ostak sense. Furthermore, we construct generalized fuzzy interior, generalized fuzzy closure on generalized fuzzy topological space and generalized fuzzy neighborhood system. Also, we introduce the concepts of generalized fuzzy -continuous, weakly generalized fuzzy -continuous, generalized fuzzy -continuous and weakly generalized fuzzy -continuous. We study their properties and discuss the relationships between these concepts.

Key words: Generalized fuzzy topological spaces, generalized fuzzy neighborhood systems, generalized fuzzy interior, generalized fuzzy closure, generalized fuzzy -continuous, weakly generalized fuzzy -continuous, generalized fuzzy -continuous, weakly generalized fuzzy -continuous.

A connection between Fuzzy Random Variables and Random Cloed Set with Application to Fuzzy Stochastic Optimiztion

M.K.Luhandjulal

Department of Decison Science University of South Africa PO Box 392 UNISA; Pretoria 0003 South Africa

Abstract: We prove that the space of fuzzy random variables can be embedded into a suitable space of random closed sets isomorphically and isomorphically. This result extends quite canonically the well known Radstrom Embedding Theorem to fuzzy random variables. An application to the emerging field of Fuzzy Stochastic Optimiztion is sketched and a numerical example carried out for the sake of illustration.

Key words: Random set, fuzzy random variable, fuzzy stochastic optimiztion.

Neighborhood structures and -sets in Intuitionistic Fuzzy Minimal Spaces

Oya Bedre ?zbakir and Gizem G¨¹nel

Department of Mathematics, Faculty of Science, Ege University, Izmir, Turkey Email:oya.ozbakir@ege.edu.tr , gizemgunell@gmail.com

Abstract: The purpose of this paper is to intruduce the intuitionistic fuzzy minimal spaces as a generalization of intuitionistic fuzzy topological spaces. After constucting the fundamental concepts, we investigate the notions of the neighborhood structures of an intuitionistic fuzzy point in the intuitionistic fuzzy minimal spaces. Moreover, we define and study the intuitionistic fuzzy -sets and -open sets in the intuitionistic fuzzy minimal spaces.

Key words: Intuitionistic fuzzy minimal spaces, intuitionistic fuzzy minimal -sets, intuitionistic fuzzy minimal -open sets, intuitionistic fuzzy neighborhood

A Note on The Lattice of -topologies

Ginu Varghese

Centre for Mathematical Sciences Pala Campus Arunapuram P. O.686574 Kottayam, Kerala, India. E-mail: ginuvettuparampil@gmail.com

Sunil C.Mathew

Department of Mathematics St. Thomas College Palai Arunapuram P. O.686574 Kottayam, Kerala, India. E-mail: sunilcmathew@rediffmail.com

Abstract: If is not a characteristic function, then we prove that no simple extension determined by can be the discrete fuzzy topoiogy. We introduce the concept of attainable F-lattice and using the same extended the above result to L-topological spaces. It is proved that if Lis attainable then on a set with atleast three elements, the lattice of L-topologies has no dual atom.

Key words: Fuzzy-topoiogy, L-topological, lattice, dual atom, simple extension.

Some Aspects of Intuitionistic 2-Fuzzy 2-normed Linear Space

Thangaraj Beaula and Lilly Esthar Rani

Department of Mathematics, TBML College , Porayar, Tamil Nadu, India.

Abstract: This paper defines the new concept of intuitionistic 2-fuzzy 2-normed linear space. Convergent and Convergent and Cauchy sequences are defined in it. As a result an intuitionistic 2-fuzzy 2-Banach space is developed. The quotient space of intuitionistic 2-fuzzy 2-Banach space with a closed subspace of it is proved to be an intuitionistic 2-fuzzy 2-Banach space.

Key words: Intuitionistic 2-fuzzy 2-normed linear space, Convergent and Cauchy sequences, intuitionistic 2-fuzzy 2-Banach space.

Applications of Fuzzy -open Sets

N.Gowrisankar

70/232, Kollupetti Steet, 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

Abstract: The aim of this paper is to introduce and study the ntions of fuzzy upper and lower -limit sets. Poperties and basic relationships among fuzzy upper -limit set, fuzzy lower -limit set and fuzzy -continuity are investigated.

Key words and phrases: Fuzzy -open sets,fuzzy lower -limit set, fuzzy upper -limit set.

Fuzzy -preirresolute Functions

N.Gowrisankar

70/232, Kollupetti Street, M. Cavady, 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

Abstract: In this paper, we have introduced and studied a new type of fuzzy irresolute functions, called fuzzy -preirresolute functions by using fuzzy preopen sets.

Key words and phrases: Fuzzy topology, fuzzy preopen sets, fuzzy -preirresolute functions.

Foldnes of -fuzy Filter in -algebras

Nganteu Tchikapa

Department of Mathematics, Faculty of Science, University of Yaounde 1, BP 812, Cameroom E-mail address: nganteu2001@yahoo.fr

Celestin Lele

Department of Mathematics, University of Dschang, BP 67, Cameroom E-mail address: lele_clele@yahoo.com

Abstract: The aim of this paper is to introduce the notion of -fuzzy -fold implicative filter and -fuzzy -fold positive implicative filter in BL-algebras.Their basic poperties are investigated and the link between them is given.

Key words: BL-algebras, -fuzzy filter, -fuzzy -fold implicative filter, -fuzzy -fold positive implicative filter.

Operation on Intuitionitic Fuzzy Ideals of Lattice

Latha S.Nair

Department of Mathematics, Mar Athanasius College, Kothamangalam, Kochi, Kerala, India E-mail: lathavichattu@gmail.com

K.V.Thomas

Dept of Mathematics, Bharata Mata College, Thrikkakara, Kochi, Kerala, India E-mail: tkapiarumala@yahoo.co.in

Abstract: In this paper, we introduced some operations on intuitionistic fuzzy sets of a lattice. Detailed studies of intuitionistic fuzzy ideals under these operation are provided. We prove that the set of all intuitionistic fuzzy ideals forms a lattice. We also study the distributivity of this lattice.

Key words: Lattice, ideals, distributive lattice, intuitionistic fuzzy set, fuzzy sublalttice, fuzzy ideal.

Intuitionitic Fuzzy Soft Rough Sets

Anjan Mukherjee

Department Mathematics, Tripura University, Surjyamaninagar, Agatala-799130, Tripura, INDIA E-mail: anjan2002_m@yahoo.co.in

Abstract: Theories of fuzzy sets and rough sets are powerful mathematical tools for modeling various types of uncertainty. Molodtsov(1999) initiated a novel concept called soft sets a new mathematical tool for dealing with uncertainities. It has been found that fuzzy sets, rough sets and soft sets are closely related concepts (Aktas and Cagman 2007). Research works on soft sets are very active and progressing rapidly in these years. In2001Maji et al proposed the idea of intuitionistic fuzzy soft set theory and established some result on them. Based on an equivalence relation on the universe of discourse, Dubois and Prade (1990) intruduced the lower and upper approximation of fuzzy sets in a Pawlak approximation space and obtained a new notion called rough fuzzy sets. Feng et al.(2009)introduced lower and upper soft rough approximation of fuzzy sets in a soft approximation space and obtained a new hybrid model soft rough fuzzy sets which is the extension of Dubois and Prade¡¯s rough fuzzy sets. The aim of this paper is to consider lower and upper intuitionistic soft rough approximation of intuitionistic fuzzy sets in intuitionistic fuzzy soft approximation space (IF soft approximation space)and obtain a new hybrid model called Intuitionistic fuzzy soft rough sets which can be seen as extension of both the previous work by Dubois and Prade and Feng et al.

Key words: Fuzzy set, Soft set, Rough Set, Soft rough fuzzy set, Intuitionistic fuzzy soft rough sets.

On Rarely -continous Functions in Smooth Fuzzy Topological Spaces

B.Amudhambigai E-mail: rbamudha@yahoo.co.in

M.K.Uma and E.Roja

Department of Mathematics Sri Sarada College for Women, Salem-16

Abstract: In this paper,the concept of relay -continous functions in the sense of A.P.Sostak [13] and Ramadan [10] is introduce. Some interesting properties and characterizations of them are investigated. Also, some applications to fuzzy compact spaces are established.

Key words: Rarely continous functions, rarely -ontinous functions, generalized -ontinous functions, fuzzy -compact spaces, rarely fuzzy -almost compact spaces and fuzzy -rarely spaces.

Initial -closure paces

A.A.Ramadan

Department of Mathematics, Facutly of Science, Beni-Suef University, Egypt.

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

Department of Mathematics, Facutly of Science, Jazan University, Saudi Arabia

Abstract: In this paper, we prove that the category L-FC is a topological category over set. From this fact, we can define subspaces and products of L-closure paces. In particular, an initial structure of L-topological spaces can be obtained by the initial structure of L-closure paces induced by those.

Key words: L-topological spaces, L-closure paces, Initial -closure paces.

Stability of Aitive Mappings in Fuzzy Normed Space

Shaban Sedghi

Department of Mathematics Qaemshahr Branch, Islamic Azad University-Ghaemshahr, Iram E-mail address: sedghi_gh@yahoo.com

Nabi Shobe

Department of Mathematics, Islamic Azad University-Babol Branch, Iram E-mail

address: nabi_shobe@yahoo.com Abstract: In this paper we introduce a notion of stability of additive mappings in fuzzy normed spaces.

Key words and phrases: Fuzzy normed spaces, stability mappings.

Some Conclusion of Filters in Lattice Implication Algebra

Shaokun Du E-mail: yzdushaokun@163.com

Yang Xu and Weitao Xu

Intelligent Control Development Center, Southwest Jiaotong University, Sichuan, Chengdu 610031, China

Abstract: In this paper we prove that a filter is an ultra-filter if the filter is an implicative filter and a prime filter. The ultra-filter and the obstinate filter are coincident in lattice implication algebra. The concept of the fixed point is proposed in lattice implication algebra. At the same time, there exists no ultra filter in the lattice implication algebra which has a fixed point or the odd element. Some properties of the filter lattice are obtained in lattice implication algebra. Finally, the submaximal filter is presented in lattice implication algebra and itspropertise are studied.

Key words: Lattice implication algebra, implicative filter, Ultra-filter, Filter lattice, Submaximal filter.

A Simulation Based Fuzzy Programming Approach to Solve Discrete Multiobjective Chance Contrained Programming Problems

R.K.Jana

Department of Business Administration Indian Institute of Social welfare and Business Management, Kolkata 700073, India E-mail: rabinjana@gmail.com,Fax:+91-33-22413975

Abstract: A simulation based fuzzy programming approach is presented for solving a class of multiobjective programming (MOP)problems. The problem considered is a MOP in which some or all the constraints are chance constraints involving discrete random variables on both sides of constraints. Classical MOP techniques are not directly applicable to solve this type of problems as the deterministic equivalents of chance constraints are not possible to derive. Simulation based techniques are useful in such cases. In this work, Monte-Carlo simulation is used to estimate the probbilities and guarantee the feasibility of solutoins. It is combined with a genetic algorithm (GA) which is used as the search technique. Fuzzy programming formulation of the problem is developed first and then the compromise solution is obtained using the GA. The proposed method provides a comprmise solution to the given MOP.It is applied to a numerical test problem.

Key words: Chance Constraint, Multiobjective Programming, Discrete Random Variable, Fuzzy Programming, Monte-Carlo Simulation, Genetic Algorithm.

Some -Hausdorff Spaces

A.Singadurai

Department of Mathematics, TDMNS College, T.Kallikulam 627113 Tamilnadu, INDIA E-mail: singadurai_59@yahoo.co.in

Abstract: We define I-Hausdorff topological spaces and exhibit some -Hausdorff topological spaces. Some results related to -Hausdorff topological spaces are established.

Key words: -topology, -norm.

Fuzzy Congruence on A Lattice

M.J.Rani and N.R.Mangalambal

Department of Mathematics St.Joseph¡¯s College, Irinjalakuda,Kerala INDIA-680121 E-mail: krvarghese@rediffmail.com; thottuvai@sancharnet.in

Abstract: The notion of fuzzy congruence on a crisp lattice has been defined in an earlier paper by the author. In that, it has been proved that the collection of all fuzzy congruence FC(X) on a lattice X is a lattice under suitably defined meet and join operations. In this paper we further prove that FC(X) is a complete distributive lattice.

Key words: Fuzzy equivalence, fuzzy join compatible, fuzzy meet compatible, complete lattice, distributive lattice, fuzzy congruence.

Two Dimensional Graph

H.I.Attiya Basic Science Department, College of Industrial Education, Bine-suef University, Egypt

Abstract: In this paper, we will define a new type of graph it is the two dimensional graph. Some transformations on this graph will be discussed. The incidence and adjacency matrices are defined. Theorems which describe these transformations on this graph will be proved.

Key words: Graphs.