THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 17, Number 1,March 2009

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Fuzzy Optimization with Partial Information about The Weight

Gang Li

Department of Mathematical and Physical Sciences Shandong Institute of Light Industry Jinan 250100, PR China

Abstract: Conventionally, the fuzzy optimization problem is defined as the simultaneous satisfaction of the constraints and the goals. No additional distinction is assumed to exist amongst the constraints and goals. In paper[1],an extension of the model was proposed for satisfying the problem constraints and the goals with preference where preference for different constraints and goals can be specified by the decision maker. The difference in the preference for the constraints and goals is represented by a set of associated weight factors. In this paper, only a precedence order in the weight is assumed. Anew method was proposed to obtain the (approximate) optimal solution of the fuzzy optimization problem through the simple computation.

Keywords: Fuzzy optimization, fuzzy linear programming, weighted constraints, partial information, weight

An Algorithm for Solving Multi-objective Fuzzy Linear Programming Problems

B.N.Sahoo

Department of Mathematics, Indian Institute of Technology, Kharagpur, INDIA E-mail: bus.iitkgp@gmail.com

M.P.Biswal*

Department of Mathematics, Indian Institute of Technology, Kharagpur, INDIA E-mail: mpbiswal@maths.iitkgp.ernet.in

Abstract: This paper presents and iterative goal programming approach for solving fuzzy multiobjective linear programming problem. This problem involves fuzzy aspiration levels of the objectives and fuzzy parameters in the right-hand side of the constraints. The concept of-level set is used to find a crisp bound of the constraints for which the objective will be optimally acheived. A Solution algorithm is described in sequential steps to solve the formulated model. An illustrative numerical example is given to clarify the theory and solution algorithm.

Keywords: Goal programming; multiobjective linear programming; fuzzy parameters; -level set.

Intuitionistic Fuzzy Topological K-algebras

M.Akram*

Punjab University College of Information Technology, University of the Punjab, Old Campus, Lahore-54000, Pakistan. E-mail: m,akram@pucit.edu.pk

Karamat H.Dar

Department of Mathematics,Govt.College,University Lahore,Katchery Road, Lahore-54000, Pakistan, E-mail address: prof_khdar@yahoo.com

Abstract: In this paper, we introduce the notion of intuitionistic fuzzy topological K-algebras and investigate some of their properties. We discuss the properties of homomorphic image and inverse image of intuitionistic fuzzy topological K-algebras. Some properties of C5-connectedness, supper connectedness,compactness and Hausdorff spaces in intuitionistic fuzzy topological K-algebras are also discussed.

Keywords: Intuitionistic fuzzy continuous maps; C5-connectedness; supper connectedness; compactness; Hausdorff spaces.

The Uniformizability of L-topological Groups

Fatma Bayoumi* and Ismail Ibedou

Department of Mathematics, Faculty of Sciences, Benha University, Benha 13518, Egypt *E-mail: fatma_bayoumi@hotmail.com

Abstract: In this paper, we show that any stratified L-topological group, is uniformizable. That is, we element of, unique left and right invariant fuzzy uniform structures on G compatible with the fuzzy topology.On the other hand ,on any group G , using a family of prefilters on G fulfills certain conditions, we construct those left and right fuzzy uniform structures which induce a stratified fuzzy topologyon G for which is a stratified L-topological group and this family of prefilters coincides with the family of prefilters corresponding to the fuzzy neighborhood filter at the identity element of. Moreover, we show the relation between the L-topological group and the GTi-spaces, such as: the fuzzy topology of an L-topological group(resp., a separated L-topological group) is completely regular, (reso., GT3?)

Keywords: Fuzzy filters; Fuzzy uniform spaces;Fuzzy topological group; GTi-spaces; completely regular spaces; GT3?-spaces; L-Tychonoff spaces.

Vague Vector Space

Randall Crist and John N.Mordeson

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

Abstract: We examine the notion of a vague vector space. We introduce the notions of vague linear independence and vague spanning of a vague vector space. We show that there is a bijection between the set of all invariant similarity relations on a vector spaces V and the set of all fuzzy subspaces of V. this bijection yields a connection between invariant similarity relations, fuzzy subspaces. This connection can be used to compare properties of each.

Keywords: Vague vector space; vague linear independence; vague spanning; invariant similarity relations; fuzzy subspaces

RS-isocompactness in L-fuzzy Topological Spaces

R.N.Bhaumik

Department of Mathematics, Tripura University, Suryamaninagar_799130, Tripura, India E-mail: bhaumik_r_n@yahoo.co.in

J.Bhattacharya

Ramesh H.S.School,Udaipur, South Tripur, India

Abstract: Bhanmik and bhattacharya introduced the concept of isocompacetness in L-fuzzy topological spaces. The aim of this paper is to introduce another from of L-fuzzy isocompacetness,namely, RS-isocompacetness and to study some of the basic properties of this space.

Keywords: L-fuzzy RS-compact spaces, L-fuzzy almost open mapping, L-fuzzy almost continuous mapping, L-fuzzy imcompact spaces, L-fuzzy Hausdorff spaces, L-fuzzy regular space.

Algorithm for The Solution of A 2-person Zero-sum Game with PureStrategy Using Fuzzy Data

Aparna Dutta

Institute of Advanced Study in Science and Technology, Guwahati-781035,Assam,India E-mail: aparnad_lasst@yahoo.co.in

Hemanta K.Baruah

Department of Statistic, Gauhatl University, Guwahati-781035,Assam,India E-mail: hemanta_bh@yahoo.com

Abstract: In this article, we have attempted to fuzzify a 2-Person Zero-sum game with pure strategy, where we have fuzzified the payoff matrix using triangular fuzzy numbers and we have also attempted to fuzzify the maximin and minimax principle to find a fuzzy solution to the game. Whave also given an algorithm for the fuzzy solution of the game.

Keywords: Fuzzy payoff matrix, fuzzy the maximin and minimax principle.

Fuzzy Limit Structures over Completely Distributive Lattices*

Yueli Yue and Jinming Fang

Department of Mathematics, Ocean University of China Qingdao,266071,People¡¯s Republic of China

Abstract: In this paper, we study the Kubiak-Sostak extension of Li¡¯s limit molecular lattices and discuss the relationship between this extension and the corresponding extension of Wang¡¯s TML. We prove that FLimML ¨Cthe extension of Li¡¯s LimML-is a topological category over CDop and FLimML is isomorphic to LimMLc([0,1]) , where LimMLc([0,1]) is the co-tower extension of LimML.

Keywords: Fuzzy co-topology; fuzzy limit structure; fuzzy remote neighborhood system.

On Fuzzy Essential Submodules

Helen K.Saikia*

Department of Mathematics, Gauhati University, Guwahati-781014 INDIA E-mail: hsaikia@yahoo.com

Mrinal C.Kalita

Department of Mathematics, Pandu college, Guwahati-781014 INDIA

Abstract: Our attempt is on to fuzzify the concept of essentiality of modules over rings. In this paper we define fuzzy essential submodules and investigate various characteristics of such submodules. Necessary and sufficient conditions for fuzzy essential submodules are established. Notions of fuzzy relative complement and fuzzy closed submodules are introduced and related properties are obtained.

Keywords: Fuzzy submodules, fuzzy essential submodules, fuzzy direct sum, fuzzy closed submodules

Statistically Convergent Sequences of Fuzzy Real Numbers

Binod Chandra Tripathy*

Mathematical Sciences Division. Institute of Advance Study in Science and Technology, Paschim Boragaon Garchuk, GUWAHATI-781035; INDIA. E-mail: tripathbc@yahoo.com; tripathbc@rediffmail.com

Paritosh Chandra Das**

Department of Mathematics, Rangia College, Rangia-781354;Kamrup, Assam, INDIA. E-mail: daspc_rangia@yahoo.com

Abstract: In this article we study different properties of the statistically convergent and statistically null sequence spaces of fuzzy real numbers, like completeness, solidness, sequence algebra, symmetricity, convergence free and nowhere denseness.

Keywords: Fuzzy real numbers, statistical convergence, solid spaces, symmetric space, sequence algebra, convergence free.

On Fuzzy Ring Homomorphism

Tazid Ali*

Department of Mathematics, Dibrugarh University, Dibrugarh Assam, India

Pradip Sarker

Department of Mathematics, Govt. Kolasib College, Kolasib Mizoram, India

Abstract: In this paper we have introduced the concept of fuzzy ring homomorphism between fuzzy subrings, and study some of their properties. We have obtained a characterization of fuzzy ring homomorphism. Finally we have proved a classical result of quotient ring in fuzzy setting.

Keywords: Fuzzy point, fuzzy subring, fuzzy ring homomorphism.

Intuitionistic Fuzzy Optimization for Linear Programming Problems

Lisy Cherian

Mar Thoma College for Women, Perumbavoor, Kerala, Pin-683542.India E-mail: thomaspt46@yahoo.co.in

Sunny Kuriakose A.

Union Christian College, Aluva, Kerala,-683102,India

Abstract: The purpose of this paper is to show that the proposed non-membership function in our first paper ¡°A note on Intuitionistic Fuzzy Analysis¡± can bu use to solve the Intuitionistic Fuzzy Linear Programming (IFLP) problems (both single and multiple objectives) with in turn give a general model for the Intuitionistic Fuzzy Optimization [IFO] problems. This will give a generalization to the work of Plamen P. Angelove on optimization in an Intuitionistic Fuzzy (IF) environment.

Keywords: Intuitionistic Fuzzy Linear Programming (IFLP), Intuitionistic Fuzzy multiple objectives Linear Programming (IFMOLP), Fuzzy Optimization (IFO), degree of acceptance and rejection.

A New Dynamic Rough Communication Model and Its Application

Jiqin Liu

Department of Statistics and Mathematics, Shandong Finance Institute, Jinan, Shandong 250014, P.R. China

Kaiquan Shi

School of Mathematics and System Sciences. Shandong University, Jinan, Shandong 250100, P.R. China

Abstract: This paper puts forward a new dynamic rough communication model using two-direction S-rough sets theory, i.e., the two-direction S-upper approximation dynamic rough communication model. We discuss its properties, and obtain relationships between knowledge and information invariability, knowledge and information gain. Basing on the properties of the model, a method of improving dynamic rough communication accuracy is given. In the end, we give an application of the model, and obtain a dynamic rough communication principle.

Keywords: Two-direction S-rough sets; Two-direction S-upper approximation dynamic rough communication; Knowledge; Information gain

On Some Results in Fuzzy Subspace of Cc(X)

Mathews M.George

Department of Mathematics, B.A.M College, Thruthicad, Kerala-689597, INDIA. E-mail: mathewjas@rediffinail.com

M.S.Samuel

Department of Mathematics and Computer Applications, MACPAST, Kerala-689101, INDIA. E-mail: samuelms@sancharnet.in

Abstract: In this paper we introduce the basic concept of fuzzy points of a fuzzy subspace of the complex vector space Cc(X), the collection of all continuous complex functions on a topological space X having a compact support. Some of their properties are also discussed.

Keywords: Support of a complex function, fuzzy linear space, fuzzy points, fuzzy norm, fuzzy normed space, positive and monotone fuzzy linear functionls, fuzzy metricspace.

Fuzzy Weak Filters in Lattice Implication Algebra

Jiajun Lai

Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, P.R. China E-mail: eagles_laijiajun7309@126.com

Yang Xu

Intelligent Control Development Center Southwest Jiaotong University, Chengdu 610031, P.R. China

Abstract: In this paper we consider the fuzzification of weak filters in lattice implication algebras, and introduce the notion of fuzzy weak filters (briefly, FW-filters), normal fuzzy weak filters (briefly, NFW-filters) and completely normal fuzzy weak filter (briefly, CNFW-filters) of lattice implication algebras, and we also studied the properties of FW-filters, NFW-filters and CNFW-filters. Finally, we study relationship among FW-filters and fuzzy filters and Lattice filters.

Keywords: Lattice implication algebras, FW-filters, NFW-filters, CNFW-filters.

Intuitionistic Fuzzy Optimization for Multiple-objective Programming with Interdependence

Lisy Cherian

Mar Thoma College for Women, Perumbavoor, Kerala, Pin-683542 E-mail: thomaspt46@yahoo.co.in

Sunny Kuriakose A.

Union Christian College, Aluva, Kerala, India

Abstract: Here we proposed a general non-membership application function for solving Multiple Objective Programming [MOP] problems with interdependence in the Intuitionistic Fuzzy [IF] environment. This gives an extension to the work of C. Carlsson and Robert Fuller for solving Fuzzy Multiple Objective Programming [FMOP] problem with interdependence by considering both the membership and non-membership of the objective into account. We define a large family of application functions with degree of satisfaction and degree of rejection and illustrate our ideas by a simple three-objective problem. Also we claim the consistency and efficiency of optimization problems considering in the IF environment than analogous crisp and fuzzy environment.

Keyword: Multiple Objective Programming [MOP], intuitionistic Fuzzy Multiple Objective Programming [IFMOP], linear interdependence, application functions.

Rough Index in Information System with Fuzziness in Decision Attributes

G.Ganesan

Department of Mathematics, Adikvi Nannaya University Andhra Pradesh-533103, India E-mail: elgee110201@yahoo.com

D.Latha

Adarsh P. G. College of Computer Sciences, Mahbunagar (A. P), India E-mail: corida_durai@yahoo.com

C.Raghavendra Rao

Department of Computer and Information Sciences University of Hyderabad (A. P), India E-mail: crrsm@uohyd.ernet.in

Abstract: The theory of rough sets found wider applications in knowledge discovery and data mining. This paper deals with indexing the records of an information system by using a fuzzy decision attribute. The method of indexing is obtained by using the hedges of the fuzzy attribute.

Keywords: Rough sets, knowledge discovery, data mining, fuzzy attribute

On Upper and Lower Fuzzy-continuous Multifunctions

Khaled M.A.Al-Hamadi

Department of Mathematics, University of Pune, INDIA. E-mail: abusuliman88@yahoo.com

S.B.Nimse

Department of Mathematics, University of Pune, INDIA. E-mail: nacasca@rediffmail.com

R.A.Mahmoud

Department of Mathematics, Faculty of Science, Menoufia University, Shebeen El-Koom, EGYPT. E-mail: ramahmoud@yahoo.com

Abstract: The aim object to this paper is to introduce and study some characterizations and basic properties of both of upper and lower fuzzy -continuous multifunctions. Moreover, the composition these two multifunctions and their graphs are discussed. Finally, the effects of these both types on some topological spaces are also established.

Keywords: Fuzzy -open set, upper fuzzy -continuous, lower fuzzy -continuous multifunctions, fuzzy -compact, fuzzy -connected and fuzzy resolvable topological spaces.

A Fixed Point Theorem in Intuitionistic Fuzzy Metric Spaces through Asymptotical Commutativity

Servet Kutukcu

Department of Mathematics, Faculty of Science and Arts, Ondokuz Mayis University, Kurupelit, 55139

Samsun, Turkey

E-mail address: skutukcu@yahoo.com

Cemil Yildiz

Department of Mathematics, Faculty of Science and Arts, Gazi University, Teknikokullar, 06500 Ankara,Turkey E-mail address: cyildiz@gazi.edu.tr

Abstract: The purpose of this paper is to introduce the concept of asymptotical commutativity in intuitionistic fuzzy metric space and prove a common fixed point theorem on metric spaces, Menger probabilistic metric spaces, uniform spaces and fuzzy metric spaces.

Keywords: Topology, analysis, asymptotically commuting maps, common fixed point, intuitionistic fuzzy metric space.

On I-bitopological Space Induced by Fuzzy Quasi Pseudo Norm and Its Conjugate*

Guo-hua Xu and Jin-xuan Fang+

School of Mathematics and Computer Science, Nanjiang Normal University Jiansu 210097, China

Abstract: N. R. Das and P. Das [Fuzzy bitopological space induced by fuzzy quasi pseudo norm and its conjugate, fuzzy sets and systems 119(2001) 539-542] introduced and studied the I-bitopological space (X, Jp, Jq), where Jp and Jq are I-topologies induced by fuzzy quasi pseudo norm p and its conjugate q on X, respectively. The purpose of this paper is to point out that some properties of I-bitopological space (X, Jp, Jq) established by N. R. Das and P. Das are incorrect. We correct and generalize these results.

Keywords: Fuzzy quasi pseudo norm; -open sphere; I-topology; I-bitopological space; Pairwise (weakly) Hausdorff I-bitopological space

Common Fixed Point Theorems for Weakly Compatible Mappings in Intuitionistic Fuzzy Metric Spaces

Sushil Sharma

Department of Mathematics, Madhav Vigyan Mahavidhyalaya, Vikram University, Ujjain-456010, India. E-mail: sksharma2005@yahoo.com

Servet Kutukcu

Department of Mathematics, Faculty of Science and Arts, Ondokuz Mayis University, 55139 Kurupelit,

Samsun, Turkey.

E-mail: skutukcu@yahoo.com

Atul Pathak

Department of Mathematics, Mahakal Institute of Technology, Ujjain-456010, India.

Abstract: The purpose of this paper is to introduce the (S-B) property in intuitionistic fuzzy metric space under the condition of weak compatible mappings. We point out that the continuity of any mapping for the existence f the fixed point is not required. Our results extend several fixed point theorems.

Keywords: Intuitionistic fuzzy metric, weakly compatible mappings, (S-B) property, common fixed point.

Locally Fuzzy s-closed Spaces

Akrur Behera

Department of Mathematics, National Institute of Technology, Rourkela-769008, India E-mail: abehera@nitrkl.ac.in

Rabinarayan Satoathy

Department of Mathematics, Hi-Tech Institute of Technology, Bhubaneswar-752057, India

Abstract: Fuzzy semiregularity concept is introduced. Some preservation theorems are obtained by using certain fuzzy functions.

Keywords: Fuzzy s-closed space, fuzzy semiregular set, fuzzy quasi-irresolute functions.