THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 18, Number 2, June 2010

CONTENT

DETAILS

Lagrangian Dual of Fuzzy Nonlinear Programming Problem and Duality

G. Panda

Department of Mathematics, Indian Institute of Technology, Kharagpur, INDIA-721302 E-mail: geetanjali@maths.iitkgp.ernet.in

S.Jaiswal

Department of Mathematics, Indian Institute of Technology, Kharagpur, INDIA-721302

Abstract: This paper deals with duality results of nonlinear programming problem in fuzzy scenario. An attempt is made to construct Langrangian dual of fuzzy nonlinear programming problem. Also some duality results for this pair of duals are proved.

Keyword: Fuzzy sets, nonlinear programming, membership function, fuzzy inequality, Langrangian dual.

E-convex Fuzzy Mappings and Its Application

Bao Yu-e

College of Mathematics and Computer, Inner Mongolia National University, Neimongolia, Tongliao 028043, P. R. China E-mail: byebed@163.com

Wu Cong-xin

Department of Mathematics, Harbin Institute of Technology, Heilongjiang, Harbin 150001, P. R. China

Abstract: In this paper, we introduce ad discuss the concepts of E-convex and quasi- E-convex fuzzy mapping, and we also obtain several characterizations of these generalized convexity for fuzzy mapping. Finally, we consider the application to fuzzy optimization for these kinds of generalized convex fuzzy mapping and give some significance results about the optimal solutions.

Keyword: Fuzzy mapping, E-convexity, Quasi E-convexity, Fuzzy optimization, Optimal solution.

Solution of Dynamic Programming Problem Using Fzuuy Data

Aparna Dutta

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

Hemanta K. Baruah

Professor, Department of statistics, Gauhati University, Guwahati-781014, Assam,India E-mail: hemanta_bh@yahoo.com

Abstract: In this article we have attempted to fuzzify two particular cases of Dynamic Programming Problem. Firstly we found a fuzzy solution of a Dynamic Programming Problem with single fuzzy additive constraint under fuzzy additively separable return using fuzzy data and secondly a fuzzy solution was obtained for a Dynamic Programming Problem with single fuzzy additive constraint under fuzzy multiplicatively separable return.

Keyword: Fuzzy additive constraint, fuzzy additively separable return, triangular fuzzy numbers, fuzzy multiplicatively separable return.

On ¦Á-fuzzy Orders

Abdelkader Stouti

UFR and Laboratory of Mathematics and Applications, Faculty of Sciences and Techniques University Sultan Moulay Slimane, P. O. Box 523,23000 Beni-Mellal, MOROCCO. E-mail: stouti@yahoo.com

Lemmaouar zedam

Laboratory of Pure and Applied Mathematics, M¡¯sila University P. O. Box 166 Ichbilia, M¡¯sila 28105, ALCERIA E-mail: l.zedam@yahoo.fr

Abstract: In this paper we study ¦Á-fuzzy orders. First, we establish some results which enable us to build new ¦Á-fuzzy orders from crisp order relations. Secondly, we give a result concerning compatible ¦Á-fuzzy orders defined on real vector spaces. Also, we characterize a subcategory of totally ¦Á-fuzzy orders which are compatible with the usual addition and multiplication on real line.

Keyword: Fuzzy set theorem, fuzzy relations, partial order, ordered linear spaces, ¦Á-fuzzy orders.

Connection between Fuzzy and Fuzzifying Topologies

A. K. Kasaras and C. G. Petalas

Department of Mathematics, University of Ioannina, Greece

Abstract: It is shown that every fuzzy topology induces a fuzzifying topology and every fuzzifying topology induces a fuzzy topology . Several of the properties of the mappings and are investigated.

Keyword: Fuzzy topology, Fuzzifying topology, Fuzzy quasi-proximity, Fuzzy quasiuniformity.

Fuzzy Programming Technique to Solve Single and Multi-objective Transportation Problem with S-curve Membership Function

Lisy Cherian

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

Sunny Kuriakose A. Union Christian College, Aluva, Kerala, India

Abstract: In this paper, we concentrate on solving single and multi-objective transportation problems with modified S-curve membership function. Here we consider the case where the parameters in the objectives of the transportation problems lie in a fuzzy interval, and also introduced a new algorithm to solve Multi-objective Fuzzy Transportation Problem. The result clearly show the superiority of the fuzzy approach in terms of best solutions for the objective function with respect to degree of satisfaction and vagueness ranging from 0 to 1. We illustrated with numerical example that the above approach infeasible and efficient. S-curve membership function,

Keyword: Fuzzy transportation problem,Multi-objective Fuzzy Transportation Problem, Fuzzy interval, Vagueness and degree of satisfaction.

Generalized Interval-valued Intuitionistic Fuzzy sets

Monoranjan Bhowmik

Department of Mathematics,T. T. T College, Paschim Medinipur-721101, India E-mail: monoranjan_bhowmik@rediffinail.com

Madhumangal Pal

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

Abstract: In this paper, we define generalized interval-valued intuitionistic fuzzy set (GIV-IFSs). In fact, all interval-valued intuitionistic fuzzy set(IVIFSs) are GIVIFSs but all GIVIFSs are not IVIFSs. Here we shown that some operations are valid for IVIFSs but not valid for GIVIFSs. Also, we studied the relational properties of GIVIFSs. Finally, we introduced some new operations over GIVIFSs and present a daily life problem regarding GIVIFSs.

Keyword: Interval-valued intuitionistic fuzzy sets, generalized interval-valued intuitionistic fuzzy sets, generalized interval-valued intuitionistic fuzzy relations.

Generalized Fixed Point Theorems and Banach Contraction Principle in Modified Intuitionistic Fuzzy Metric Space through Implicit Relations

Shobha Jain

Quantum Institute of Technology, Roork, Utrakhand, India. E-mail: shobajainl@yahoo.com

Shishir Jain

Shri Vaishnav Institute of Technology, Indore (M. P.). India. E-mail: jainshishirll@rediff.com

Lal Bahadur

Retried Principal Govt. Arts & Commerce College, Indore (M. P.), India. E-mail: lalbahadur@rediff.com

Abstract: In [17] R. Saadati et al. (Chaos Solution and Fractal 2006) prove some fixed point theorems in modified intuitionistic fuzzy metric spaces. In this paper it has been proved that they are true in a more general setting as well. This paper establishes two generalized fixed point theorems in modified intuitionistic fuzzy metric spaces using two implicit relations and lattice concept which generalizes some results of [17] apart from leading to two generalized Banach contraction principles in an intuitionistic fuzzy metric space. A characterization of an implicit relation has been established with some examples. All the results presented in this paper are new.

Keyword: Modified intuitionistic fuzzy metric spaces, common fixed points, implicit relation, weak compatible maps, t-norm, t- conorm.

A Theoretical Development of Similarity Measure between Intuitionistic Fuzzy Sets and Its Applications in Multiple Attribute Decision Making

Debashree Guha and Debjani Chakraborty

Department of Mathematics, IIT-Kharagpur, Kharagpur-721302, India E-mail: debjani@maths.ittkgp.erent.in

Abstract: In this paper, a new method to measure the degree of similarity between two intuitionistic fuzzy sets is presented. Example are given to compare the proposed method with the existing similarity measures. The results show that the new similarity measure can overcome the drawbacks of the existing methods. Finally, the proposed similarity measure is applied to multiple attribute decision making problems under intuitionistic fuzzy environment.

Keyword: Intuitionistic fuzzy sets, similarity measures, multiple attribute decision making.

Monte Carlo Methods in Fuzzy Multivariate Regression

Areeg Abdalla

University of Alabama at Birmingham Department of Mathematics Birmingham, Alabama, 352945, USA E-mail: abdalla@math.uab.edu

James J. Buckley

University of Alabama at Birmingham Department of Mathematics Birmingham, Alabama, 352945, USA E-mail: buckley@math.uab.edu

Abstract: We apply our new fuzzy Monte Carlo method to certain fuzzy multivariate linear and non-linear regression problems to estimate the best solution. The best solution is a vector of trapezoidal fuzzy numbers, for the fuzzy coefficients in the model, which minimizes an error measure. We use a quasi-random number generator to produce random sequences of these fuzzy vectors which uniformly fill the search space. In certain cases, where we know the structure of fuzzy function that generated the fuzzy data, we use an analytical method to find the fuzzy parameters in the fuzzy function.

Keyword: Fuzzy multivariate regression, Monte Carlo, random fuzzy vectors.

On Invertible Fuzzy Topological Spaces

Sunil C. Mathew

Department of Mathematics, St. Thomas College Palai, Arunapuram P. O. -686574,Kottayam(dist.). Kerala, India E-mail: sunil@stcp.ac.in, sunilmathew@rediffmail.com

Anjaly Jose

Department of Mathematics, St. Thomas College Palai, Centre for Mathematical Science (Pala Campus) Arunapuram P. O., Kottayam(Dt), Kerala 686574, India

Abstract: In this paper some conditions for an invertible fuzzy topological space to satisfy certain separation axioms are obtained. If the inverting set as a subspace satisfies separated, regular or normal properties, then it is proved that the completely invertible fuzzy topological space also do satisfy the respective properties. It is shown also that the same conclusion holds for the first and second axioms of countability of an invertible fuzzy topological space.

Keyword: Homeomorphism, invertible fts, completely invertible fts.

-fuzzy Subnear-rings and -fuzzy Ideals of Near-rings

R. Ezhilarasi a

Department of Mathematics, Annamalai University Annamalainger-608002, Tamil Nadu, India E-mail: rearas@gmail.com

S. Sriram

Mathematics Section, Faculty of Engineering and Technology, Annamalai University Annamalainger-608002, Tamil Nadu, India E-mail:sriramcdm@gmail.com

Abstract: In this paper, we introduce the notions of -fuzzy subnear-ring, -fuzzy ideal and -fuzzy quasi-ideal of near-rings and find more generalized concepts than those introduced by others. The characterization of such -fuzzy ideals are also obtained.

Keyword: -fuzzy subnear-ring, -fuzzy ideal , -fuzzy quasi-ideal .

Approximate Reasoning with Generalized Quantifier in the Lattice-value First-order Logic (¢ñ)

Zhou Ping Dept. of Math., Sichuan Normal University, Chengdu, Sichuan 610066, P. R. China

Jiang Ming

Dept of Physics, Southwest University for Nationalities, Chengdu, 610041, P. R. China

Sun Xipeng

Department of Mathematics, Southwest Finance and Economics University, Sichuan, 610074, P. R. China

Abstract: In the present paper, approximate reasoning with generalized quantifier in the lattice-valued first-order logic is focused. Some approximate reasoning results with generalized quantifier are proved. We also discuss the comparison of the generalized quantifier and get the generalized results of reasoning. Those will become the foundation of the resolution principle with generalized quantifier in lattice-valued first-order logic . Some approximate reasoning rules such as with generalized quantifier are proved. This will become the foundation of the linguistic logicreasoning with generalized quantifier in lattice-valued first-order logic.

Keyword: Approximate reasoning, lattice-valued first-order logic , generalized quantifier, comparison of the generalized quantifier.

-resolution Principle with Generalized Quantifier in the Lattice-valued First-order Logic (¢ò)

Zhou Ping

Dept. of Math., Sichuan Normal University, Chengdu, Sichuan 610066, P. R. China

Jiang Ming

Dept of Physics, Southwest University for Nationalities, Chengdu, 610041, P. R. China

Sun Xipeng

Department of Mathematics, Southwest Finance and Economics University, Sichuan, 610074, P. R. China

Abstact: In the prsent paper,it is disxussed the concepts of -resolution principle with generalized quantifier in the lattice-valued first-order logic . The Herbrand theorem with the generalized quantifer is proved.It is a theoretic foundation of automated reasoning for lattice-valued first-order logic .

Keyword: -resolution principle, generalized quantifier, lattice-valued first-order logic . Lattice implication algebra.

Some Classes of -convergent Sequences of Fuzzy Numbers Generated by Infinite Matrices

Ayhan Esi

Department of Mathematics, Science and Art Faculty, Adiyaman University, Adiyaman 02040, Turkey E-mail: aesi23@hotmail.com; aesi@adiyaman.edu.tr

Abstact: In this paper we define some classes of -convergent sequences of fuzzy numbers by using the A-transforms on generalizing the classes of sequences of fuzzy numbers , and , which were defined by Saves[9]. We also examine topological properties and some inclusion relations for these new classes of sequences of fuzzy numbers.

Keyword: Fuzzy numbers, fuzzy sets, complete, invariant means, metric space.

Tietze Extension Theorem for Pairwise Ordered Fuzzy Pre-extremally Disconnected Spaces

M. K. Uma and E. Roja,

Department of Mathematics, Sric and Sarada College for Women, Salrm-636016 Tamilnadu India

G. Thangaraj

Department of Mathematics, Jawahar Science College, Neyveli Tamilnadu India V. Seenivasan Department of Mathematics, Anna University, Trichy, Tamilnadu India

Abstract: In this paper, a new class of fuzzy topological spaces called pairwise ordered pre-extremally disconnected space is introduced. Tietze extension theorem for pairwise ordered fuzzy pre-extremally disconnected space has been discussed as in ¡®Kubiak [J. Appl., 25(1987), 141-153.]¡¯, besides proving several other propositions and lemmas.

Keyword: Pairwise ordered pre-extremally disconnected space, ordered -fuzzy pre-continuous function, lower (resp. upper) -fuzzy pre-continuous function¡£

Some Classes of Strongly Almost Convergent Sequences of Fuzzy Numbers Generated by Infinite Matrices

Ayhan Esi

Department of Mathematics, Science and Art Faculty, Adiyaman University, Adiyaman 02040, Turkey E-mail: aesi23@hotmail.com; aesi@adiyaman.edu.tr

Abstract: In this paper we define some classes of strongly almost convergent sequences of fuzzy numbers by using the infinite matrices. We also examine topological properties and some inclusion relations for these new classes of sequences of fuzzy numbers.

Keyword: Fuzzy numbers, almost convergence.

Double Fuzzy Semi-topogenous Structures

A. M. Zahram

Department of Mathematics, Faculty of Science, Al Azhar University, Assuit, Egypt. E-mail: amzahran@yahoo.com

M. Azab Abd-Allah

Department of Mathematics, Faculty of Science, Assuit University, Assuit, Egypt. E-mail: mazab57@yahoo.com

Kamal EL-Saady and A. Ghareeb

Department of Mathematics, Faculty of Science, South Valley University, Qena, 83523, Egypt. E-mail: el_saady@lycos.com, nasserfuzt@aim.com

Abstract: In this paper, double fuzzy semi- topogenous structures was introduced and characterized. The relationships with double fuzzy topology, double fuzzy quasi-proximity are introduced.

Keyword:

L-locally Uniform Spaces

Dipak K. Mitra

Department of Mathematics, Tezpur University Napaam-784028, India E-mail: dkmitra@tezu.ernet.in

Debajit Hazarika

Department of Mathematical and Science, Tezpur University Napaam-784028, India E-mail: debajit@tezu.ernet.in

Abstract: We develop L-local uniformity by localizing Hutton¡¯ uniformity. Every L-locally uniform space generate an L-topological spaces, the converse is also true if the space is regular. Every L-locally uniform space with countable base is shown to be pseudo-metrizable. An L-locally uniformity in a compact space turns out to be unique. It is also shown that L-weakly uniformly continuity which is a generalization of uniform continuity would imply continuity.

Keyword: L-topology, L-locally uniformity, fuzzy regularity, fuzzy pseudo-metrizablity, fuzzy compactness, fuzzy continuity.

A common Fixed Point Result in Fuzzy Metric Spaces Using Altering Distances

B. S. Choudhury

Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah-711103, West Bengal, INDIA. E-mail: binayakl2@yahoo.co.in

Kundu

Department of Mathematics, Sciliguri Institute of Technology, Siliguri, Derjeeling-734009, West Bengal, INDIA. E-mail: kunduamaresh@yhoo.com

Abstract: In this present work we extend the use of altering distances to the fixed point problems on fuzzy metric spaces. We introduce of a generalization of R-weakly commuting mappings on fuzzy metric space defined in the sense of George and Veeramani and prove a unique common fixed point theorem. We also cite an example.

Keyword: GV-fuzzy metric space, altering distance function, fixed point, -R-weakly commuting mapping of type .