THE JOURNAL OF FUZZY MATHEMATICS
  Introduction of The Journal   Instructions to Authors   Archive

The Journal of Fuzzy Mathematics

Volume 8, Number 4, December 2000

CONTENT

DETAILS

A Multi-item Fuzzy Displayed Inventory Model under Limited Shelf-space

T. K. Roy

Department of Mathematics, B.E. College (D.U.)

Howrah -711103, West Bengal, India

M. Maiti

Department of Applied Mathematics

Vidyasagar University Midnapore, West Bengal, India

Abstract: A multi item inventory model with displayed inventory level dependent demand has been formulated and solved in fuzzy environment under shelf-space constraint. Here, items are displayed in the shelves of limited area in the show-room along with the inventory in a back-room ware house. The shelves are always kept fully stocked and the demands are met from the backroom storage. Items are reordered as soon as the inventory in backroom storage is zero. In this model, fuzziness has been introduced in the inventory costs, profit goal and shelf-area. Fuzzy nature has been described by non-increasing and non-decreasing linear membership functions. The problem has been solved by generalized fuzzy geometric programming method and illustrated with a numerical example.

Keywords: Fuzzy sets, inventory, geometric programming

On Fuzzy Topological Subalgebras of BCH-algebras

Eun Hwan Roh

Department of Mathematics Education

Chinju National University of Education

Chinju 660-756, Korea

E-mail: ehroh@ns.chinju-e.ac.kr

Abstract: The aim of this paper is to introduce the concept of fuzzy topological subalgebras of BHC-algebras, and to obtain its some result.

Keywords: BHC-algebras, fuzzy subalgebras, fuzzy topological subalgebras.

On the Ultra-fuzzy Compactness of L-fuzzy Subsets

Zhou Wu-Neng Jingzhou Teachers¡¯ College, Jingzhou, Hubei, 434104 PR.China

Abstract: In this paper, the conception of the ultra-fuzzy compactness of L-fuzzy subsets is established. Moreover, the properties and the characterization of the compactness are discussed.

Keywords: L-fuzzy topological space, -net, -filter, ultra-fuzzy compactness.

A Note on the Article Fuzzy Less Strongly Irresolute Mappings and Fuzzy Less Strongly Semi-connected Sets

A.M. Zahran

Department of Mathematics,Faculty of Education for Girls

Bisha, Saudi Arabia

Abstract: The concept of fuzzy strongly semiopen sets, fuzzy strongly semicontinuity, fuzzy strongly semiopen _semiclosed), fuzzy S-irresolute and fuzzy S-irresolute open (closed) mappings, fuzzy S-separation axioms and fuzzy S-connectedness wre introduced by Bai Shi Zhong [5,6]. In 1995, Fang Jin Ming[1] has introduced the concepts of fuzzy less strongly semiopen sets, fuzzy less strongly semicontinuity and fuzzy less strongly semiopen (semiclosed) mappings. Finally,the concepts of fuzzy less strongly irresolute, fuzzy pre-less strongly semiopen, fuzzy pre-less strongly semiclosed mappings,fuzzy less strongly semi- axioms and fuzzy less strongly semi-connected sets were introduced by J H. Park and Y B. Park[2]. In this note we show that the concepts which due to both Bai Shi Zhong [Fuzzy Mathematics 4(2)(1996), 397-411] and J H. Park and Y B. Park [Fuzzy Mathematics 5(4)(1997), 975-987] are equivalents and hence J H. Park and Y B. Park¡¯s paper does not add thing for this field.

Keyword: Fuzzy strongly semiopen sets, fuzzy strongly semicontinuity, fuzzy S-irresolute, fuzzy less strongly semiopen, fuzzy less strongly irresolute.

Regression Model with T-Fuzzy Variables and Its Application in the Energy Sources Forecast ***

Cao Bing-yuan

Department of Mathematics

Shantou University, Shantou 515063, P. R. China

Abstract: This paper builds a new of energy sources regression forecast model with T-fuzzy variables, which is used to deal with the T-fuzzy variables gained by measures and tests in reality world. This model is of effect shown by a numerical example calculation.

Keywords: T-fuzzy variables, energy resources, regression forecast model, crude oil.

Primary Decompositions of Fuzzy Submodules

A.B. Makamba

Department of Mathematics, University of Fort Hare

Alice 5700 South Africa

V. Murali

Department of Mathematics (Pure&Applied), Rhodes University

Grahamstown 61340 South Africa

Abstract: This paper deals with decomposing a given fuzzy submodule into an intersection of primary fuzzy submodules. We firstly prove two uniqueness theorems concerning such a decomposition. Secondly we prove that such a decomposition exists when the ground module is Noetherian. The allied notions of reduced or irredundant primary decompositions, irreducible decompositions, isolated and embedded prime ideals are defined and their inter-relationship are studied while proving counter-examples where certain implications fail. We end the paper with an application of such a primary decomposition.

Keywords: Prime, primary fuzzy submodules, residual, primary decomposition, reduced primary decomposition, isolated or minimal primes, irreducible fuzzy submodules, isolated or minimal primes.

On the Prime Submodules and Radicals

B. Makamba

Department of Mathematics, University of Fort Hare

Alice 5700 South Africa

V. Murali

Department of Mathematics(Pure&Applied), Rhodes University

Grahamstown 61340 South Africa

Abstract: This paper deals with the notions of prime, primary and radical in the context of fuzzy submodules over a commutative ring. It is shown that these are extensions of the usual notions in the crisp setting. Several examples are provided where the results of crisp theory are not valid. The approach of reasoning with fuzzy point method is used innovatively. Radicals have been described as the intersection of minimal primes. We end with some open problems on finite-valued and finitely generated fuzzy submodules.

Keywords: Prime, primary fuzzy submodules, fuzzy ideals, fuzzy radicals, finitely generated, fuzzy direct sum, minimal prime and fuzzy subspaces.

Some Bifuzzy Topologies Induced by A Fuzzifying Topology: Part (I): Fundamental Concepts

K. M. Abd El-Hakeim and F. M. Zeyad

Department of Mathematics, Faculty of Science

Assiut University, Assiut 71516, Egypt

Abstract: We introduce four bifuzzy topologies induced by a fuzzifying topology and study the neighborhood structure of a point, derived operation, interior operation, closure operation and boundary operation for these bifuzzy topologies.

Keywords: Fuzzifying topology, bifuzzy topology, neighborhood structure, closure, interior, boundary.

On Prime Fuzzy Submodules

F. I. Sidky and M Ati A. Mishref

Mathematics Department, Faculty of Science,

Zagazig University, Zagazig, Egypt

Abstract: We introduce in this paper is the concepts of strongly prime, weakly prime and prime fuzzy submodules and prove some of their properties.

Keywords: Fuzzy Algebra, fuzzy subgroups, fuzzy ideals, fuzzy submodules, radical of fuzzy submodules, primary fuzzy submodules, prime fuzzy submodules.

Fixed Point Theorems in Fuzzy Metric Spaces

P.Vijayaraju and M. Marudai

Department of Mathematics Anna University

Chennai (Madras)-600 025 India

Abstract: The purpose of this paper is to prove some theorems in each of which the completeness of the spaces is omitted and the same conclusion is obtained as in Grabiec¡¯s fixed point theorem in fuzzy metric spaces but with different sufficient conditions.

Keywords: Fuzzy set, t-norm, fuzzy metric, fixed point.

On Fuzzy q-ideals of BCI-algebras

Yong Lin Liu

Department of Mathematics, Nanping Teachers College

Nanping 353000, Fujian, P. R. China

E-mail:ylliun@163.net

Jie Meng

Department of Mathematics, Northwest University

Xian 710069, P. R. China

E-mail:mengjie@pub.xa-online.sn.cn

Abstract: In this paper, we investigate the properties of fuzzy q-ideals in BCI-algebras. The characterizations and the extension theorem about fuzzy q-ideals are given. We introduce the notion of zero fuzzy ideal of fuzzy q-BIC(BCK)-algebras and give the several fuzzy ideal of characterization quasi-associative BIC-algebras.

Keywords: (Fuzzy) q-ideal, zero fuzzy ideal, (quasi-associative) BIC-algebra.

Absolute Value of Fuzzy Real Numbers and Fuzzy Sequence Spaces

A.K. Tripathy* and Sudarsan Nanda

Department of Mathematics, IIT Kharagpur

Kharagpur -721 302, W. B. India

Abstract: The absolute value of a fuzzy real number is redefined as the earlier definition in [1] is found to be incomplete. Some new fuzzy normed linear space valued sequence spaces have been defined and their properties are studied. Finally, two errors in the earlier papers[2]and [3] have been pointed out.

Keywords: Fuzzy real numbe, fuzzy normed linear space, sequence space, monotone and normal.

-convergence of Fuzzy Filters

Ali Ahmed Nouh

Mathematics Department, Faculty of Science

Mansoura University, Egypt

Abstract: The concepts of -convergence, -adherent and -adherent for fuzzy filters (filter bases) are introduced and studied. As applications of concepts, -closure of fuzzy sets, fuzzy Hausdorff, Urysohn, regular and semi regular spaces, fuzzy -continuous and fuzzy weakly continuous mappings and strong Q.H-closedness are characterized in terms of -convergence, -adherent and -adherent for fuzzy filters (filter bases).

Keywords: Fuzzy point, Q-neighborhood, fuzzy filters (filter bases), -limit, -adherent and -adherent point of fuzzy filters (filter bases), , , and -spaces, fuzzy -continuity, fuzzy weakly continuity, strong Q. H-closed spaces.

Intuitionistic Fuzzy Numbers and Intuitionistic Distribution Numbers

Liu Huawen

Department of Mathematics and Physics,

Shangdong University, Jinan 250061, Shandong, China

Shi Kaiquan

Department of Automation Engineering,

Shandong University, Jinan 250061, Shandong, China

Abstract: First, we define the cut-sets of intuitionistic fuzzy sets, and then, the decompositions of intuitionistic fuzzy set are established. Based on this, we define intuitionistic fuzzy numbers and intuitionistic distribution numbers, and give their extended operations. Furthermore, some applications of generalized pseudo-probability metric spaces and pseudo-metric spaces are discussed.

Keywords: Cut-sets, decompositions, intuitionistic fuzzy numbers, intuitionistic distribution numbers, generalized pseudo-probability metric.

On the Generalized Variational Inequalities and Quasi-Variational Inequalities for Fuzzy Mappings

Jong Yeoul Park

Department of Mathematics, Pusan National University

Pusan 609-735, South Korea

Jae Ug Jeong

Department of Mathematics, Dongeui University

Pusan 614-714, South Korea

Abstract: The purpose of this paper is to investigate the existence of solution for a class of generalized variational inequalities and quasi-variational inequalities for fuzzy mappings in locally convex Hausdorff topological vector spaces. The result presented in this paper generalize corresponding recent sesults of Chang and Zhang[4].

Keywords: Generalized variational inequalities, fuzzy mappings.

Perturbed Proximal Point Algorithms of Generalized Quasivariational Inclusions for Fuzzy Mappings

Jong Yeoul Park

Department of Mathematics, Pusan National University

Pusan 609-735, South Korea

Jae Ug Jeong

Department of Mathematics, Dongeui University

Pusan 614-714, South Korea

Abstract: In this paper, we study a class of generalized quasivariational inclusions for fuzzy mappings. By using the properties of the resolvent operator associated with a maximal monotone mapping in Hilbert space, we have established an existence theorem of solutions for generalized quasivariational inclusions for fuzzy mappings, suggesting a new iterative algorithm and a perturbed proximal point algorithm for finding approximate solutions which strongly converge to the exact solution of the generalized quasivariational inclusions for fuzzy mappings.

Keywords: Variational inequalities, iterative algorithms, fuzzy mapping.

Generalized Random Strongly Nonlinear Complementarity Problems for Random Fuzzy Mappings

Y. J. Cho*, J. H. Kim and S. M. Kang*

Department of Mathematics,Gyeongsang National University

Chinju 660-701, Korea

N. J. Huang**

Department of Mathematics, Sichuan University Chengdu, Sichuan 610064, P. R. China

Abstract: In this paper, we introduce a class of generalized random strongly nonlinear complementarity problems for random fuzzy mappings and construct some new iterative algorithms. We prove the existence of random solutions for this class of generalized random strongly nonlinear complementarity problems and the convergence of random iterative sequences generated by the algorithms. Our result extend some recent results in this field.

Keywords: Generalized random strongly nonlinear complementarity problem, random fuzzy mapping, algorithm, existence and convergence theorems.

The Structure of Fuzzy Power Ring

Yao Bingxue

Department of Mathematics, Liaocheng Teachers University

Shangdong 252059, P. R. China

Abstract: The problem of upgrade of some mathematics structure, such as ordered structure, topological structure, has been emphasized with the development of fuzzy mathematics. It is also interesting to consider the upgrade of the algebraic structure. All kinds of the structures are upgraded not only from their universes to their power sets but also from their universes to their fuzzy power sets. In this paper, the concept of fuzzy power ring is introduced and the structure of fuzzy power ring is discussed.

Keywords: Fuzzy power ring, fuzzy ideal, fuzzy semiideal, fuzzy quotient ring, fuzzy quasiquotient ring.

The Membership Dimension of A Fuzzy Subspace

Chuan-zhi Zhang

Department of Mathematics, Shangdong University

Jinan. Shandong 250100, P. R. China

Abstract: In this paper we introduce the concept of fuzzy subspace of a vector space. Some of their properties are investigated. Then we consider the membership dimension of the fuzzy subspace. Several results are obtained. Finally, we also consider the fuzzy congruencies on a vector space and show that there is one-to-one correspondence between the fuzzy subspaces and fuzzy congruencies.

Keywords: Fuzzy subspace, membership vector, membership dimension, flag basis, fuzzy congruence.

Compact and Bounded Sets in Fuzzy Metric Space

A. George and P. Veeramani

Department of Mathematics,Indian Institute of Technology

Mardas, Chennnai,-600 036, India.

Abstract: We define q-bounded,semibounded,totally bounded and unbounded sets in a fuzzy metric space X and study the relation between F-bounded sets and the above mentioned sets. Finally we prove that the staments (a) X is compact (b) X is sequentially compact and (c) X is complete dand totally bounded are all equivalent in a fuzzy metric space X.

Keywords: Fuzzy metric space, topology, analysis, unifoum,space.

Semi-open Sets and Semi-continuity in Fuzzying Topological Spaces

Guangji Zhang Department of Mathematics, Dalian University

Dalian 116622, P. R. China

Abstract: In this paper the concept of fuzzy semi-open sets and fuzzy semi-continuos mapping due to Azad (1981) .have been generalized to fuzzying topological space, and some of their properties are studied.

Keywords: Fuzzying topology space, Semi-open set, Semi-meighbourhood, Semicontinous mapping.

Fuzzying H-ideals in BCI-algebras

Zhang guangji and Lifu

Department of Mathematics, Dalian University

Dalian 116622, P. R. China

Abstract: n this paper, we define fuzzying H-ideals in BAI-algbra and sudy its several properties.

Keywords: Fuzzying H-ideals, BAI-algbra.

Resolvent Equations and Multivalued Variational Inequalities for Fuzzy Mappings

Muhanmmad Aslam Noor

Department of Mathematics,Statistics and Computer Science,

Dalhouse University, Halifax ,Nvva Scotia,Canda B3H 3J5.

Eissa A.Al-Sad

Department of Mathematics,College of Science University,

P.O. Box 2455,Riyadh 11451,Saudi Arabia.

Abstract: In this pwe paper, we introduce and stuy some new classes of multivalued variational inequalities for fuzzy mappings. These classes are more general and include the previously known classes of variational inequalities and related optimization problems as special cases.We also introduce some new reslvent fou fuzzy mappings.We prove that multivalued variational inequalities are equivalent to the fuzzy fixed point problems and the resovent equations for fuzzy mappings.This equivalence is used to discuss the existence of the solution of the multivalued variational inequalituies and suggest iterative algorithms for computing the approximate solutions. The convergence analysis is also studied. Our main results include the previously known results as special cases.

Keywords: Variational inequalities, resolvent equations, iterative methods, fuzzy mathematical programming.

The Prime Ideals and Congruence Relations of Double MS-algebras

Li Aiping

Department of Mathematics, Shang Rao Teacher¡¯s College

Jiangxi,334001,P.R.China

Pei Liwen

Department of Mathematics,Wuhan University

Wuhan,Hubei,430042,P.R.China

Abstract: - In this paper, any congruencers relation of double MS-alegebras L,and the congruence lattice Con(L) of double MS-algebras L is embed into the dual lattice X(P(L)) of the power set lattice of P(L).

Keywords: Double MS-algebras,prime ideal,congruence relation.

On Proper Fuzzfication of Finite Sate Machine

H.V. Kumbhokar and S.R.Chaudhri

Department of Mathematics,Shivaji University

Kolhpur,(M.S.)416004,INDIA

Abstract: In this note a problem of proper fuzzfication of a finite state machine is discussed and is shown that the concept of generalized state machine needs much to be desiered. A better fuzziffication is sugegested. The smallest completion of a fuzzy finite state machine is also propeosed.

Keywords: Fuzzy relation ,fuzzy finite state machine,generalized state machine, homomophism.