The Journal of Fuzzy Mathematics

Volume 2, Number 2, June 1994

CONTENT

DETAILS

Algebraic Knowledge Classification

M. Mashinchi

Department of Mathematics, Kerman University, Kerman,Iran.

M. Mukaidono

Department of Computer Science, Meiji University,214 Japan.

Abstract: This paper deals classification of knowledges when they are endowed with some fuzzy algebraic structures. By using the quotient group of symmetric knowledges we give an algebraic method to classify them. Also, by imposing the (anti) fuzzy subgroup construction we show how these knowledges can be classified. Several operations on knowledges are discussed.

Keywords: Generalized (t-conorm) t-norm, (anti) fuzzy subgroup, fuzzy coset, fuzzy quotient subgroup, isomorphic fuzzy subgroups, knowledge representation.

The Problem of Consumer's Selection in Fuzzy Conditions

Wieslaw Luczynski

Depatment of Microeconomics, University of Economics, Al, Niepodleglosci 10,60-967 Poznan, Poland

Marian Matloka

Depatment of Microeconomics, University of Economics, Al, Niepodleglosci 10,60-967 Poznan, Poland

Abstract: The paper concerns consumer's s it is election in fuzzy conditions,i.e.,it is assumed that both the functions of utility and budgetary restrictions are not "strictly" defined.

Keywords: The utility function, budgetary restrictions, fuzzy decision.

Fuzzy Almost Integer Varizbles in Integer Programming Problems

F. Herrera and J. L. Verdegay

Depatment of Computer Science and Artificial Intelligence University of Granada, 18071-Granada, Spain

Abstract: This paper deals with the study of integer programming problems in which there is some lack of precision of a vague nature in their variables considered. We propose a special type membership function for representing the lack of integrity of the variables, and a resolution metod to solve the model using -cuts of the fuzzy feasible set.

Keywords: Fuzzy integer programming, fuzzy variables .

On Semiregularization FuzzyTopologies

A. S. Mashhour

Depatment of Mathematics, Faculty of Science, Assiut University , Aswan, Egypt

K. M. Abd El -Hakeim

Depatment of Mathematics, Faculty of Science, Assiut University , Assiut, Egypt

Abstract: This paper discussed several properties of fuzzy topological spaces and how they are reflected by corresponding properties of the associated semiregualrization fuzzy topologies. For example a space is fuzzy nearly Lindelof if and only if its semiregualrization is fuzzy Lindelof. Various separation, Connectedness and mapping properties are considered.

Keywords: Fuzzy regular open, fuzzy separation, fuzzy almost locally connected, fuzzy nearly Lindelof.

Order Norms on Bounded Partially Ordered Sets

G. De Cooman and E. E. Kerre

Vakgroep Toegepaste Wiskunde en Informatica, Universiteit Gent, Belgium

Abstract: In this paper, we extend the domains of affirmation and negation operators, and more important, of triangular (semi) norms and (semi) conorms from the unit interval to bounded partially orded sets. The fundamental properties of the original operators are proven to be conserved under this extensions. This clearly shows that they are essentially based upon order-theoretic notions. Consequently, a rather general order-theoretic invariance study of these operators is undertaken.Also, in a brief algebaaic excursion, the notion of weak invertibilty of these operators is introduced, and the relation with the order-theoretic concept of residuals is studied. The importance of these results for fuzzy set theory and possibility theory is briefly discussed.

Keywords: Affirmation and negation operators, triangular norms and conorms,partially ordered sets, weak invertibility, residuals.

The Structure of Fuzzy Matrices

Liu Xiaodong Depatment of Basic Science, Dalian Maritime University , Da Lian,P. R.China

Abstract: In this paper, we have given the concept of fuzzy idempotent prime matrices of fuzzy idempotent prime matrices, each fuzzy matrix equals the sum of some idempotent fuzzy matrices. They are the important structure description of fuzzy matrices.

Keywords: Fuzzy algebra, fuzzy matrix, lattice, Schein rank, quasi-order.

The Solution of Fuzzy Equations

Liu Xiaodong Depatment of Basic Science, Dalian Maritime University , Da Lian,116024, P. R.China

Abstract: In this paper, we use the structure theorem of fuzzy idempotent matrix in [3] to study the solution of fuzzy equation, We have given the solution set of the fuzzy equation whose coefficient matrix is idempotent.

Keywords: Idempotent, Fuzzy idempotent prime matrix.

Fuzzy -irresolute Mappings

R. Prasad

Depatment of Mathematics and Statistics Dr. H.S.Gour Vishwavidyalaya, AGAR(M.P.) 470003 India

S. S. Thakur

Depatment of Applied Mathematics Government Engineering College, JABALPUR(M.P.) 482011 India

R. K. Saraf

Depatment of Mathematics Government Autonomous Science College, JABALPUR(M.P.).

Abstract: The purpose of this paper is to introduce and study the concept of -irresolute mappings in fuzzy topological spaces.

Keywords: Fuzzy Topologicals Spaces, Fuzzy -open, fuzzy -closed, fuzzy -irresolute, -closure, -interior.

The Second Adjoint Matrix of a Fuzzy Idempotent Matrix

Jin Bai Kim

Depatment of Mathematics ,West Virginia University Morgantown, WV 266506, USA

Kyu Hyuck Choi

Wonkwang University, IRI 570-749 Korea

Abstract: Let A be an fuzzy matrix and . We proved that if A is idempotent, then the second adjoint matrix adj(adj(A)) is idempotent, where adj(A) denotes the adjoint matrix of A, and gave a property of an idempotent matrix, an example and a theorem about idempotent fuzzy matrices.

Keywords: Idempotent fuzzy matrices, adjoint matrices of idempotent matrices.

Fuzzy Propositional Logic System FP(X)(I)

Qin Keyu and Xu Yang

Dept. Of App. Math, Southwest Jiaotong University, Chengdu,Sichuan 610031, China

Abstract: The paper presents a fuzzy logical system FP(X) with the Lukasiewicz implication operator, which is based on the methods of free-T algebra and lattice implication algebra. The semantical problems and the validity of FP(X) are discussed.

Keywords: Lattice implication algebra, free-T algebra, Lukasiewicz implication, validity.

Extension of Additive Fuzzy Measure

Ai-Bing Ji

Depatment of Administration, HeBei Staff Medical College ,China

Guang-Quan Zhang

Depatment of Mathematics ,HeBei University, China

Abstract: In this paper, we discuss the additive fuzzy measure which defined on generated fuzzy algebra, the extension theorem of normal additive fuzzy measure is given.

Keywords: Generated class of fuzzy sets, Normal additive fuzzy measure, Extension of additive fuzzy measure.

The Group of Fuzzy Closure Isomorphisms

T. P. Johnson

Depatment of Mathematics ,Fatima Mata National College, Kollam 691 1001, Kerala State, India.

Abstract: In this paper we study some relations between the group of fuzzy closure isomorphisms of a fuzzy closure space X and the group S(X) of permutations of the ground set X. It is proved that some proper subgroup of S(X) can be represented as group of fuzzy closure isomorphisms for some fuzzy closure operator on X. Also we discuss homogeneous fuzzy closure spaces.

Keywords: Fuzzy sets, fuzzy closure spaces, fuzzy closure isomorphism, homogeneous fuzzy closure space.

The -additive Measures Generated by Density Functions

Li Lushu

Depatment of Basic Science, Tax College of Yangzhou University,

Yanzhou, Jiangshu 225002, P. R. China

Abstract: In this paper we introduce a kind of density functions on a classical measure space, and we prove that this kind of density functions can generate -additive measures. The -independence concerning the density function is also studied. Some properties and results about this -independence, such as the analogous of the extension theorem of independent classes and Borel-Cantelli's lemma, are obtained.

Keywords: Measure space, density function, -additive measure, -independence

Fuzzy Bitopological Space and Separation Axioms

N. R. Das and P. C. Baishya

Depatment of Mathematics ,Gauhati University Guwahati 781014, India

Abstract: A fuzzy bitopological space is a non-empty set X equipped with two fuzzy topologies on it. Different pairwise separation axioms are defined as generalization of natural separation axioms in the sense that such a notion reduces to the natural separation axiom of a fuzzy topological space when two topologies of a fuzzy bitopological space. Relations between separation axioms of the mixed fuzzy topology with the corresponding pairwise separation axiom of the fuzzy bitopological space are main features of this paper.

Keywords: Bitopological space, mixed topology, pairwise Hausdorff, regular, -compact.

Fuzzy Normal Subgroups, Solvability of Fuzzy Subgroups and Congruence Relations

D. S. Malik, John N. Mordeson and M. K. Sen

Depatment of Mathematics and Computer Science Creighton University, Omaha, Nebraska-68178, USA

Abstract: Let be fuzzy subgroups of a group G such that is fuzzy normal in and , where is the identity of G. In this paper we show that is a Clifford semigroup. We study the notion of fuzzy congruence relations in fuzzy subgroup. Congruence relations in are also studied. The notion of solvability of a fuzzy subgroup is also introduced. It is shown that if is a solvable fuzzy subgroup of G and is a fuzzy subgroup of G, then is also solvable.

Keywords: Fuzzy normal subgroup, solvability , congruence relation, Clifford semigroup, regular semigroup, inverse semigroup.

Fuzzy Exact Sequence in Category of Fuzzy Modules

M. M. Zahedi and R. Ameri Depatment of Mathematics , Kerman University Kerman, Iran

Abstract: In this note, at first the concept of a fuzzy exact sequence of fuzzy modules is defined and some related results are given. Then by using the concepts of push-out and pull-back in the category of R-fzmod, some results are given. It is shown by examples that the behavior of these notions in the crisp and fuzzy cases is different.

Keywords: Fuzzy R-module, fuzzy exact sequence, pull-back and push-out

-structure of FTS(III):Fuzzy Separation Axioms

Hu Cheng-ming

International Fuzzy Mathematices Institute P. O. Box 649, San Gabriel, CA 91778, USA

Abstract: In paper [1], the author introduced a group of fuzzy separation axioms which are generalizations of corresponding axioms in general topology [2]. Here we will relate these axioms in the -structure of FTS [4][5].

Keywords: Weakly separated, separated, strongly separated, disconnected, FSi axioms, FTi axioms, FCN axiom, FPN axiom.

S-closed Symmetric Topological Molecular Lattices

Guo-Jun Wang

Shanxi Teachers University Xi'an, 710062, China

Abstract: The aim of this paper is to continue the discussion for the properties of S-closeness introduced in [13] within the frame of symmetric topological molecular lattices that take fuzzy topological spaces as special cases. It is noteworthy that M. Erne's "translation h" can not move even a single step whenever there exists an order-reversing involution on the lattice.

Keywords: Symmetric topological molecular lattice, regular open (closed), S-closed externally disconnected, 0-dimensional.