THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 2, Number 4, December 1994

CONTENT

DETAILS

Fuzzy Control System with Trend Relational Predictor

Mian-Yun Chen

Department of Automatic Control Engineering, Huazhong University of Science and Technology, Wuhan 430074, P.R. China

Abstract: In this paper, a new fuzzy control system, i.e., fuzzy control system with trend relational predictor, is presented. At the same time, the trend relational analysis and SCGM(1,h)c-model are discussed. The simulational study for actual objects proved the system given here to be of good control effect.

Keywords: Fuzzy control system, system cloud, prediction control, trend relational analysis.

On Local Compactness in Fuzzifying Topology

Jizhong Shen

Department of Mathematics, Jiangxi Normal University, Nanchang 330027, P.R. China

Abstract: In this paper, we introduce the concept of local compactness in fuzzifying topology and establish some of its properties.

Keywords: Fuzzifying topology, local compactness.

Fuzzy Semi-Closure

Phullendu Das

Department of Mathematics, Visva-Bharati University, Bantiniketan, West Bengal, India

Abstract: The goal of this paper is to introduce the concepts of fuzzy pre-semi-closure operator, fuzzy semi-closure operator and examine the validity of the fuzzy version of the results obtained by Crossley and Hildebrand in the crisp case. Also a sufficient condition for a given collection of fuzzy sets in a ¢ú to form the collection of all fuzzy semi-closed sets of a fuzzy topology on ¢ú is obtained.

Keywords: Fuzzy topology, fuzzy semi-open set, fuzzy pre-semi-closure operator, fuzzy semi-closure operator.

Some Forms of Fuzzy Continuity

S.P.Arya and Neeru Singal

Maitreyi College, Bapu Dham Complex, Chanakyapuri, New Delhi-110021; Dept. of Mathematics, University of Delhi, Delhi-110007, India.

Abstract: The theory of fuzzy topological spaces and fuzzy continuity was introduced by Chang [2]. Since then, various weaker, stronger and independent forms of fuzzy continuity have been introduced and studied by different authors. The purpose of this paper is to investigate mutual relationships among some of these. In the process, we prove some characterizations of fuzzy o-closure, fuzzy 0-open sets and fuzzy strong 0-continuity,

Keywords:

Fuzzy Cosets of T-fuzzy Subloops

Phullendu Das

Department of Mathematics, Visva-Bharati University, Santiniketan, West Bengal, India

Abstract: Fuzzy cosets determined by T-fuzzy subloops of a loop are defined and the validity of some results analogous to those for fuzzy cosets of fuzzy subgroups of a group are examined. Given a T-fuzzy normal subloop u of a loop, the problem of defining a T-fuzzy quotient subloop determined by u is dealt with in the present paper. If u be a T-fuzzy normal subloop of a finite loop G, then it is proved that the index of u i.e., the cardinality of the set of all fuzzy cosets of u is a divisor of the order of G. But this result is not true if u is not normal.

Keywords: Fuzzy algebra, fuzzy cosets, fuzzy subloops, fuzzy quotient subloops.

The Covergence of Generalized Fuzzy Integrals on L-Fuzzy Sets: Part ¢ñConvergence in Fuzzy Measure Theorems

Wu Congxin and Song shiji

Dept. of Math, Harbin Inst. Of Technology Harbin 150001, China

Abstract: In this paper, the concept of generalized fuzzy integrals on L-fuzzy sets is introduced, and several convergence in fuzzy measure u theorems are obtained.

Keywords: L-fuzzy sets, generalized fuzzy integrals on L-fuzzy sets, convergence in fuzzy measure u

The Covergence of Generalized Fuzzy Integrals on L-Fuzzy Sets: Part ¢ò Monotone Convergent Theorems

Song Shiji, Wu Congxin

Dept. of Math, Harbin Inst. Of Technology Harbin 150001, China

Li Mingzhi

Zhejiang University, China

Abstract: In this paper, the concept of generalized fuzzy integrals on L-fuzzy sets are introduced, and several monotones convergent theorems are obtained.

Keywords: L-fuzzy sets, generalized fuzzy integrals on L-fuzzy sets, monotone convergent theorems.

A Note on Stable Subconstructs of FTS Determined by Level Sets

G. Elsalamony

Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt

R.Lowen

Department Wiskunde en Information, Universiteit Antwerpen, RUCA, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium

Keywords: Stable subconstructs of FTS.

Submachines of Fuzzy Finite State Machines

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

Department of Mathematics and Computer Science Creighton University, Omaha, NE-68178. USA

Abstract: In this paper we introduce the notions of submachine of a fuzzy finite state machine, retrievable, separated and connected fuzzy finite state machines and discuss their basic properties. A decomposition theorem for fuzzy finite state machines in terms of primary submachines is obtained.

On a Fuzzy Smirnov Compactification

J. Gutierrez Garcia and M.A. de Prada Vicente

Departmento de Mathematicas, Facultad de Ciencias Universidad del Pais Vasco-Euskal Herriko Unibertsitatea Apartado 644. 48080. Bilbao, Spain

Abstract: There are several different approaches to the concept of fuzzy proximity. In this paper we deal with the notion of fuzzy proximity introduced and studied by Artico and Moresco [1], which is compatible with Lowen¡¯s uniformities and consistent with Chang¡¯s fuzzy topologies (or with Lowen¡¯s fuzzy topologies as a special case of Chang¡¯s). For these kinds of proximities we give and extension that is strong-compct in the sense of Lowen [6]. In Section 1, preliminaries, some basic facts about Artico-Moresco¡¯s proximities, their associate topologies and the characterization given by Morsi [8] of these proximities in terms of characteristic functions that allows the whole proximity to be retrieved are stated. Section 2 is devoted to fuzzy cluster. The notion of fuzzy cluster is introduced and its nature is analized. The special relation between clusters and prime prefilters is revealed, the important fact being that this connection is established preserving the characteristic set. In Section 3, strong-compactness is characterized in terms of fuzzy clusters. To do so, we use the characterization of strong-compactness in terms of prefilters whose characteristic set is open, as shown in [4]. These results allow us to give a separate extension of proximity space, including the given one as a dense subset, that turns to be strong-compact. This is the goal of Section 4.

Keywords: Fuzzy proximity; fuzzy cluster; prefilter; Smirnov compactification.

Fuzzy N-continuous Functions

S. Dang

Department of Mathematics, Government College, Rourkela-769004, India

A. Behera

Department of Mathematics, Regional Engineering College, Rourkela-769008, India

Abstract: The concept of fuzzy N-continuous function is introduced. Several characterizations and properties of such functions are explored using both localized and non-localized approaches available in the fuzzy literature.

Keywords: Fuzzy point, q-coincidence, fuzzy N-closed set, fuzzy o-continuous function, fuzzy N-continuous function.

Multiobjective Programming with Normal Fuzzy and Normal Random Variables

Debjani Chakraborty, R.N. Tiwari and J.R. Rao

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

Abstract: This paper presents a mathematical programming problem in a mixed environment where the parameters of some objectives and /or constraints are mutually min-related normal fuzzy variables and the other objecyives/constraints are with mutually independent normal random variables. A numerical example is given.

Keywords: Possibility distribution, normal fuzzy variable, normal random variable, chance-constrained programming techniques.

On Minimax Inequalities for Fuzzy Mappings

Byung-soo Lee

Department of Mathematics Kyaungsung University, Pusan 608-736, Korea

Shih-sen Chang

Department of Mathematics Sichuan University, Chengdu 610064, Sichun, China

Abstract: This paper presents the concepts of minimax inequalities for fuzzy mappings. Using this result, we give a generalization of Ky Fan¡¯s fixed point theorem to the case of fuzzy mappings on locally convex Hausdorff topological vector spaces.

Keywords: Fuzzy mappings, minimax inequality, fixed point theorem.

Unfuzzy Non-dominated Elements In Fuzzy Collective Choice Problems

Michael Wagenknecht

Technical University of Berlin, Institut fur Prozep-und Anlagentechnik, Project SVT Rudower Chausssee 5(Geb. 10.5) 12484 Berlin, Germany

Abstract: In our paper we deal with the existence of unfuzzy non-dominated elements(UND-elements) for fuzzy social relations(FSR) over finite sets. FSR¡¯s aggregate information given by single experts in form of fuzzy preferences by suited mean operators. For decision-making, the UND-element play an essential role, but their existence is not ensured for arbitrary fuzzy relations. Thus special conditions to the quality of decision (i.e. knowledge of the experts) and the class of mean operators are necessary. The investigations are carried out for rather a wide class of t-norms.

Keywords: Fuzzy preference relations, unfuzzy non-dominated elements, fuzzy social preferences

Degree of Approximation of Fuzzy Mappings by Fuzzy Polynomials

S.G. Gal

Department of Mathematics, University of Oradea Str. Armatei Romane 5, 3700 Oradea, Romania

Abstract: Introducing fuzzy polynomials of Bernstein-type, in Section 2 we give a constructive proof for the fuzzy variant of the Weierstrass¡¯s approximation theorem in [1] and the degree of approximation in terms of the modulus of continuity is obtained. Section 3 contains estimates for the approximation of periodic fuzzy mappings by trigonometric fuzzy polynomials of Jackson-type.

Keywords: Fuzzy mapping on closed interval, periodic fuzzy mapping, fuzzy polynomial of Bernstein-type, trigonometric fuzzy polynomial of Jackson-type, Hausdorff distance between fuzzy mappings, modulus of continuity.

On Some N-person L-game

Marian Matloka Department of Mathematics, University of Economics. Al.Niepodleglosci 10, 60-967 Poznan, Poland

Abstract: The aim of this paper is to explain a concept of solution for n-person game, which is called L-game. For such a game an equilibrium point is defined and Equilibrium Theorem is proved.

Keywords: n-person game, equilibrium point.

B.S. Lee, G.M. Lee, D.S. Kim

Department of Mathematics Kyungsung University, Pusan 608-736, Korea

Department of Natural Sciences, University of Technology, Pusan 608-739, Korea

Department of Applied Mathematics, National Fisheries University of Pusan, Pusan 608-737, Korea

Abstract: In this paper we obtain some fixed point theorems for fuzzy mappings defined on probabilistic metric spaces.

Keywords: Common fixed point, fuzzy mapping,

Menger probabilistic metric space Structure of L-fuzzy Groups and Relations

Laszlo Filep

Department of Mathematics, Bessenyei College, Nyiregyhaza, Pf. 166, H-4401, Hungary

Abstract: In this paper the membership set of a fuzzy set is a lattice ordered monoid. To define L-fuzzy groups and compatible L-fuzzy relations Zadeh¡¯s extension principle is used. Then the structures of these generalized concepts are studied, and many properties are established by this method.

Keywords: L-fuzzy sets, L-fuzzy groups, L-fuzzy relations, Zadeh¡¯s extension principle, lattice ordered monoid.

On Some Notions of a Fuzzy Multiobjective Nonlinear Programming Problems with General Parameters in the Objecyive Functions

Elsaid Ebrahim Ammar

Department of Mathematics, Faculty of Science, Tanta university, Egypt

Abstract: Different basic notions for fuzzy linear and nonlinear programming have been discussed in several papers. In this paper we give a formulation: The fuzzy optimization problem of the multiobjective nonlinear programming with general parameters in the objective functions by use of arbitrary transformation functions. The connections between the two problems are given. Since the stability concept plays a role in the ordinary and fuzzy optimization to describe the optimal solutions set, we introduce some fuzzy stability sets of the fuzzy problem. Some properties of these notions are presented.

Keywords: Parametric optimization, stability, efficient solution, weak-efficient solution, fuzzy theory, fuzzy solution.

Fuzzy Programming Approach to Multiobjective Assignment Problem

A.K. Bit, M.P. Biswal and S.S. Alam

Department of Mathematics, India Institute of Technology, Kharagpur-721 302, India

Abstract: The linear multiobjective assignment problem is a special type of vector minimum problem in which constraints are all equality type and the objectives are non-commensurable and conflicting in nature. All existing methods generate a set of efficient solutions for a multiobjective assignment problem. This paper presents a fuzzy programming technique and applies it to the linear multiobjective assignment problem. It gives efficient solutions as well as an optimal compromise solution. This method is compared with an existing algorithm using a numerical example.

Keywords: Multicriteria decision making; assignment problem; fuzzy programming.

A Note on a Fixed Point Theorem in Fuzzy Metric Spaces

Osmo Kaleva

Department of Mathematics, Tampere University of Technology, Tampere, Finland

Seppo Seikkala

Department of Electrical Engineering,Section of Mathematics, University of Oulu, Oulu, Finland

Keywords: Fuzzy metric space, fixed point theorem. Fuzzy Subgroups and Minimal Fuzzy p-subgroups Jae-Gyeom Kim Department of Mathematics, Kyungsung University, Pusan 608-736, South Korea Abstract: We investigate some conditions for a fuzzy subgroup to be written as the intersection of its all minimal fuzzy p-subgroups. Keywords: Fuzzy subgroup, fuzzy order, fuzzy p-subgroup.