THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 8 Number 2 June 2000

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Topological De Morgan Algebras and Kleene-Stone Algebras

Luo Congwen

Department.of Mathematics, Hubei Three Gorges university

Yichang 443000,Hubei,P.R.China

Abstract: In this paper we investigate some properties of topological de Morgan algebras and Kleene-Stone algebras, the theory of Fiters and congruences and establish the relationship between them.

Keywords: Topological de Morgan algebra,Kleene-stone algebra,I-filter.

Fuzzy LI-Ideals in Lattice Implication Algebras II

Young Bae Jun

Department of Mathematics Education

Gyeongsang National University,Chinju 660-701,Korea

E-mail:ybjun@nongae.gsnu.ac.kr

Yang Xu, Keyun Qin and Jun Liu

Department of Applied Mathematics Southwest jiaotong university, Chengdu 610031,China

E-mail:yxu@center2.swjtu.edu.cn

Abstract: In[6],Y. B. Jun and Y.Xu fuzzified the concept of LI-ideals in lattice implication algebras, and investigated some properties. As a continuation of the paper [6],in this paper, we discuss the further properties of fuzzy LI-ideals.

Keywords: Lattice implication algebra,(fuzzy)LI-ideal,implication homomorphism

The Fuzzy Lattices with shell and Dangerous Signal Recognition Logic Systems Yalin Zheng and Winxiu Zhang

Institute of Information and System Science, Faculty of Science

Xi¡¯an Jiaotong university,Xi¡¯an.710049,the People¡¯s Republic of China

Abstract: In this paper ,a new kind of nonclassical logic is established. First, some new concepts such as Fuzzy lattices with shell, its Zadeh heart, its Boolean heart ,Fuzzy power set lattice with shell, Boolean algebra with shell , and unit interval with shell are proposed. The properties of Fuzzy lattices with shell are researched. Secondly, a new implication operator, Z-operator, is proposed, and a new valuation lattice, Z-valuation lattice is established. Thirdly, a new kind of nonclasscial logic, which takes a Fuzzy lattice with shell as valuation lattice, and is called dangerous signal recognition logic, is established. The properties of the new logic are investigated. Some interesting Results are obtained.

Keywords: Fuzzy logic; Dangerous signal recognition logic; Fuzzy lattice with shell; Zadeh heart; Boolean heart; Z-implication operator; Z- valuation lattice; approximate reasoning.

On the Controllability of Fuzzy Dynamical Systems (II)

Zouhua Ding and Abraham Kandel

Computer science and Engineering Department

University of South Florida, Tampa, FL 33620-5350 USA

Abstract: In this paper, we extend our investigation of the Fuzzy Dynamic System (FDS)-a new fuzzy logic system that provides a way to combine differential equations with fuzzy rules. FDS can be regarded as a new approach to intelligent control. One of the properties of FDS, controllability, is being studied, and the significance of our results is that given a deterministic system and a Fuzzy state with rule base. We can determine the rule base for the control which transfers the initial state to the given state to in a finite time. Moreover a formula is presented to determine the control of FDS.

Keywords: Fuzzy dynamic control system: controllability: fuzzy differential equation

Fuzzifying Codes and Fuzzifying prefix Codes

Xiang fu Zou

Department of Mathematics, Wuyi university, Jiangmen, 529000, China

Jizhong Shen

Department of Mathematics, Jiangxi Normal university

Nanchang,330027,China

Abstract: In this paper, We introduce the concepts of fuzzifying prefix codes on free monoid and discuss their elementary algebraic properties

Keywords: Free monoid, fuzzifying code, fuzzifying prefix code

Fuzzy Subsets and Fuzzy Subalgebras

J.Neggers

Department of Mathematics, university of Alabama

Tuscaloosa,AL35487-0350,U.S.A.

jnegger@gp.as.ua.edu

Hee Sik Kim

Department of Mathematics, Hanvang university

Seoul 133-791,Korea

heekim@email.hangyang. ac.kr

Abstract: In this paper we provide a method of families of fuzzy subsets using as images semigroups and d-algebrals instead of lattices or the interval[0,1] without additional conditions. These fuzzy subsets are fuzzy subsets are fuzzy subalgebras. It is possible to equip the internal[0,1]with extra structure so as to associate with a regular fuzzy subset one of the type introduced here. As well as worth nothing in its own right, it appears that this method may be useful in enriching standard fuzzy structure by adding additional information at little or no cost.

Keywords: Fuzzy subset, poset, (internal) d-algebral,BCK-algebra.

Gray Prediction PID Controller Design Using Fuzzy Grain Scheduling

Ching-Chang Wong

Department of Electrical Engineering, China Institute of Technology &Commerce

No.245 Sec .3,Yen-Chiu-Yuan Road, Taipei, Taiwan, Republic of China

Abstract: In this paper, based on the scheme of gain scheduling, a novel architecture of grey prediction Proportional-Integral-Derivative(PID) controller is proposed. The well-known PID control is a popular control technique used in industrial processes. Since it has simple structure and the Ziegler-Nichols tuning algorithms have been well developed. To simplify the design scheme as well as to enhance the ability of PID controller¡¯s design. According to different prediction is injected into the PID controller¡¯s design. According to different prediction step used in gray prediction PID controller responses of a closed-loop control system. Considering these different characteristics of grey prediction PID controllers, the fuzzy gain scheduling (FGS) is incorporated to determine the individual gain of the selected grey prediction PID controllers. Therefore, both good performances in transient and steady state can be easily achieved simultaneously. Simulation results exhibit the superiority of the proposed method over the conventional ones.

Keywords: Fuzzy gain scheduling, Grey systems, Grey prediction, PID control.

On Stability Fuzzy Vector Optimization Problems Mohamed Abd El-Hady Kassem Department of Mathematics, Faculty of Education Nizwa 699, postal code 611,Sultanate of Oman

Abstract: This paper deals with fuzzy decision making for multiobjective nonlinear programming problems (FMONLP) by using a parametric approach. The existing results concerning parameters in the objective functions are reformulated to characterize and decompose the parametric space in (FMONLP).An algorithm for obtaining any subset of the parametric space which has the same corresponding fuzzy efficient solution, is presented. An illustrative example is given to clarify the obtained results.

Keywords: Multiobjective nonlinear programming, Fuzzy decision making, fuzzy numbers, parametric programs, stability.

Fuzzy programming Approach to Bi-level Linear Programming Problems Surabhi Sinha

Department of Mathematics, Indian Institute of Technology

Kharagpur-721302, India.

M.P.Biswal*

Department of Mathematics, Indian Institute of Technology

Kharagpur-721302, India.

Email:mpb@maths.iitkgp.ernet.in

Abstract: In This paper we apply the Fuzzy programming approach to bi-level linear programming problems. We compare the present approach with the Kuhn-Tuker(K-T)transformation method. Kuhn-Tuker¡¯s optimality conditions are the necessary and sufficient conditions for the existence of an optimal solution to a bi-level programming problem (BLPP). By this method, the problem becomes a single objective Non-linear programming problem involving several variables and several constraints. Fuzzy programming approach to this problem is a supervised search procedure (supervised by upper lever decision maker ) which will generate a (non-dominated) satisfactory solution.

Keywords : Bi-level linear programming, kuhn-Tucker¡¯s optimality conditions, fuzzy programming, linear membership function, optimal solution, satisfactory solution. Fuzzy Automaton and Fuzzy Language Based on Complete Residuated Lattice-valued Logic (I) Huan Huang, Jizhong Shen Department of Mathematics, Nanjing normal university Nanjing 210097, China Abstract: We extend language over an alphabet X and study the relation between L-fuzzy automaton and L-fuzzy language. Some properties of L-fuzzy language. Some properties of L-fuzzy language is investigated

Keywords: Logic, language, Automaton.

On Fuzzy Translation BH-ideals

in BH-algebras Young Bae Jun

Department of Mathematics Education

Gyeongsang National University.

Chinju 660-701, Korea

Email:ybjun@nongae.gsnu.ac.kr

Eun hwan Roh

Department of Mathematics Education, Citinju National

University of Education,Chinju 660-756,Korea

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

Qun Zhang Department of Mathematics, Education Affairs of South-Central University for Nationalities.

Wuhan430074, P.R.China

Email:znmyjwc@public.wh.hb.cn

Abstract : We consider the fuzzification of (translation) BH-ideals in BH-algebras, and investigate some related properties.

Keywords: (Fuzzy)BH-ideal,(fuzzy) translation BH-ideal, level translation BH-ideal, (fuzzy) characteristic Translation BH-ideal.

Solving Functional Equations for Fuzzy sets

G.Elsalamony

Department of Mathematics, Faculty of science

Benha University, Benha, Egypt

Abstract: In this paper, we find the general solution of the functional equation, for fuzzy sets ,where S is a continuous t-conorm, T is a continuous t-norm and N is strong negation on the unit interval. This equation is the natural generalization of the classical relation in set theory A . Also, we find the solution of the excluded-middle laws for fuzzy sets. We discuss special solutions of the equation , which is a generalization the equivalence formula in classical set theory.

Keywords Functional equation, t-norm, strong negation, fuzzy sets, logical connectives.

Fubini Theorems for Set-valued and Fuzzy Integrals on Banach Spaces Wu Jianrong**

Department of Mathematics,

Harbin institute of Technology Harbin Heilongjing,150001,P.R.China

Abstract: In this paper, Fubini theorem is established for a set-valued integral, where the integral is defined in the manner of Pettis-Aumann; on this base, the corresponding result is proved for a fuzzy integral on a Banach space.

Keywords: Fubini theorem, set valued integral, fuzzy integral, Banach space.

Strong-AE and Strong-ANE Fuzzy Topological Spaces

F.S.Mahmoud and M.A Fath Alla

Department of Mathematics, Faculity of Science(82524),Sohag-Egypt

Email:Science@Sohag.Jwnet.Eun.Eg

Abstract: This paper is an attempt to give some applications of fuzzy topological concepts in the theory of retracts. Given a fuzzy topological space (X, ),we introduce new notions of fuzzy retraction, fuzzy contractibility, fuzzy neighborhood retraction, fuzzy absolute extensors and fuzzy absolute neighborhood extensors, using the family of its level-topologies . We check that these are well-defined fuzzy topological concepts and we compare some of them with the analogous fuzzy ones. We verify that these notions are not equivalent, and we give a lot of examples which illustrate this fac. Furthermore, some results connecting the new concepts have been established.

Keywords: , Strong-retract, Strong-contractibility, strong-neighborhood retract, strong absolute extensor, strong-absolute neighborhood extensor.

Genetic Algebras Their Fuzzy Analog

Elias Deeba and Andre de korvin

Department of computer and Mathematical Sciences

UH-D, 1 Main Street, Houston Texas77002,USA email deebae@dt.uh.edu

Abstract: Generally speaking, a genetic algebra is a mathematical realization of genes interaction. Since such interactions may involve a good deal of uncertainty, it becomes natural to consider the fuzzy analog of these algebras. In this paper, we study and extend the ideas of genetic algebras to the fuzzy setting.

Keywords: Genetic algebra, fuzzy logic.

Fuzzy Indirect Adaptive Output Tracking Control of Nonlinear Systems

Shaocheng Tong, Tao wang and Cai Min

Department of Basic Mathematics, Liaoning Institute of Technology

JinZhou, Liaoning 121001, P.R.China.

Abstract:

In this paper, a stable adaptive fuzzy output tracking control scheme is developed for a single-input-single-output unknown nonlinear system. The main characteristics of the proposed adaptive fuzzy are:i) it does not need the assumption that all the states of the system are available for full feedback, but introduces a high gain observer to estimate them.ii) it is composed of a robust control term and an equivalence fuzzy control so that it not only ensures the stability of closed-loop system, but also attenuates the effect of fuzzy approximation error on the tracking error of the system to arbitrary small level.iii) it is proved that the designed output feedback output feedback adaptive fuzzy control can recover the performance achieved under the state feedback controller.

Keyword: Fuzzy control, adaptive control, high-gain observer, nonlinear systems, output feedback.

Fuzzy Differential Equations and Solution Mapping .J.Y.PaxK,I.H.Jeong,and S.Y.lee

Department of Mathematics,Pusan

National university, Pusan 609-735, Korea

Abstract: We investigate asymptotic behavior of for the fuzzy initial value problem and the solution mapping is continuous for the fuzzy initial value problem.

Keywords: Fuzzy initial value problem, existence of solution, asymptotic behavior, solution mapping.

A Concept of Completeness of Fuzzy Quasi-uniform Spaces

Kamal El-Saady

Mathematical. Department, Faculty of Science

South Valley , Qena 83511, Egypt

E-mail:el-saady@mailcity.com

Abstract: In[5], Katsaras introduced the concept of fuzzy quasi-uniformity as a generalization of the Lowen¡¯s fuzzy uniformity [8].The aim of this paper is to introduce and study the concept of completeness of fuzzy quasi-uniform spaces.

Keywords: Fuzzy uniformities, fuzzy quasi-uniformities, Cauchy prefilters and fuzzyuniform completeness.

Stability of Stochastic Vector Optimization Problems

Mohamed Abd El-Hady Kassem and Elsaid Ebrahim Ammar

Department of Mathematics, Faculty of Science

Tanna University. Tanta, Egypt

Abstract: This paper deal with multiobjective nonlinear programming problems with random variables in the constraints. The existing results concerning the qualitative analysis of the notions; like the rest of the second kind; which were defined and analyzed in parametric convex programs are reformulated to study the stability of multiobjective nonlinear programming problems with random variables in the constraints under the concept of chance constrained. Given the numerical example to clarify the results.

Keywords: Multiobjective nonlinear programming, Stability, Stochastic programming, Parametric programming, Random variables.

Stability Fuzzy Approach for Solving Multiple Criteria and Multiple Constraint Level Nonlinear Programming Problem

Mohamed Abd El-Hady Kassem

Department of Mathematics, Faculty of Science

Tana University,Tana, Egypt

Abstract : This paper deals with a solution method to the multiple constraint level nonlinear programming(MC NLF) problem using the stability fuzzy nonlinear programming approach. This method finds a potential solution to the problem by solving a fuzzy nonlinear programming problem and determine the stability set of the first kind corresponding to this solution, therefore obtain the range of parameter which find the potential solution of this problem. A numerical example is used to illustrate this approach.

Keyword: Multiple Criteria Nonlinear Programming, Stability, Fuzzy Programming, Potential Solution, Parametric Programming.

The Structure of Fuzzy Power Group

Bingxue Yao

Department of Mathematics, Liaocheng Teachers University

Shangdong 252059,P.R.China

Hongxing Li Department of Mathematics, Beijing Normal University

Beijing 100875, P. R. China

Abstract: The upgrade of all kinds algebraic structure has been emphasized with the development of fuzzy mathematics. In this paper, the algebraic structures of a group is upgraded from their universes to their fuzzy power sets . Under some conditions, some relations between regular fuzzy power groups and fuzzy quasi-quotient groups are obtained. Also some relations between uniform fuzzy power groups and fuzzy quotient groups are obtained.

Keywords: Fuzzy power group, regular fuzzy power group, uniform fuzzy power group, fuzzy quotient group, fuzzy quasi-quotient group.

Associated Fuzzy Convexity and Completely Spaces

M.V.Rosa

Department of Mathematics, Bharata Mata College

Thrikkakara Cochin 682 021, India

Abstract: In this paper we introduce the concept of associated fuzzy convexity in a given convexity space introduced by R.E. Jamison[1]and study certain concepts related to this . We introduce completely spaces as a continuation of the study of separation axioms in fuzzy convexity spaces in [6].We also study subspace and product in this context.

Keywords: Fuzzy convexity, fuzzy convexity spaces, fuzzy subspace, fuzzy topology fuzzy convexity spaces.

Fuzzy Totally Semi-R Continuous Functions

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

Department of Mathematics, Faculty of Science,

Assiut University, Assiut, 71516, Epypt

Abstract: In this paper we show that Theorem 4.14(S.P.Sinha and S.Malakar 1994) is incorrect. Therefore we introduce the concept of fuzzy totally semi-R continuity condition then the result will be correct. Characterizations and properties of this new type of continuity are investigated.

Keywords: Fuzzy topology, fuzzy totally semi R-continuous functions.

The Property (p.g.p) and the Property (p.p.g.p)of Non-additive Lattice-valued Measures on Lattice Guangquan Zhang,Yong-Hong Wu

School of Mathematics and Statistics, Curtin University of Technology GPO Box U 1987,perth, Western Australia 6845, Australia

K.L.Teo

Department of Applied Mathematics, The Hong Kong Polytechnic University

Hung Hom, Kowloon, HongKong

Email:mateokl@polyu.edu,hk

Abstract: In this paper, the property (p.g.p) and the property (p.p.g.p) of non-additive lattice-valued measures are introduced. The relations of the property(p.g.p) with autocontinuity from below and the property (PSB) of non-additive lattice-valued measure are developed and presented.

Keywords: Non-additive measures, fuzzy measures, lattice, autocontinuity from above, pseudo-autocontinuity from below.

L-Fuzzy Relations and L-fuzzy subgroups

Fu-Gui Shi

Department of Mathematics, Capital Normal University

Beijing 100037, P.R.China

Abstract: In this paper the characterizations of L-fuzzy relations and L-fuzzy equivalence relations are presented by means of four kinds of cut sets of L-fuzzy sets. The characterizations of L-fuzzy subgroups and L-fuzzy normal subgroups are given by means of L-fuzzy left (right) congruence relations and level subgroups.

Keywords: L-fuzzy algebra, L-fuzzy relation, L-fuzzy equivalence relation, L-fuzzy subgroup, L-fuzzy normal subgroup.

-convergence Theory in L-fuzzy Topology

Shui-Li Chen

Department of Mathematics, Jianghan Petroleum Institute

Jingzhou, Hubei 434102,P.R. China

Xiang-Gong Wang

Department Geophysical Exploration, Jianghan Petroleum Institute

Jingzhou, Hubei 434102,P.R. China

Abstract: Fuzzy convergence theory is one of the most important objects of study in fuzzy topology. In this paper, a kind of new fuzzy convergence theory which calls -convergence with regard to molecular nets and L-fuzzy ideas is established. The concepts of L-fuzzy -continuity and L-fuzzy -irresoluteness in L-fuzzy topological are introduced and discussed. Some important properties of L-fuzzy -continuity and L-fuzzy -irresoluteness are characterized with the aid of the -convergence theory.

Keywords: L-fuzzy topological Molecular net, L-fuzzy ideas, -closure, -convergence, L-fuzzy -continuity, L-fuzzy -irresoluteness.

Generalized Continuity in Fuzzifying Topology Spaces

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

Department of Mathematics, Faculty of Science,

Assiut University, Assiut, 71516, Epypt

Abstract: We extent the concept of g-open set in fuzzifying topology and by making use of it several types of fuzzifying continuity are introduced and studied.

Keywords: Fuzzifying topology, g-open sets, g-continuity.