The Journal of Fuzzy Mathematics
Volume 4, Number 1, March 1996
CONTENT
DETAILS
On the Fredholm Integral Equation of the First Kind and Ascoli-Arzela
Theorem of Fuzzy Set-Valued Function
Liu Yi Hun
Hebei University of Technology, Tianjin, China
Abstract: In this paper, the Fredholm integral equation of the first kind of fuzzy set-valued function is discussed. It is pointed out that the solution of the equation is unstable. By a functional defined on the space of continuous fuzzy set-valued function C(I, E1), the approximate solution of the equation is given. And the well known Ascoli-Arzela theorem is generalized in C(I, E1).
Keywords: Fuzzy set-valued function, integral equation, stability, Ascoli-Arzela theorem.
A Note on Fuzzy Factorizations
Nistala V.E.S. Murthy
Department of mathematics
Andhra University P.G.Center
Srikakulam-532402, A.P.State, India
Abstract: In this note, we essentially show that there are no non-trivial, (unique) fuzzy factorization and principal ideal, structures on a commutative ring with unity and without zerodivisors. Further, fuzzy simple rings are determined.
Keywords: Complelte Brouwerian lattice, L-fuzzy point, semiring, semidomain.
How Fuzzy are the Fuzzy Ideals?
Nistala V.E.S. Murthy
MIG-B 171, Sagar Nagar
VIZAG-530043, A.P.State, India
Abstract: In this paper, we establish a one-one correspondence, between the meet complete lattice of all fuzzy ideals of a ring and the meet complete lattice of all closed (crisp) ideals of the associated fuzzy-point semiring of the given ring, in such a way that it defines a complete meet homomorphism.
Keywords: Complete Brouwerian lattice, L-fuzzy point, m-semiring, s-semiring.
On Solving Multiobjective Nonlinear Programming Problems with General
Parameters in the Constraints Using the Fuzzy Mathematical Programming
Abou-Zaid H.El-Banna and El-Said E.Ammar
Department of mathematics, Faculty of Science, Tanta University, Tanta-Egypt.
Abstract: In this paper, a formulation of parametric multiobjective nonlinear programming problems in fuzzy mathematics as fuzzy nonlinear programming problems is presented. A special and general fuzzy problems will be considered. Also, some basic notions of the two fuzzy problems are defined. Moreover, the relations between these notions and the basic concepts of the ordinary problem are also introduced. An illustrative example is given.
Keywords: Vector optimization, parametric programming, efficient and weak efficient solutions, fuzzy programming, fuzzy solutions.
On Fuzzy Isomorphism
Sh.Salili And M.Mashinchi
Faculty Of Mathematics and Computer Science, Kerman University, Kerman, Iran
Abstract: In this paper we formulate a generalized definition of homomorphism (isomorphism) between T-fuzzy subgroups and compare it with the recent definition of isomorphism due to Ray(1992).
Keywords: t-norm (t-conorm), -admissibility, T-fuzzy (normal) subgroup, convex T-fuzzy subset.
Generalized Fuzzy Similitudes
Pratyayananda
Das
Department of mathematics, Burdwan University Burdwan, West Bengal, Pin-713-104, India
Abstravt:
Given a subinterval (a, b] of [0, 1], weak and strong (a, b)-similitudes and weak and strong (a, b)-fuzzy partition are defined. It is proved that a weak (resp. strong) (a, b)-similitude deterines a weak (resp. strong) (a, b)-fuzzy partition and conversely. Finally a generalized similitude which is a weak similitude in some subintervals and a strong similitude in some other subintervals and the corresponding fuzzy partitions are investigated.
Keywords: Fuzzy algebra, fuzzy relation, w-similitude, q-similitude, fuzzy partition, q-fuzzy partition.
A Parametric Study on Fuzzy Multiobjective Integer Linear ProgrammingProblems(Parameters in the Objective Functions and in the Constraints)
Mohamed S.Osman
Department of mathematics, Higher Technological Institue.
Ramadan 10th city, Cariro, Egypt
Omar M.Saad
Department of mathematics, Helwan University, Cariro, Egypt
Azza G.Hassan
Department of mathematics, Ain Shams University, Cariro, Egypt
Abstract: This paper deals with multiobjective integer linear programming problems with fuzzy parameters in the objective functions and in the constraints by using the concept of level set of fuzzy numbers. A parametric study is carried out on the problem of concern. In addition, a solution algorithm is described to soluion algorithm is described to solve the formulated model. This algorithm is based mainly on the weighting method together with the technique of Gupta and Ravindran. A numerical simple example is included to clarify the theory developed in the paper.
Keywords: Fuzzy multiobjective linear programming, Mixed-integer programming, Fuzzy parameters, Fuzzy numbers, Stability.
De Morgan Algebra of Topology V
Zike Deng
Department of mathematics, Hunan University
Changsha 410082, Hunan, China
Abstract:
We give a necessary and sufficient condition for a de Morgan Algebra of topology to be uniformizable. Among its special cases are traditional uniformization theorem and the fuzzy one.
Keywords:
De Morgan Algebra of topology, De Morgan Algebra of uniformity.
Pseudo-Linear Algebra
A.Markova
STU Radlinskeho 11 81368 Bratislava, Slovakia
Abstract: For a given additive generator g, basic notions of pseudo-linear algebra based on g are introduced, such as g-inverse matrix, g-determinant, etc. Colosed connection of some integrals for fuzzy measure (PAN-integral, Pap's integral) with generator g promisses to introduce several applications.
Keywords:
Additive generator, fuzzy measure, g-integral, pseudo-addition, pseudo-multiplication.
On Disconnectedness In FTS
Arun K.Srivastava and Anuranwaj Singh
Department of mathematics, Faculty of Science,
Banaras Hindu Universtiy, Varanasi-221005, India
Abstract:
The purpose of this paper is to initiate a study of (Preuss' concept of) 'disconnectedness' in the category of fuzzy topological spaces. Connections between this concept and certain separation axioms in fuzzy topology are also pointed out.
Keywords: Connectedness, disconnectedness, fuzzy T0 and T1-separation axioms.
Fuzzy Linear Order-Homomorphism and Its Structures
Fang Jin-Xuan
Department of mathematics, Nanjing Normal University
Nanjing, Jiangsu 210097, P.R.China
Abstract: In this paper, the concept of fuzzy linear order-homomorphism is introduced and its structures are studied. We prove a decomposition theorem and a pointwise characterization theorem for fuzzy linear order-homomorphism.
Keywords: Order-homomorphism, fuzzy linear ordear order homomorphism, fuzzy linear operator.
Approximate Reasoning Based on Regular Inference Functions
Wangming Wu* and Ho Chung Lui
Institute of Systems Science,
National University of Singapore, Singapore 0511
Bo Yuan
Department of Systems Science and Industrial Engineering
Thomas J.Watson School, Binghamton University-SUNY,
Binghamton, New York 13902 USA
Abstract: In this paper, a parametric approach based upon regular inference functions for approximate reasoning is presented. Inferences in approximate reasoning systems are realized by either the compositional rule of inference (CRI for short) or the compatibility modification inference (CMI for short). In general, CRI and conventional CMI inference methods do not satisfy the basic inference criterion, modus ponens (MP for short). It seems a disadvantage to apply these two methods. In order to overcome this anomaly, we introduce the concept of regular inference functions with which the MP criterion is satisfied. Via parametric regular inference functions introduced in this paper, we present a parametric inference method for approximate reasoning with several parallel rules. Finally, the regular inference functions with set-valued fuzzy consequences for set-valued approximate reasoning are also discussed.
Keywords: Modus ponens, compositional rule of inference, compatibility modification, parametric disjunction, regular inference functions, approximate reasoning.
Posynomial Geometric Programming
Gao Bing-Yuan
Department of Mathematics,
Changsha University of ElectricPower,
Hunan, 410077, China
Abstract: With a weak dual theorem extended, the author gets some corresponding theorems in terms of fuzzy subconsistency, discusses a fuzzy converse theorem and builds a fuzzy strong dual theorem as he has developed the relationship between fuzzy posynomial geometric programming and its dual programming built on a fuzzy weak dual theorem[1, 2].
Keywords:
Fuzzy posynomial geometric programming, strong(or weak) dual, converse theorem.
Fuzzy Weakly Pre-Irresolute and Strongly Pre-Irresolute Mapping
Jin Han Park
Department of Natural Sciences, Pusan
National University of Technology,
Yongdang-dang Nam-ku, Pusan 608-739, Korea
Hoe Young Ha
Department of Mathematics, In-Je University, Obang-dong,
Kimhae, 621-749,Korea
Abstract:
In this paper, we introduce and study fuzzy weakly pre-irresolute and strongly pre-irresolute mappings between fuzzy topological spaces, which are stronger and weaker respectively than fuzzy pre-irresolute mappings.
Keywords: fuzzy weakly pre-irresolute mapping, fuzzy strongly pre-irresolute mapping, fuzzy topological spaces, fuzzy pre-irresolute mappings.
On Possibilistic and Interval Multi-Objective Programming
M.Wagenknecht
TU Berlin, Institut fur Proze und Anlagentechnik
Rudower. Chaussee 5 (Geb. 10.5), 12484 Berlin, Germany
A.V.Yazenin
Tver State University, Dept. Of Algorithmic Languages
Ul. Zhelyabova 33, 170000 Tver, Russia
Abstract: In the present paper we consider certain possibilistic multi-object programming problems. It shown that they can be reduced to interval programming for which powerful algorithms are available. The linear case is considered as special application.
Keywords: Possibilistic multi-object programming, interval optimization, linear programming.
Variational Inequality with Fuzzy Function
Hsiao-Fan Wang and Hsueh-Ling Liao
Department of Industrial Engineering, National Tsing-Hua University
Hsinchu, taiwan, ROC
Abstract: In this study, we discuss a kind of variational inequality problem with fuzzy functions, denoted by VI ( ) . According to the existence theorm, an approach derived from the concepts of multiple objective mathematical programming problems for solving the VI( ) is proposed, and an algorithm is developed to find its fuzzy optimal solution set. Furthermore, the LCP with fuzzy will also be discussed.
Keywords:
Ariational inequality, generalized complementarity problems, linear complementarity problems, fuzzy function.
Fuzzy Homomorphisms of Rings and Algebraic Structures of Fuzzy Subrings
Yao Bingxue
Department of mathematics, Liaocheng Teachers College,
Shandong 252000, P.R.China
Abstract: In this paper, the concept of fuzzy homomorphism of a ring is introduced and the fuzzy subring generated by a fuzzy subset is discussed.
Keywords:
Fuzzy homomorphism, fuzzy subring , fuzzy ideal.
Graded Mapping and Its Application
Marian Matloka
Department of mathematics, Academy of Economics
al. Niepodleglosci 10, 60-967 Poznan, Poland
Abstract:
The aim of this paper is to explain a concept of fixed-point theorem for graded mapping. Next, the game is described and the equilibrium theorem is proved.
Keywords: Graded mapping, fixed point, graded game, equilibrium play.
Remarks on Convergent in Fuzzy Measure Theorem of Generalized Fuzzy Integrals on L-fuzzy Sets*
Wu Congxin
Department of Mathematics,Harbin Institute of Technology
Harbin 150001,P.R.China
Abstract: In this paper,our purpose is to modify the convergent in fuzzy measure theorem of generalized fuzzy integrals on L-fuzzy sets,which is shown in [2].
Keywords: Generalized triangle norm,generalized fuzzy integrals on L-fuzzy sers,convergent in fuzzy measure theorem.
Application of Fuzzy Loglinear Regerssion Analysis toEvaluation of Efficiency for DMUs
Yoshiki Uemura
Faculty of Education,Mie University,
Tsu,Mie 514 Japan
Masaki Kobayashi
Faculty of Economics,Osaka University
Toyonaka,Osaka 560 Japan
Kazuki Hiro
Nara National College of Technology
Koriyama,Nara 639-11,Japan
Abstract: The evaluation of efficiency for DMUs (Decision Making Units) in some company is very important. In this view point, the study of evaluation of efficiency is every active, on the basis of the formulation for the production function. Up to this time, loglinear method does not have the lower limit of the production set but the upper limit of one. Because we consider that the real problem has the production set from lower limit to upper limit, in this paper we construct the possibility production function by introducing the fuzzy theory into the loglinear production function. Every fuzzy parameter in the possibility production function is identified very easily by the concept of the fuzzy regression analysis. As we try to evaluate the efficiency by thes possibility production function, this method can obtain two efficiency ratings from upper limit and lower limit. By these two efficiency ratings, this methid can have the more exact ranking for DMYs than loglinear method. And the efficiency of loglinear model can be evidenved by non-efficiency ratings from the lower limit of possibility production function. We call this proposed method as the fuzzy loglinear regression anlysis.
Keywords: Loglinear model, possibility production function, possibility production set, fuzzy regression analysis, evaluation of efficiency.
Constructing Fuzzy Measures by Transformations
George J. Klir, Zhenyuan Wang and Wei Wang
Department of Systems Science and Industrial EngineeringThomas J. Wastson School of Engineering and Applied Science
Binghamton University-SUNY, Binghamton, New York 13902-6000, USA
Abstract: In a similar way as obtaining quasi-measures from classical measures, fuzzy measures can be constructed by transformations from other fuzzy measures. The relation berween the given fuzzy measures and the constructed ones is shown as a necessary and some typical transformations are discussed.
Keywords: Fuzzy measures, quasi-measures, Sugeno measures, order-isomorphism, structural characteristics of set functions.
On N-dimensional Fuzzy Integrals
Ma Ming1, Menahem Friedman2 and Abraham Kandel
Computer Science and Engineering Department
University of South Florisda, Tampa, FL 33620-5350 USA
Abstract: The concept of the one-dimensional fuzzy integral is extended to the -dimensional case. Twodifferent approaches which lead to an identical result are implemented and their applicability is illustrated with suitable examples.
Keywords: Fuzzy measure; fuzzy integral; abstract fuzzy measure; abstract fuzzy integral; vector lattice.
-filterbase and -semi -compactness in Fuzzy Topological Spaces
A.M. Zahran
Department of Mathematics, Faculty of Science,
Al-Azhar University, Assiut 71511, Egypt
Abstract: The concept of -semicompact fuzzy topological spaces (henceforth fts, for short) was introduced by A.S. Mashhour et al [9] and the concept of -closed fts was introduced by A.M. Zahran [14]. Inthis paper we study the cincept of -semi -compact fts which lie between the above teo concepts and we characterize -semi -compact spaces in terms of the concept of fuzzy - filterbase. Also, we show that an fts is -semi -compact iff is -compact, where is a fuzzy topology in which has as a subbase. Finally preservation of some fuzzy topological structures under some types of fuzzy continuity are studied.
Keywords: Fuzzy topology, -filterbase, fuzzy semi -cluster point, -semi -compact spaces, fuzzy semi irresolute function. |