The Journal of Fuzzy Mathematics
Volume 14, Number 1, March 2006
CONTENT
DETAILS
New Proof to First Dual Theorem on Fuzzy Posynomial Geometric
Programming
Cao Bing-yuan
School of Mayhematics and Information Sciences,Guangzhou University,
Guangzhou,ZIP 510405 ,P.R.China
Email:bycao@stu.edu.cn
Abstract: Based on the first dual theorem previously obtained on a fuzzy posynomial geometric programming,
a general fuzzy posynomial geometric one is changed into a monomial fuzzy posynomial geometric one.Since the latter is equivalent to a fuzzy linear one,a new proof is given to the theorem,which will play an important role in the study of a fuzzy strong dual theorem and of a more general fuzzy posynomial geometric one as well as a directly repeated algorithm to it.
Keywords: Geometric programming, Fuzzy posynomial, First dual theorem, New proof
Minimization Algorithm of Mizumoto Type of Fuzzy Finite Automata
Wei Cheng
College of Computer Sciences and Egeneering
University of Electronic Science and Technology of China
Chengdu 610054 ,P.R.China
Email:weicheng@uestc.edu.cn
Zhi-Wen Mo
College of Mathmetics and Software Science
Sichuan Normal University, Chengdu 610066 ,P.R.China
Department of Applied Mathematics
Southwest Jiaotong University, Chengdu 610031 ,P.R.China
Email:mozhhiwen@263.net
Abstract: In this paper,a calss of fuzzy finite automata with a fuzzy initial state-i.e.,so-called Mizumoto type of fuzzy finite automata-is considered,and also two type of statewise equivalence relations are introduced.
Based on the statewise equivalence relations,a minimal form is difined and a minimization algorithm of Mizumoto type of fuzzy finite automata is obtained.
Keywords: Fuzzy finite automata, Mizumoto type of fuzzy finite automata, Minimization, Minimization algorithm
Principal T-ideals of Lattices
M.M.Atallah,
Math Dept.,Faculty of Science,Tanta Univ.,Tanta,Egypt.
F.I.Sidky and M.A.Miserif
Math Dept.,Faculty of Science,Zagazig Univ.,Zagazig,Egypt
Abstract: The purpose of this paper is to give a construction theorems of T-ideal generated by a fuzzy subset of a lattice L as a result the principal fuzzy ideal generated by a fuzzy subset is given. Also ,we prove some basic properties of the principal fuzzy ideal of a lattice L and two examples are given to show that the behavior of the principal fuzzy ideals is different from the principal ideals of a distributive lattice L.
Keywords: Algebra, Distributive lattice, T-ideals, Generators.
Fuzzy Topology on Fuzzy Sets:
Fuzzy Retracts
F.S.Mahmoud,M.A.Fath Alla and S.M.Abd Ellah
Department of mathematics, Faculty of Science ,Sohag, Egypt
Abstract: The concept of fuzzy topology on a fuzzy set was introduced by Chakrabarty and Ahsanullah in 1992.The concept of fuzzy retract was introduced by Rodabaugh in 1981.The aim of this paper is to introduce various fuzzy retracts in this new situation and establish some of their properties. Also, the relations between these new concepts are discussed.
Keywords: Fuzzy topology, fuzzy proper function, fuzzy retract, fuzzy semiretract.
The Saturation and Different Notions of Fuzzy Topogenous Orders
G.Elsalamony
Department of Mathematics ,Faculty of Science , Benha University ,Benha, Egypt
Abstract: Different notions of fuzzy tpogenous orders are introduced by many authors,e.g.,Katsaras [6],Manshour [9] and Gahler [4]. These three notions are each related to other by the notion of saturation of fuzzy topogenous order .Moreover,The notion of saturation is given in different forms (cf [1,4,5,9]) .In this paper ,we show that the saturated fuzzy topogenous orders ,in the sense of Mashhour [9],are in one-to-one correspondence with KatSaras fuzzy topogenous orders ,restricted to crisp sets. Also,the saturated fuzzy topogenous orders, in the sense of Gahler [4], restricted to crisp sets can be identified with Katsaras fuzzy topogenous orders, restricted to crisp sets.We show that [1,theorem3.5] lacks to a missing axiom ,so a correction is made and the equivalence of the two notions of saturation of Chung [1] and Kandil [5] is established .Finally ,some basic properties of these different notions of saturated fuzzy topogenous orders are investigated.
Keywords: Fuzzy neighbouhood spaces; Fuzzy topogenous order ; saturation fuzzy topogenous order ;fuzzy syntopogenous spaces.
On Perturbation Properties of Fuzzy Relation Equations
Zhang Chengyi
Depart. of Math.And Compu.Sc.,Hainan Normal University ,571158,Hainan,Haikou ,P.R.of china
Depart. Of math.,Zhumadian Theacher¡¯s College ,463000,Henan , P.R.of china
Lu changjiang
Depart. of Compu.Sc.,Sanming College ,365000,Fujian, Depart. P.R.of china
Li Dongya
Depart. Of math.,Zhumadian Theacher¡¯s College ,463000,Henan , P.R.of china
Abstract: In this paper ,the solving process of two kind of fuzzy relation equations are simplified .By the fuzzy solution invariant matrices ,the perturbation properties of fuzzy relation equations are considered and the open problem in [1]is solved .
Keywords: Fuzzy relation equation ,Solution invariant matrix ,Perturbation .
On Generalized Capacities and Para-regularity Theorems for Fuzzzy Measures
Jiongqi Wu
Depart. of Math., Zhangzhou Normal Univ.,36 Xianqianzhi Street ,
Zhangzhou 363000,Fujian,China.
E-mail:wujiongqi@263.net
Abstract: Suppose You is a Hausdorff space and Z is a non-empty set ,W is a cone of some positive functions on Z.The generalized capacity in this paper is defined to be some non-additive set mapping from to W. The capacitability theorem and some related properties of the generalized capacities are investigated .And from them a pararegulurity theorem for finite fuzzy measure on the Borel algebra of a metric space Y is obtained without other restrictions imposed on .
Keywords: non-additive set mapping, generalized capacity, capacitability, fuzzy measure, regularity.
Some Properties of Implication Operators
Yong Chan Kim and Jung Mi Ko
Department of Mathematics ,Kangnung National University ,
Gangneung,Gangwondo,210-702,Korea
Abstract: In this paper ,we introduce the t-norms,t-conorms and implications introduced by the product t-norm. We investigate the relations among implication operators ,Archimedean t-conorm(t-norm)and strictly decreasing (increasing )continuous functions .
Keywords: implication operators, t-norms, t-conorms, fuzzy negations
On Choquet Integrals of Fuzzy-valued Functions
Rui-sheng Wang
Academy of Mathematics and Systems Science£¬Chinese Academy of Science£¬
Beijing£¬100080£¬People¡¯s Republic of China
Ming-hu Ha
College of Mathematics and Computer Science ,Hebei University ,
Baoding,071002, People¡¯s Republic of China
Abstract: In this paper ,we give a further discussion on Choquet integrals of fuzzy-valued functions, including some properties and various kinds of convergence theorems like Lebesgue convergence theorem,Fatou¡¯s lemma ,a.e. convergence theorem, convergence in fuzzy measure theorem ,etc.
Keywords: Choquet integrals; fuzzy-valued functions; convergence theorems
On n-fold Fuzzy Implicative Filters of Lattice Implication Algebras with Operators
Jianming Zhan and Zhisong Tan
Department of Mathematics ,Hubei Institute for Nationalities,
Enshi, Hubei Province, 445000,P.R.China
Email: zhanjianming@hotmail.com
Abstract: E fuzzify n-fold implicative filters of lattice implication algebras, and investigate some of their properties. Moreover, we introduce the concept of n-fold M-fuzzy implicative filters and M-lattice implication algebras and obtain some related results. We give characterizations of M-lattice implication algebras. Finally, we study the normalization of n-fold M-fuzzy implicative filters.
Keywords: n-fold fuzzy implicative filters, n-fold M-fuzzy implicative filters, M-lattice implication algebras, M- normalization.
Nilpotent Faithful Fuzzy Ideals
P.Dheena and S.Coumaressane
Department of Mathematics,Annamalai University,
Annamalainagar-608 002,Tamilnadu,India.
E-mail: dheenap@yahoo.com and coumaressane_s@yahoo.com
Abstract: In this paper we have introduced the definitions like point insertion of factors property (PIFP),
insertion of factors property (IFP) and nilpotent faithful fuzzy ideal(NFFI). We have shown that a fuzzy ideal f of R is PIFP iff it has IFP and if f is a completely fuzzy semiprime ideal of R, then f has IFP. We have proved that R is a 2-primal ring iff FPR(R) is NFFI. We have also proved that R is 2-primal ring iff FPR(R) has IFP.
Keywords: fuzzy ideal, fuzzy point, fuzzy prime ideal, completely fuzzy prime ideal, fuzzy prime radical, nilponent faithful fuzzy ideal, completely fuzzy semiprime ideal, fuzzy left symmetric, fuzzy right symmetric.
On Generalized Multivalued Co-variational Inequalities with Fuzzy Mappings in Banach Spaces
Salahuddin and M.K.Ahmad
Department of Mathematics Aligarh Musilm University£¬Aligarh-202 002(U.E),India
Emails: salahuddin12@mailcity.com; mk_ahmad@postmark.net
Abstract: In this paper we consider a new class of generalized multivalued co-variational inequality problems with fuzzy mappings in Banach spaces. We establish an equivalence relation between a class of the generalized multivalued co-variational inequality problems with fuzzy Mappings and a class of implicit Wiener-Hopf equations with f Mappings in Banach spaces. This equivalence is used to suggest and analyze some iterative algorithms for finding the approximate solutions of generalized multivalued co-variational inequality problems with fuzzy mappings. Further, we prove the existence of solutions of this class of prolems and discuss the convergence of iterative sequences generated by the iterative algorithms.
Keywords: Generalized multivalued co-variational inequalities, implicit Wiener-Hopf equations, fuzzy mappings, Hausdorff metric, normalized duality mappings, Banach spaces, strongly accretive and Relaxed accretive mppings, g- strongly accretive and g-relaxed accretive mppings.
Choquet Integrals on L-fuzzy Sets
Rui-sheng Wang
Academy of Mathematics and Systems Science£¬Chinese Academy of Science£¬
Beijing£¬100080£¬P.R. China
Li-min Wang
College of basic Science, China University of mining and technology, Beijing, 100080, P.R. China
Ming-hu Ha
College of Mathematics and Computer Science ,Hebei University ,
Baoding,071002, P.R. China
Abstract: In this paper, we consider Choquet Integrals with respect to real-valued fuzzy measure on L-fuzzy sets. We first give the definition of Choquet Integral on L-fuzzy sets and discuss its some properties, then establish various kinds of convergence theorems like monotone convergence theorem, Fatou¡¯s lemma, bounded convergence theorem, a.e. convergence theorem, convergence in fuzzy measure theorem, etc.
Keywords: Lattice; L-fuzzy set; Choquet integrals; convergence theorems
Structure of Lattice Implication Algebra
Jun Ma
Department of Mathematics, School of Science, Southwest Jiaotong University
Chengdu, 610031, P.R.China
Wenjiang Li
School of Electric Engineering, Southwest Jiaotong University
Chengdu, 610031, P.R.China
Tianrui Li and Yang Xu
Department of Mathematics, School of Science, Southwest Jiaotong University
Chengdu, 610031, P.R.China
Abstract: Lattice implication algeria is an important logical algebra. In this paper, we discussed its construction on distributive lattice by analyzing the structure properties of it. We have show that a no-chain and non-Boolean lattice implication algebra must has at least two dual atoms, and it is impossible to build lattice implication algebra on some kinds of distributive lattice.
Keywords: Uncertainty reasoning, non-classical logic, lattice-valued logic, lattice implication algebra
An -fuzzy Version of Amann¡¯s Fixed Point Theorem for -fuzzy Monotone Multifunctions
Abdelkader Stouti
Department of Mathematics, Faculty of Science and Techniques
University Casdi Ayyad, P.O.Box 523. Beni-Mellal 23000, Morocco
E-mail: stouti@math.net
Abstract: An ¨Cfuzzy version of Amann¡¯s fixed point theorem for ¨Cfuzzy monotone multifunctions is given. Furthermore, we obtain the existence of greatest fixed point for ¨Cfuzzy monotone multifunctions.
Keywords: Fuzzy set, ¨Cfuzzy order relation, ¨Cfuzzy monotone multifunction, least fixed point.
Fuzzy Algebras and Directions
P.J.Allen,J.Neggers
Department of Mathematics University of Alabama
Tuscaloosa, AL 35487-0350 U.S.A.
Email: pallen@gp.as.ua.edu; jneggers@gp.as.ua.edu
Hee Sik Kim
Department of Mathematics Hanyang University Seoul 133-791, Korea
Email: heekim@hanyang.ac.kr
Abstract: Given an set X, a direction on X is a triple of functions from to used in modeling very general versions of (asymmetric ) order relations. Many natural examples of directions results from modeling a variety of systems including digraphs, fuzzy posets and intuitionistic fuzzy sets. Because of the naturally fuzzy from of directions there are many possible and interesting connections between directions on sets X and fuzzy subalgebras of (binary) algebras or fuzzy relations on X, i.e., fuzzy subsets of . In this paper we investigate some of the possibilities. We introduce the notion of P-proper binary operations, fuzzy coalgebras (directions), (directions) order and compare the latter to the order on BCK-algebras associated with these structures among other results.
Keywords: Directions (order), P-proper, pogroupoid, fuzzy subalgebra, fuzzy coalgebra, BCK-algebra.
Countably Paracompactness in L-topological Spaces
Meng Han and Meng Guangwu
Department of Mathematics, Liaocheng University,
Shandong 252000, People¡¯s Republic of China
Abstract: In this paper, the concept of countably paracompactness in L-topological space is introduced. The characterizations and properties of countably paracompact spaces are systematically discussed. In order to embody fuzzy the stratiform character of L-topology, the concept of ¨Cclosed set, which is a generalization for L-closed set, used in the paper.
Keywords: L-topology; countable paracompactness; ¨Cclosed set; Fuzzy lattice.
On Convering Dimension and Finitistic Spaces in L-topology
Dalip Singh Jamwal and Shakeel Ahmed
Department of Mathematics, University of Jammu,Jammu-180006 J&K, India
Abstract: In this paper, we have defined Covering Dimension and Finitistic Spaces in L-topology and proved some of their basic properties. According to [7], all L-fuzzy topological spaces defined in [9] are L- topological spaces. In this paper, we have also considered L-fuzzy topological spaces of [9] as L- topological spaces. Throughout this paper, the pair means an L- topological space where X is a set and is an L- topology on X. there are many types of covers defined in [9] (page no 817 to 190) . One among these is defined as a subfamily is said to be an open cover of an L- topological space if . We have used this cover in defining Covering Dimension and Finististic Space in L-topology.
Keywords: L-topology, Covering Dimension, Finististic Space, Topology.
Fuzzy - Paracompactness in Fuzzy Box Products
D.Susha
Department of Mathematics, Catholicate College
Pathanamthita Kerala, India.
Email: sushasivam@yahoo.com
Abstract: In this paper we characterize fuzzy ¨Cparacompactness fuzzy entourages. The preservation of fuzzy ¨Cparacompactness in fuzzy box products is also discussed.
Keywords: Fuzzy box products, fuzzy uniformity, -shading, ¨Cparacompact, locally finite, fuzzy entourage, fuzzy topologically complete.
Fixed Point Theorem for Six Maps in Fuzzy Metric Spaces
Bijendra Singh
S.S. in Mathematics Vikram university Ujjain (M.P.)456010
Shishir Jain
Shrink Vaishnav Institute of Technology and Science Gram
Baroli, Post Alwasa, P.O.Palia,Indore
Email: jainshishir11@rediffmail.com
Abstract: Sushil Sharma [11](Fuzzy Sets and Systems, 2002) established a fixed point theorem for six maps satisfying a contractive condition in a fuzzy metric space. The object of this paper is to correct, generalized and improve this result using compatibility of type ( ) and weak-compatibility of self-maps.
Keywords: Fuzzy metric space, t-norm, common fixed points, compatible maps, compatible maps of type ( ),compatible maps of type ( ), weak- compatible maps.
Fuzzy Multiplicative Ideal Theory II
Hwankoo Kim
Information Security Major, Division of Computer Science and Engineering, Hoseo University, Asan 336-795, Korea
E-mail: hkkim@office.hoseo.ac.kr
Myeong Og Kim,Sung-Mi Park,Young Soo Park
Department of Mathematics, Kyungpook National University, Taegu 702-701,Korea
E-mail: yngspark@knu.ac.kr
Abstract: In this paper, we characterize UFD¡¯s valuation domains and Prufer domains as Kaplansky-type theorem. We also characterize ¨Cdomains and Mori domains. Finally we introduce the concept of nonfactorable Fuzzy ideals and characterize Dedekind domains in terms of nonfactorable Fuzzy ideals.
Keywords: (Fuzzy) Algebra, fractionary fuzzy ideal, fuzzy invertible, nonfacterable fuzzy ideal, Dedekind domain, Prufer domain, UFD, valuation domain, ¨Cdomains ,Mori domain. |