The Journal of Fuzzy Mathematics
Volume 4£¬Number 4, December 1996
CONTENT
DETAILS
On the Relationship of Extended Necessity Measures to Implication Operators on the Unit interval, ¢ò
A. A. Abdeel-Hamid and Nehad N. Morsi
Department of Mathematics, Military Technical College, Cairo, Egypt
Abstract: By an (extended) necessity measure on a set X we mean a function, from to the unit interval , that preserves arbitrary meets. We continue to address the question of whether a given necessity measure on X is induced, through a given implication operator I on I and from some (unknow) normalized fuzzy subset of X, in the following manner£ºthe measure of is the degree of containment of in ; according to the implication I.
In the first part of this work, we provided characterizations to answer this question, in the cases of three types of implication operators. We here do the same for a fourth type of implications; the reciprocals of reciprocals of residuated implications, whose necessity measures we call the reciprocal-residuated ones. We investigate those (extended) generalized necessity measure (functions from to that preserve finite meets) that are obtained as superma of directed families of reciprocal-residuated necessity measures. We also seek conditions for necessity-possibility compatibility in some types of necessity and possibility measures.
Keywords: Necessity measure; generalized necessity measure; possibility measure; triangular norm; multiple-valued logic.
Fuzzy Congruence and Quotient Semiring of a Semiring
T. K Dutta and B. K.Biswas
Abstract: The aim of this paper is to introduce fuzzy congruence on a semiring, to obtain the relation between fuzzy congruence and fuzzy ideal of a semiring and to define and study fuzzy quotient semiring of a semiring over a fuzzy ideal or over a fuzzy congruence.
Keyword: Semiring, congruence, ideals, -ideals, fuzzy-congruences, fuzzy ideals, fuzzy -ideals, quotient semiring.
An Introduction to Fuzzy Subspaces in Intuitionistic Fuzzy Topological Spaces
Dogan Coker
Hacetiepe University,Department of Mathematics Education, Beytepe, 06532-Ankara, Turkey
Abstract: The purpose of this paper is to investigate fuzzy subspaces in intuitionistic fuzzy topological spaces introduced by Coker [7]. After giving the fundamental concepts such as intuitionistic fuzzy sets, intuitionistic fuzzy points, intuitionistic fuzzy topological spaces and fuzzy continuity in these spaces we present fuzzy subspaces, fuzzy A-topology, fuzzy A-continuity and other related topological concepts.
Keywords: Intuitionistic fuzzy set, intuitionistic fuzzy point, intuitionistic fuzzy topology, intuitionistic fuzzy topological space, fuzzy continuity, fuzzy subspace, fuzzy A-interior, fuzzy A-closure, fuzzy A-continuity. (TOP)
Interval-valued Fuzzy Relations in a Set Structures
H. Bustince
Department de Matem¨¢tica e Inform¨¢tica, Universidad P¨²blica de Navarra, 31006, Campus Arrosad¨ªa, Spain
Phone: 3448169254, Fax: 3448169565, E-mail: bustince@si.upna.es
P. Burillo
Department de Matem¨¢tica e Inform¨¢tica, Universidad P¨²blica de Navarra, 31006, Campus Arrosad¨ªa, Spain
Abstract: In this paper we analyze the interval-valued fuzzy relations in a set and their properties. Besides, we also study the properties of the composition of these relations with different t-norms and t-conorms. We present an order in the referential set induced by interval-valued fuzzy relations of order. We can see how this induced order justifies the definition given of interval-valued fuzzy antisymmetry.
Keywords: Interval-valued fuzzy sets, interval-valued fuzzy relations, t-norm and t-conorm, interval-valued fuzzy relations in a set, composition of interval-valued fuzzy relations, interval-valued ordering relation.
Fuzzy Logic Functional True Value Equation
Liu Jin Lu
Department of Mathematics, Liaocheng Teachers College Shandong 252000, P. R. China
Abstract: In this paper some conceptions about logic functional true value equation are introduced, a constructive solution theorem of the theorem of the fuzzy logic functional equation is presented. Moreover, a judgment condition is given by using the corresponding Boolean equation. Finally a basic method of solutions to those equations is suggested.
Keywords: Fuzzy logic function, fuzzy logic function true value equation, F-true.
On the F-quadratic Equation
Jinlu Liu and Kaiquan Shi
Institute of fuzzy System, Liaocheng Teachers Collegen Shandong 252000, P. R.China
Abstract: In this paper the conception of fuzzy quadratic form is given, same properties of this kind of functions are discussed. Basing on those results, a new kind of fuzzy quadratic equation is researched, a compatible condition of this equation is suggested, and the solution structure is put forward. This research includes the case of fuzzy linear equations.
Keywords: F-quadratic form, F-true, F-quadratic equation.
A Classification Method of Alternatives for Multiple Preference Ordering Criteria Based on Fuzzy Majority
F. Chiclana, F. Herrera, E. Herrera-Viedma, M. C. Poyato
Department of Computer Science and Artificial Intelligence E. T. S. de Ingenier¨ªa Inform¨¢tica
University of Granada, 18071-Granada, Spain
E-mail: Herrera, viedma@robinson.ugr.es
Abstract£º The purpose of this paper is to present a classification method of alternatives for multiple preference ordering criteria based on the concept of fuzzy majority. The fuzzy majority is represented by a fuzzy quantifier, and applied in the aggregation by means of OWA operator whose weights are calculated by the fuzzy quantifier.
For every preference ordering criterion we derive a preference ordering relation and form the set of preference ordering relations we derive a collective preference ordering relation, distinguishing between the two experts¡¯ opinions intensity possibilities, i.e. homogeneous group and heterogeneous group. We present two different choice degrees of alternatives acting over the collective preference ordering relation, a dominance degree and a non-dominance degree that generalizes Orlovski¡¯s non-dominated alternative concept. The application of the two alternative choice degree is carried out according to two different selection processes, a sequential choice process and a conjunction choice process.
Keywords: Multiple criteria, preference ordering, fuzzy majority, fuzzy quantifiers.
Compactness and Some Characterizations of Fuzzy Neighborhood Algebraic Structures
M. A. Qureshi
Department of Mathematics, King Saud University Riyadh, 11451, Saudi Arabia
T. M. G. Ahsanullah
Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh
Abstract:
In this article, we study Lowen compactness of fuzzy neighborhood groups, rings and modules, and provide with some other characterizations of the structures involved. Finally we add a result as an application of net-convergence in fuzzy neighborhood groups.
Keywords: Fuzzy neighborhood system, groups, rings, modules, compactness, net-convergence.
A Fuzzy Programming Approach to Fuzzy Linear Fractional Programming with Fuzzy Coefficients
Li Dengfeng
Department of Basic Science, Dalian Naval Academy, Dalian 116023, P. R. China
Chen Shouyu
Department of Civil Engineering, Dalian University of Technology, Dalian 116024, P. R. China
Abstract: In practice, coefficients of the objective function and constraints for the linear fractional programming are always imprecise. In this paper, a fuzzy linear fractional programming (FLFP) model with fuzzy coefficients is established. The method and an approximate algorithm for solving the FOV are given. A numerical example is solved for illustrating the appropriateness and efficiency of the proposed method.
Keywords: Linear fractional programming, fuzzy number, continuity, possibility.
Nonstructured Decision Making Analysis and Fuzzy Optimum Seeking Theory for Multiobjective Systems
Chen Shouyu
Dalian University of Technology, Dalian 116023, P. R. China
Abstract: This paper proposes a rank consistency, presents an ordered two-dimensional comparison method for determination of membership grade on fuzzy characteristics and a new fuzzy optimum method for nonstructured decision making problems in multiobjective systems.
Keywords: Rank consistency, membership grade, decision making, fuzzy optimum method.
Fuzzy Modules Over Fuzzy Rings in Connection with Fuzzy Ideals of Fuzzy Rings
Luis Martinez
Department of Mathematics University of the Basque Country, Spain
E-mail: mtpmafel@g.ehu.es
Fuzzy Implicative Semigroups
S. M. Hong, Y. B. Jun, S. J. Kim, S. H. Park
Department of Mathematics, Gyeongsany National University, Chinju 660-701, Korea
J. Meng
Department of Mathematics, Northeast University, Xian 710069, P. R. China
Abstract: In this paper, we fuzzify the concept of implicative semigroups, investigate some their properties, and give a characterization of fuzzy implicative semigroups in the terms of level sub-implicative semigroups. We also construct a normal fuzzy implicative semigroup, and investigate its properties.
Keywords£º (Fuzzy) implicative semigroup, (level) sub-implicative semigroup, normal fuzzy implicative semigroup.
Products of -fuzzy Subgroups
Pratyayananda Das
Department of Mathematics, Burdwan University Golapbag, Burdwan, West Bengal, India
Abstract: Interval direct product, semidirect product, subdirect product and amalgamated product of -fuzzy subgroups are discussed. Some results concerning level subgroups are obtained.
Keywords: Fuzzy algebra, fuzzy subgroup, internal direct product, subdirect product, amalgamated product.
Stability of General Fuzzy Parametric Multiobjective Nonlinear Programming Problems without Differentiability
Mohamed Abd El-Hady Kassem
Department of Mathematics, Faculty of science Tanta University, Tanta, Egypt
Abstract: This paper deals with multiobjective nonlinear programming problems without differentiability, involving general fuzzy parameters in the objective functions. These fuzzy parameters are characterized by fuzzy numbers. The existing results concerning the stability notions of parametric mulitiobjective programming problems without differentiability are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of -pareto
optimality without differentiability.
Keywords: Multiobjective nonlinear programming problems, stability, fuzzy parameters, fuzzy numbers, -pareto optimality.
Conceptual Knowledge from L-fuzzy Contexts
A. Burusco and R. Fuentes-Gonzalez
Departamento de Autom¨¢ticaay Computaci¨¢ Universidad P¨²blica de Navarra.
Campus de Arrosad¨ªa. 31006 Pamplona. Espa?a. E-mail: burusc@si.UPNA.es, rfuentes@si,UPNA.es
Abstract: Taking as departure point the concept theorem of R. Wille [7] and the fuzzy Sets theory, in this paper we develop a new model called L-Fuzzy concept theory using L-Fuzzy relations between objects and attributes.
We begin this paper with the definitions of some new operators that serve to make the L-Fuzzy concepts. We will obtain the concepts using a constructive version of fixed points theorem of Tarski. We introduce an order relation that expresses the hierarchy between L-Fuzzy concepts, and we prove below the lattice structure of the L-Fuzzy concept set. Also, we recover the Wille¡¯s theory as a particular case when and we give the iso-structured L-Fuzzy context definition that is used to analyze certain L-Fuzzy contexts from others. In particular, we will be able to study L-Fuzzy contexts form Wille¡¯s context. Finally, we provide an example to illustrate this theory.
Keywords: Concepts, L-Fuzzy concepts, knowledge representation, fuzzy sets, lattices, fixed points.
Fuzzy Random Variables, Conditional Expectations and Fuzzy Valued Martingales
Shoumei Li and Yukio Ogura
Department of Mathematics, Saga University, Japan
Abstract: The purpose of this paper is to study the fuzzy random variables whose level sets are not compact in general. We obtain the completeness of the spaces of fuzzy random variables, the existence theorem of conditional expectations, and regularity theorem and convergence theorems of fuzzy valued martingales.
Keywords: Fuzzy random variable, conditional expectation, fuzzy valued martingale.
The Relation between the Middle Ideals and the Congruence Relation in Fuzzy Lattices
Jia Wu
Department of Mathematics, Luo Jia Dun #122 Wu Han, Hu bei 430035, P. R. China
Abstract: On the research of fuzzy lattices, we find that the ideal theorem of lattices is not very convenient. For example, some ideals have not the corresponding congruence relations whose kernels are the ideals. In the articles [1], [2], the author firstly gave the concept of middle ideals. In this paper, we try to discuss the relation between the middle ideals and the congruence relations in fuzzy lattices. We show that every middle ideal has its corresponding congruence relation whose central kernel of exactly the middle ideal; we also show that every middle ideal is the central kernel of a fuzzy homomorphism, and construct the largest and the smallest congruence relations. Finally, we discuss some properties of middle ideals.
Keywords: Middle ideal, central kernel, congruence relation of fuzzy lattice, prime middle ideal, maximal middle ideal.
A Study on Fuzzy Parametric Multiobjective Nonlinear Programming Problems without Differentiability
Elsaid Ebrahim Ammar
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.
Abstract: In this paper we investigate the stability of a multiobjective nonlinear programming problem with fuzzy parameters in both of the vectors of the vectors of the objective and of constraint functions. The basic notions like the feasibility, solvability and some stability sets (the first, the second, the third and the fourth kind) have been defined and analyzed without differentiable assumption on the considered functions. Some of these notions for the dual problem will be defined and analyzed.
Keywords: Multiobjective nonlinear programming, fuzzy number, -level set, stability, duality. |