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EXACT AND APPROXIMATE SOLUTIONS OF FUZZY LR LINEAR
SYSTEMS :NEW ALGORITHMS USING A LEAST SQUARES MODEL
AND THE ABS APPROACH
R. Ghanbari, N. Mahdavi-Amiri and R. Yousefpour
Abstract. We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables.As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible then the fuzzy LR system lacks exact solutions. We show that the fuzzy LR system has an exact solution if and only if the corresponding crisp system is compatible (has a solution) and the solution of the corresponding least squares problem is equal to zero. In this case, the exact solution is determined by the solutions of the two corresponding problems. On the other hand, if the corresponding crisp system is compatible and the optimal value of the corresponding constrained least squares problem is nonzero, then we characterize approximate solutions of the fuzzy system by solution of the least squares problem. Also, we characterize solutions by defining an appropriate membership function so that an exact solution is a fuzzy LR vector having the membership function value equal to one and, when an exact solution does not exist, an approximate solution is a fuzzy LR vector with a maximal membership function value. We propose a class of algorithms based on ABS algorithm for solving the LR fuzzy systems. The proposed algorithms can also be used to solve the extended dual fuzzy linear systems. Finally, we show that, when the system has more than one solution, the proposed algorithms are flexible enough to compute special solutions of interest. Several examples are worked out to demonstrate the various possible scenarios for the solutions of fuzzy LR linear systems.
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FUZZY LINEAR REGRESSION MODEL WITH CRISP COEFFICIENTS:
A GOAL PROGRAMMING APPROACH
H. Hassanpour, H. R. Maleki and M. A. Yaghoobi
Abstract. The fuzzy linear regression model with fuzzy input-output data and crisp coefficients is studied in this paper. A linear programming model based on goal programming is proposed to calculate the regression coefficients.In contrast with most of the previous works, the proposed model takes into account the centers of fuzzy data as an important feature as well as their spreads in the procedure of constructing the regression model. Furthermore, the model can deal with both symmetric and non-symmetric triangular fuzzy data as well as trapezoidal fuzzy data which have rarely been considered in the previous works.To show the efficiency of the proposed model, some numerical examples are solved and a simulation study is performed. The computational results arecompared with some earlier methods.
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FUZZY CONVEX SUBALGEBRAS OF COMMUTATIVE
RESIDUATED LATTICES
S. Ghorbani and A. Hasankhani
Abstract. In this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. In particular, we will show that there exists one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. Then we study fuzzy convex subalgebras of an integral commutative residuated lattice and we will prove that fuzzy filters and fuzzy convex subalgebras of an integral commutative residuated lattice coincide.
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ORDERED SEMIGROUPS CHARACTERIZED BY THEIR
INTUITIONISTIC FUZZY BI-IDEALS
A. Khan, Y. B. Jun and M. Shabir
Abstract. Fuzzy bi-ideals play an important role in the study of ordered semigroup structures. The purpose of this paper is to initiate and study the intiuitionistic fuzzy bi-ideals in ordered semigroups and investigate the basic theorem of intuitionistic fuzzy bi-ideals. To provide the characterizations of regular ordered semigroups in terms of intuitionistic fuzzy bi-ideals and to discuss the relationships of left(resp. right and completely regular) ordered semigroups in terms intuitionistic fuzzy bi-ideals.
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M -FUZZIFYING DERIVED OPERATORS AND DIFFERENCE
DERIVED OPERATORS
X. Xin, F.G. Shi and S. G. Li
Abstract. This paper presents characterizations of M-fuzzifying matroids by means of two kinds of fuzzy operators, called the M-fuzzifying derived operators and M-fuzzifying difference derived operators.
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ACTIONS, NORMS, SUBACTIONS AND KERNELS OF
(FUZZY) NORMS
J. S. Han, H. S. Kim and J. Neggers
Abstract. In this paper, we introduce the notion of an action asYX a generalization of the notion of a module, and the notion of a norm$\vt: Y_X\to F$, where F is a field and $\vartriangle(xy)\vartriangle(y') =$ $ \vartriangle(y)\vartriangle(xy')$as well as the notion of fuzzy norm, where $\vt: Y_X\to [0, 1]\subseteq {\bf R}$, with R the set of all real numbers. A great many standard mappings on algebraic systems can be modeled on norms as shown in the examples and it is seen that Ker $\mathrm{Ker}\vt =\{y|\vt(y)=0\}$ has many useful properties. Some are explored, especially in the discussion of fuzzy norms as they relate to the complements of subactions NX of YX.
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FUZZY SUBGROUPS OF RANK TWO ABELIAN P-GROUP
S. Ngcibi, V. Murali and B. B. Makamba
Abstract. In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the subgroups of maximal chains in a special way which enables us to count the number of fuzzy subgroups.
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FUZZY LOGISTIC REGRESSION: A NEW POSSIBILISTIC MODEL
AND ITS APPLICATION IN CLINICAL VAGUE STATUS
S. Pourahmad, S. M. T. Ayatollahi and S. M. Taheri
Abstract. Logistic regression models are frequently used in clinical research particularly for modeling disease status and patient survival. Usually, the clinical studies have some limitations in practice. For instance, in rare diseases and also due to ethical considerations in some clinical researches, the issue of small sample sizes arises. In addition, lack of suitable and advanced measuring instruments lead to non-precise observations. Thirdly, scientists’ disagreements in defining some disease criteria have brought out vague diagnosis. Also, linguistic terms have a key role in clinical research so that specialists often report their opinion in linguistic terms rather than exact merical ones. Usually, these limitations may lead to breaking statistical models’ assumptions and consequently their use. Since the above situations do not lend to analysis by the classical statistical models we, therefore, need to develop new methods of modelling and analyzing. In this study, a model named “fuzzy logistic model” is proposed which is applicable when the explanatory variables are crisp, and the amount of the binary response variable is reported as a number between zero and one (indicating the possibility of having the property). In this regard, “possibilistic odds” is introduced as a new term. Then, the methodology and formulation of this model is explained in detail. To estimate the model’s parameters, a linear programming pproach is followed. Some goodness-of-fit criteria of the obtained models are proposed. Finally, in a numerical example, the model’s application in a clinical study is shown.
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SOLVING BEST PATH PROBLEM ON MULTIMODAL TRANSPORTATION
NETWORKS WITH FUZZY COSTS
A. Golnarkar, A. A. Alesheikh and M. R. Malek
Abstract. Numerous algorithms have been proposed to solve the shortest path problem; many of them consider a single-mode network and crisp costs.Other attempts have addressed the problem of fuzzy costs in a single-mode network, the so-called fuzzy shortest-path problem (FSPP). The main contribution
of the present work is to solve the optimum path problem in a multimodal transportation network, in which the costs of the arcs are fuzzy values. Metropolitan transportation systems are multimodal in that they usually contain multiple modes, such as bus, metro, and monorail. The proposed algorithm is based on the path algebra and dioid of k-shortest fuzzy paths. The approach considers the number of mode changes, the correct order of the modes used, and the modeling of two-way paths. An advantage of the method is that there is no restriction on the number and variety of the services to be considered. To track the algorithm step by step, it is applied to a pseudo-multimodal network.
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LOCAL BASES WITH STRATIFIED STRUCTURE IN
I-TOPOLOGICAL VECTOR SPACES
J. X. Fang
Abstract. In this paper, the concept of local base with stratified structure in I-topological vector spaces is introduced. We prove that every I-topological vector space has a balanced local base with stratified structure. Furthermore, a new characterization of I-topological vector spaces by means of the local base with stratified structure is given.
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ABOUT THE FUZZY GRADE OF THE DIRECT PRODUCT OF
TWO HYPERGROUPOIDS
I. Cristea
Abstract. The aim of this paper is the study of the sequence of join spaces and fuzzy subsets associated with a hypergroupoid. In this paper we give some properties of the membership function $\widetilde\mu_{\otimes}$ corresponding to the direct product of two hypergroupoids and we determine the fuzzy grade of the hypergroupoid $\langle H\times H, \otimes\rangle$ in a particular case.
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A NEW PERSPECTIVE TO THE MAZUR-ULAM PROBLEM IN
2-FUZZY 2-NORMED LINEAR SPACES
C. ALACA
Abstract. In this paper, we introduce the concepts of 2-isometry, collinearity, 2-Lipschitz mapping in 2-fuzzy 2-normed linear spaces. Also, we give a new generalization of the Mazur-Ulam theorem when X is a 2-fuzzy 2-normed linear space or $\Im (X)$ is a fuzzy 2-normed linear space, that is, the Mazur-Ulam theorem holds, when the 2-isometry mapped to a 2-fuzzy 2-normed linear space is affine.
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NUMERICAL METHODS FOR FUZZY LINEAR PARTIAL DIFFERENTIAL EQUATIONS UNDER NEW DEFINITION FOR DERIVATIVE
T. Allahviranloo and M. Afshar Kermani
Abstract. In this paper numerical methods for solving ”fuzzy partial differential equation” (FPDE) are considered. We present difference methods to solve the FPDEs such as fuzzy hyperbolic equation and fuzzy parabolic equation and examine the existence and conditions for stability. Examples are presented showing the Hausdorff distance between exact solution and approximate solution is small.
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REGULAR ORDERED SEMIGROUPS AND INTRA-REGULAR
ORDERED SEMIGROUPS IN TERMS OF FUZZY SUBSETS
X. Y. Xie and J. Tang
Abstract. Let S be an ordered semigroup. A fuzzy subset of S is an arbitrary mapping from S into [0, 1], where [0, 1] is the usual interval of real numbers. In this paper, the concept of fuzzy generalized bi-ideals of an ordered semigroup S is introduced. Regular ordered semigroups are characterized by means of fuzzy left ideals, fuzzy right ideals and fuzzy (generalized) bi-ideals. Finally, two main theorems which characterize regular ordered semigroups and intraregular ordered semigroups in terms of fuzzy left ideals, fuzzy right ideals, fuzzy bi-ideals or fuzzy quasi-ideals are given. The paper shows that one can pass from results in terms of fuzzy subsets in semigroups to ordered semigroups. The corresponding results of unordered semigroups are also obtained.
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ON PRIME FUZZY BI-IDEALS OF SEMIGROUPS
A. Khan, Y. B. Jun and M. Shabir
Abstract. In this paper, we introduce and study the prime, strongly prime, semiprime and irreducible fuzzy bi-ideals of a semigroup. We characterize those semigroups for which each fuzzy bi-ideal is semiprime. We also characterize those semigroups for which each fuzzy bi-ideal is strongly prime.
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FUZZY BASIS OF FUZZY HYPERVECTOR SPACES
R. Ameri and O. R. Dehghan
Abstract. The aim of this paper is the study of fuzzy basis and dimension of fuzzy hypervector spaces. In this regard, first the notions of fuzzy linear independence and fuzzy basis are introduced and then some related results are obtained. In particular, it is shown that for a large class of fuzzy hypervector space the fuzzy basis exist. Finally, dimension of a fuzzy hypervector space is defined and the basic properties of it are investigated.
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A RELATED FIXED POINT THEOREM IN n FUZZY METRIC SPACES
F. Merghadi and A. Aliouche
Abstract. We prove a related fixed point theorem for n mappings which are not necessarily continuous in n fuzzy metric spaces using an implicit relation one of them is a sequentially compact fuzzy metric space which generalize results of Aliouche, et al. [2], Rao et al. [14] and [15].
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BEST SIMULTANEOUS APPROXIMATION IN FUZZY NORMED SPACES
M. Goudarzi and S. M. Vaezpour
Abstract. The main purpose of this paper is to consider the t-best simultaneous approximation in fuzzy normed spaces. We develop the theory of t-best simultaneous approximation in quotient spaces. Then, we discuss the relationship in t-proximinality and t-Chebyshevity of a given space and its quotient space.
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OPTIMIZATION OF LINEAR OBJECTIVE FUNCTION SUBJECT TO FUZZY RELATION INEQUALITIES CONSTRAINTS WITH
MAX-PRODUCT COMPOZITION
E. Shivanian and E. Khorram
Abstract. In this paper, we study the finitely many constraints of the fuzzy relation inequality problem and optimize the linear objective function on the region defined by the fuzzy max-product operator. Simplification operations have been given to accelerate the resolution of the problem by removing the components having no effect on the solution process. Also , an algorithm and some numerical and applied examples are presented to abbreviate and illustrate the steps of the problem resolution.
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SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM OF OPERATORS
A. Hasankhani, A. Nazari and M. Saheli
Abstract. In the present paper we de ne the notion of fuzzy inner product and study the properties of the corresponding fuzzy norm. In particular, it is shown that the Cauchy-Schwarz inequality holds. Moreover, it is proven that every such fuzzy inner product space can be imbedded in a complete one and that every subspace of a fuzzy Hilbert space has a complementary subspace. Finally, the notions of fuzzy boundedness and operator norm are introduced and the relationship between continuity and boundedness are investigated. And, it is shown that the space of all fuzzy bounded operators is complete.
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ORDERED INTUITIONISTIC FUZZY SOFT MODEL OF FLOOD ALARM
S. J. Kalayathankal, G. Suresh Singh, P. B. Vinodkumar
S. Joseph and J. Thomas
Abstract. A ood warning system is a non-structural measure for ood mit- igation. Several parameters are responsible for ood related disasters. This work illustrates an ordered intuitionistic fuzzy analysis that has the capability to simulate the unknown relations between a set of meteorological and hydro- logical parameters. In this paper, we rst de ne ordered intuitionistic fuzzy soft sets and establish some results on them. Then, we de ne similarity mea- sures between ordered intuitionistic fuzzy soft (OIFS) sets and apply these similarity measures to ve selected sites of Kerala, India to predict potential ood.
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EXTRACTION-BASED TEXT SUMMARIZATION USING FUZZY ANALYSIS
F. Kyoomarsi, H. Khosravi, E. Eslami and M. Davoudi
Abstract. Due to the explosive growth of the world-wide web, automatic text summarization has become an essential tool for web users. In this pa- per, we present a novel approach for creating text summaries. Using fuzzy logic and word-net, our model extracts the most relevant sentences from an original document. The approach utilizes fuzzy measures and inference on the extracted textual information from the document to nd the most signi cant sentences. Experimental results reveal that the proposed approach extracts the most relevant sentences when compared to other commercially available text summarizers. Text pre-processing based on word-net and fuzzy analysis is the main part of our work.
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ON n-ARY HYPERGROUPS AND FUZZY n-ARY HOMOMORPHISM
O. Kazanci, S. Yamak and B. Davvaz
Abstract. The aim of this paper is to introduce the notion of fuzzy homomorphism and fuzzy isomorphism between two n-ary hypergroups and to extend the fuzzy results of fundamental equivalence relations to n-ary hypergroups. We study some of their properties and prove the decomposition theorems for fuzzy homomorphism and fuzzy isomorphism.
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FUZZIFYING CLOSURE SYSTEMS AND CLOSURE OPERATORS
X. Luo and J. Fang
Abstract. In this paper, we propose the concepts of fuzzifying closure systems and Birkhoff fuzzifying closure operators. In the framework of fuzzifying mathematics, we find that there still exists a one to one correspondence between fuzzifying closure systems and Birkhoff fuzzifying closure operators as in the case of classical mathematics. In the aspect of category theory, we prove that the category of fuzzifying closure system spaces is isomorphic to the category of Birkhoff fuzzifying closure spaces. In addition, we obtain an important result that the category of fuzzifying closure spaces and that of fuzzifying closure system spaces can be both embedded in the category of Birkhoff I-closure spaces. Finally, using fuzzifying closure systems of the paper, we introduce a set of separation axioms in fuzzifying closure system spaces, which offer a try how to research the properties of spaces by fuzzifying closure systems.
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TOWARDS THE THEORY OF L-BORNOLOGICAL SPACES
M. Abel and A. ˇSostak
A bstract. The concept of an L-bornology is introduced and the theory of L-bornological spaces is being developed. In particular the lattice of all L-bornologies on a given set is studied and basic properties of the category of L-bornological spaces and bounded mappings are investigated.
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NORM AND INNER PRODUCT ON FUZZY LINEAR SPACES
OVER FUZZY FIELDS
C. P. Santhosh and T. V. Ramakrishnan
Abstract. In this paper, we introduce the concepts of norm and inner product on fuzzy linear spaces over fuzzy elds and discuss some fundamental properties.
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Semisimple Semihypergroups in terms of Hyperideals and Fuzzy Hyperideals
P. Corsini , M. Shabir and T. Mahmood
In this paper, we define prime (semiprime) hyperideals and prime (semiprime) fuzzy hyperideals of semihypergroups. We characterize semi- hypergroups in terms of their prime (semiprime) hyperideals and prime (semiprime) fuzzy hyperideals.
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DISCRETE TOMOGRAPHY AND FUZZY INTEGER PROGRAMMING
F. Jarray
Abstract. We study the problem of reconstructing binary images from four projections data in a fuzzy environment. Given the uncertainly projections, we want to find a binary image that respects as best as possible these projections. We provide an iterative algorithm based on fuzzy integer programming and linear membership function.
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VAGUE RINGS AND VAGUE IDEALS
S. Sezer
Abstract. In this paper, various elementary properties of vague rings are obtained. Furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.
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MODIFIED K-STEP METHOD FOR SOLVING FUZZY INITIAL
VALUE PROBLEMS
O. Solaymani Fard and A. Vahidian Kamyad
Abstract. In this paper, we are concerned with the development of k-step scheme for the numerical solution of fuzzy initial value problems. Convergence and stability of the method are also proved in detail. Moreover, a specific method of order 4 is found. The numerical result shows that the proposed fourth order method is efficient for solving fuzzy differential equations.
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NET-THEORETICAL L-GENERALIZED CONVERGENCE SPACES
W. Yao
Abstract. In this paper, the definition of net-theoretical L-generalized con- vergence spaces is proposed. It is shown that, for L a frame, the category of enriched L-fuzzy topological spaces can be embedded in that of L-generalized convergence spaces as a re°ective subcategory and the latter is a cartesian- closed topological category.
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ACCEPTANCE SINGLE SAMPLING PLAN WITH FUZZY PARAMETER
E. Baloui Jamkhaneh, B. Sadeghpour Gildeh and G. Yari
Abstract. The acceptance sampling plan problem is one of the main topics in quality control where both theory of probability and theory of fuzzy sets may be used. In this paper, we discuss the acceptance single sampling plan when the proportion of nonconforming products is a fuzzy number. We have shown that the operating characteristic (OC) curve of the plan is like a band having high and low bounds, their width depends on the ambiguity proportion parameter in the lot when the sample size and the acceptance number are xed. When the acceptance number equals zero, this band is convex for di erent n;s, and for large n the convexity will be more. Finally, we have given some examples and then compared the OC bands for some value of c.
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LATTICE-VALUED CATEGORIES OF LATTICE-VALUED
CONVERGENCE SPACES
G. J¨ager
Abstract. We study L-categories of lattice-valued convergence spaces. Such categories are obtained by “fuzzifying” the axioms of a lattice-valued convergence space. We give a natural example, study initial constructions and function spaces. Further we look into some L-subcategories. Finally we use this approach to quantify how close certain lattice-valued convergence spaces are to being lattice-valued topological spaces.
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CREDIBILISTIC PARAMETER ESTIMATION AND ITS APPLICATION IN FUZZY PORTFOLIO SELECTION
X. Li, Z. Qin, D. Ralescu
Abstract. In this paper, a maximum likelihood estimation and a minimum entropy estimation for the expected value and variance of normal fuzzy variable are discussed within the framework of credibility theory. As an application, a credibilistic portfolio selection model is proposed, which is an improvement over the traditional models as it only needs the predicted values on the security returns instead of their membership functions.
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POWERSET OPERATOR FOUNDATIONS FOR CATALG FUZZY SET THEORIES
S. A. Solovyov
Abstract. The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the xed-basis forward powerset operator of L. A. Zadeh. On the next step, we provide a direct lift of the backward powerset operator using the notion of categorical biproduct. The obtained framework is readily extended to the variable-basis case, justifying the powerset theories currently popular in the fuzzy community. At the end of the paper, our general variety-based setting postulates the requirements, under which a convenient variety-based powerset theory can be developed, suitable for employment in all areas of fuzzy mathematics dealing with fuzzy powersets, including fuzzy algebra, logic and topology.
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( A)Δ- DOUBLE SEQUENCE SPACES OF FUZZY NUMBERS VIA ORLICZ FUNCTION
E. Savas
Abstract. The aim of this paper is to introduce and study a new concept of strong double (A )Δ-convergent sequence of fuzzy numbers with respect to an Orlicz function and also some properties of the resulting sequence spaces of fuzzy numbers are examined. In addition, we define the double (A,Δ)-statistical convergence of fuzzy numbers and establish some connections between the spaces of strong double
(A )Δ-convergent sequence and dou ble (A ,Δ)-statistical convergent sequence.
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BIPOLAR FUZZY HYPER BCK-IDEALS IN HYPER BCK-ALGEBRAS
Y. B. JUN, M. S. KANG and H. S. KIM
Abstract. Using the notion of bipolar-valued fuzzy sets, the concepts of bipolar fuzzy (weak, s-weak, strong) hyper BCK-ideals are introduced, and their relations are discussed. Moreover, several related properties are investigated.
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FUZZY SOFT SET THEORY AND ITS APPLICATIONS
N. Cagman, S. Enginoglu and F. Citak
Abstract. In this work, we define a fuzzy soft set theory and its related properties. We then define fuzzy soft aggregation operator that allows constructing more efficient decision making method. Finally, we give an example which shows that the method can be successfully applied to many problems that contain uncertainties.
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GENERALIZED REGULAR FUZZY MATRICES
A. Meenakshi and P.Jenita
Abstract. In this paper, the concept of k-regular fuzzy matrix as a generalization of regular matrix is introduced and some basic properties of a k-regular fuzzy matrix are derived. This leads to the characterization of a matrix for which the regularity index and the index are identical. Further the relation between regular, k-regular and regularity of powers of fuzzy matrices are discussed.
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$\psi -$ WEAK CONTRACTIONS IN FUZZY METRIC SPACES
M. ABBAS, M. IMDAD, AND D. GOPAL
Abstract. In this paper, the notion of $\ psi -$ weak contraction [18] is extended to fuzzy metric spaces. The existence of common fixed points for two mappings is established where one mapping is $\ psi -$ weak contraction with respect to another mapping on a fuzzy metric space. Our result generalizes a result of Gregori and Sapena [9].
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A SOLUTION TO ECONOMIC DISPATCH PROBLEM BY FUZZY ADAPTIVE GENETIC ALGORITHM
H. NEZAMABADI-POUR, S. YAZDANI-SHARBABAKI, M. M.FARSANGI AND
M. NEYESTANI
Abstract. Finding the global optimum solution is dicult for the practical economic dispatch (ED) problem with ramp rate limits and prohibited operating zones.This paper presents a new and ecient method for solving the economic dispatch problems with non-smooth cost functions, by Fuzzy Adaptive Genetic Algorithm (FAGA). The proposed algorithm deals with the issue of controlling of exploration and exploitation capabilities of a heuristic search algorithm in which the real version of Genetic Algorithm (RGA) is equipped with the Fuzzy Logic Controller (FLC) which can eciently explore and exploit the optimum solutions. To validate the results obtained by the proposed FAGA, a Real Genetic Algorithm (RGA) is applied for comparison. Also, the results obtained by FAGA and RGA are compared with the previous approaches reported in the literature. It has been observed that the FAGA outperforms the other methods in solving power system economic load dispatch problem in terms of convergence rate, and quality and success rate.
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GRADATION OF CONTINUITY IN FUZZY TOPOLOGICAL SPACES
R. THAKUR, K. K. MONDAL, S. K. SAMANTA
Abstract. In this paper we introduce a definition of gradation of continuity in graded fuzzy topological spaces and study its various characteristic properties. The impact of the grade of continuity of mappings over the N-compactness grade is examined. Concept of gradation is also introduced in openness, closedness, homeomorphic properties of mappings and T2 separation axiom. Effect of the grades interrelated with N-compactness, closedness, T2 separation and homeomorphism of mappings are studied.
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ON FELBIN’S-TYPE FUZZY NORMED LINEAR SPACES AND FUZZY BOUNDED OPERATORS
M. JANFADA, H. BAGHANI AND O. BAGHANI
Abstract. In this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the Bag and Samanta’s operator norm on Felbin’s-type fuzzy normed spaces. In particular, the completeness of this space is studied. By some counterexamples, it is shown that the inverse mapping theorem and the Banach-Steinhaus’s theorem, are not valid for this fuzzy setting. Also finite dimensional normed fuzzy spaces are considered briefly. Next, a Hahn-Banach theorem for weakly fuzzy bounded linear functional with some of its applications are established.
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MEASURING STUDENTS MODELLING CAPACITIES: A FUZZY APPROACH
M. Voskoglou
Abstract. A central object of educational research taking place in the area of Mathematical Modelling and Applications is to recognize the attainment level of students at de ned states of the modelling process. In the present paper we introduce principles of fuzzy sets theory and possibility theory to describe the process of mathematical modelling in classroom. The main stages of the modelling process are represented as fuzzy sets in a set of linguistic labels indicating the degree of student's success in each of these stages. We use the total possibilistic uncertainty on the ordered possibility distribution of all student pro les as a measure of students' modelling capacities. An application (classroom experiment) is also presented illustrating our results.
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