The Journal of Fuzzy Mathematics
Volume 23, Number 3, September 2015
CONTENT
DETAILS
Controllability Results for The Nonlinear First Order Impulsive Fuzzy Integrodifferential Equations with Nonlocal Conditions
S. Narayanamoorthy
Department of Applied Mathematics, Bharathiar university, Coimbatore-641046, INDIA
E-mail: snm_phd@yahoo.co.in
M. Nagarajan
Department of Applied Mathematics, Bharathiar university, Coimbatore-641046, INDIA
E-mail: mnagarajanphd@gmail.com
Abstract:
In this paper, we devoted study the existence and controllability for the nonlinear impulsive fuzzy integrodifferential equations control system in . Moreover we study the fuzzy solution for the normal, convex, upper semicontinuous, and compactly supported interval fuzzy number. The results are obtained by using the Banach Fixed point theorem. An example is provided to illustrate the theory.
Key words:
Integrodifferential equations, Fixed point theorem, controllability.
g-closed Sets in Intuitionistic Fuzzy Topology
Rekha Chaturvedi
Department of Engineering Mathematics St. Aloysius Institute of Technology Jabalpur, (M. P.), India E-mail: rekha_mgmm@rediffmail.com
Abstract:
The purpose of this paper is to extend the concept of g-closed sets in intuitionistic fuzzy topological spaces. Further more the concept of intuitionistic fuzzy g-compactness have been introduced and studied.
Key words and phrases:
Intuitionistic fuzzy g-closed sets, Intuitionistic fuzzy g-open sets, Intuitionistic fuzzy g-compactness.
Invariant Fuzzy Rough Sets and Fuzzy Rough Orbits
S. Padmapriya, M. K. Uma and E. Roja
Department of Mathematics, Sri Sarada College for Women, Salem, Tamil Nadu, India. E-mail: priyasathi17@gmail.com
Abstract:
The purpose of this paper is to introduce the concepts of fuzzy rough subgroups, fuzzy rough topological groups, fuzzy rough topological transformation groups, invariant fuzzy rough sets, fuzzy rough orbits and fuzzy rough orbit closure are introduced and studied. Some interesting properties are also discussed.
Key words: fuzzy rough subgroup, fuzzy rough topological group, fuzzy rough topological transformation group, invariant fuzzy rough set, fuzzy rough orbit and fuzzy rough orbit closure..
A Study on Intuitionistic Fuzzy Clustering
Sharmistha Bhattacharya (Halder) and Amarjit Chanda
Dept of Mathematics, Tripura University, Tripura, India
Abstract:
Intuitionistic fuzzy set (IFS) is a set of 2-tuple arguments, each of which is characterized by a membership degree and a non membership degree. The membership value indicates the degree of belongingness, whereas the non membership value indicates the degree of non-belongingness of an element to that set. have been found to be very useful to describe vagueness and uncertainty and hesitancy. The aim of this paper is to introduce a Intuitionistic Fuzzy clustering method for non numeric data such as sequences of activities. The Intuitionistic fuzzy approach is suitable as there is a certain amount of hesitancy degree in numeric as well as non numeric data which cannot be considered in fuzzy clustering. For numeric data to measure the distance between pairs of data we can make use of the Hamming distance, the weighted Hamming distance, the normalized Hamming distance, the Euclidean distance, the weighted Euclidean distance, the normalized Euclidean distance [9]. But for non numeric data to measure the distance between the pair we make use of the Levenshtein distance. Here we introduced Levenshtein distance-based Intuitionistic Fuzzy C-medoids (L-IFCMd) clustering model. We also introduced a noise version of the (L-IFCMd) for noisy clusters.
Key words:
Levenshtein distance; Intuitionistic Fuzzy C-medoids clustering, Noise cluster
Separation Axioms via Generalized Alpha Intuitionistic Fuzzy Topological Spaces
C. S. Gowri
Department of Mathematics, Velalar College of Engineering and Technology, Erode, Tamil Nadu, India. E-mail:csgowri.vcet@gamil.com
D. Kalamani
Department of Mathematics, Kongu Engineering College, Perundurai Tamil Nadu, India E-mail:drkalamani@kongu.ac.in
R. Dhavaseelan
Department of Mathematics, Sona college of Technology, Salem Tamil Nadu, India E-mail:dhavaseelan.r@gmail.com
Abstract:
The purpose of this paper is to develop a new type of separation axiom called intuitionistic fuzzy GaT spaces based on the separation axioms on intuitionistic fuzzy topological spaces determined by Coker and et al [2]. Some characterizations of separation axioms T1 and T2 in IFGaT spaces will be introduced.
Key words:
Intuitionistic fuzzy generalized alpha closed set, Intuitionistic fuzzy generalized alpha T1 space and Intuitionistic fuzzy generalized alpha T2 space, Intuitionistic fuzzy separation axioms.
C12-Fuzzy Closure on Smooth Bitopological Spaces
O. A. Tantawy
Department of Mathematics, Faculty of Science, Zagazig University, Cairo, Egypt.
S. A. El-Sheikh
Department of Mathematics, Faculty of Education, Ain Shams University, 11757 beside Tabary school, Roxy, Cairo, Egypt.
R. N. Majeed
Department of Mathematics, Faculty of science, Ain Shams University, Abbassia, Cairo, Egypt. Department of Mathematics, College of Education Ibn-Al-Haitham, Baghdad University, Baghdad, Iraq.
Abstract:
Kim et.al [12], introduced the concept of (ti,tj)¦È -fuzzy closure which was denoted by T in fuzzy bitopological spaces in view of Sostak¡¯s definition. In this paper, we introduce a new concept of¦È-fuzzy closure C12 (say) in smooth bitopological spaces by using the supra smooth topological space (X,t12) which generated from smooth bitopological space (X,t1,t2) [1]. We show that C12 &< T thus, our study of smooth bitopological space (X,t1,t2) by its associated supra smooth topological spaces (X,t12), enable us to obtain results which are more general than that studied directly in (X,t1,t2). In addition, we introduce the definition of t-t12-¦È-closed (respectively, open) fuzzy sets and we show the class of all t-t12-¦È-open fuzzy sets generate a supra smooth topology t12 which is coarser than supra smooth topology t12. Finally, the concepts of almost strongly¦È-fuzzy continuous, ¦È-fuzzy continuous and weakly¦È-fuzzy continuous mappings has introduce and some of their properties have investigated.
Key words:Smooth topology, t-t12-¦È-cluster point, fuzzy C12-fuzzy closure, t-t12-¦È-closed fuzzy set, r¦È-fuzzy neighborhood, almost strongly¦È-continuous, ¦È-continuous, weakly¦È-continuous mappings.
Rules of Inferences in Rough-fuzzy Predicate Calculus
G. Ganesan
Department of Mathematics, Faculty of Science, Zagazig University, Cairo, Egypt.
S. A. El-Sheikh
Department of Mathematics, Faculty of Education, Ain Shams University, 11757 beside Tabary school, Roxy, Cairo, Egypt.
R. N. Majeed
Department of Mathematics, Faculty of science, Ain Shams University, Abbassia, Cairo, Egypt. Department of Mathematics, College of Education Ibn-Al-Haitham, Baghdad University, Baghdad, Iraq.
Abstract:
Kim et.al [12], introduced the concept of (ti,tj)¦È -fuzzy closure which was denoted by T in fuzzy bitopological spaces in view of Sostak¡¯s definition. In this paper, we introduce a new concept of¦È-fuzzy closure C12 (say) in smooth bitopological spaces by using the supra smooth topological space (X,t12) which generated from smooth bitopological space (X,t1,t2) [1]. We show that C12 &< T thus, our study of smooth bitopological space (X,t1,t2) by its associated supra smooth topological spaces (X,t12), enable us to obtain results which are more general than that studied directly in (X,t1,t2). In addition, we introduce the definition of t-t12-¦È-closed (respectively, open) fuzzy sets and we show the class of all t-t12-¦È-open fuzzy sets generate a supra smooth topology t12 which is coarser than supra smooth topology t12. Finally, the concepts of almost strongly¦È-fuzzy continuous, ¦È-fuzzy continuous and weakly¦È-fuzzy continuous mappings has introduce and some of their properties have investigated.
Key words:Smooth topology, t-t12-¦È-cluster point, fuzzy C12-fuzzy closure, t-t12-¦È-closed fuzzy set, r¦È-fuzzy neighborhood, almost strongly¦È-continuous, ¦È-continuous, weakly¦È-continuous mappings.
Compactness in Fuzzy Rough Topological Spaces
S. Padmapriya, M. K. Uma and E. Roja
Department of Mathematics, Sri Sarada College for Women, Salem, Tamil Nadu, India. E-mail address:priyasathi17@gmail.com
Abstract: The purpose of this paper is to introduce the concepts of fuzzy rough topological spaces, fuzzy rough continuous functions, fuzzy rough compactness, fuzzy rough almost compactness, fuzzy rough near compactness, fuzzy lightly compactness, fuzzy rough mildly compact spaces, fuzzy rough closed compact spaces and locally fuzzy rough com-pact spaces are introduced and studied. Some interesting properties are also discussed.
Key words: Fuzzy rough topological spaces, fuzzy rough continuous functions, fuzzy rough compactness, fuzzy rough almost compactness, fuzzy rough near compactness, fuzzy lightly compactness, fuzzy rough mildly compact spaces, fuzzy rough closed compact spaces, locally fuzzy rough compact spaces.
Matrix Games with Triangular Intuitionistic Fuzzy Pay Offs
Sanjiv Kumar and Ritika Chopra
Department of Mathematics, University of Delhi, Delhi, India. E-mail:sanjivkg82@gmail.com
Ratnesh R. Saxena
Department of Mathematics, Deen Dayal Upadhyay College, University of Delhi, Delhi, India
Abstract: In this paper, a two person zero-sum games with fuzzy payoffs are considered. The payoff elements are taken to be triangular intuitionistic fuzzy numbers. The aim of this paper is to develop a method to solve such games. Each triangular intuitionistic fuzzy number is converted to an interval valued fuzzy number using (¦Á,¦Â)-cuts. P. Grezgorzewski¡¯s theorem [7] has been used to transform the obtained intervals to Grzegorzewski¡¯s intervals. The intervals are then compared using acceptability index to get the saddle point.
Key words: Two person zero-sum game, fuzzy payoff, Triangular intuitionistic fuzzy number, (¦Á,¦Â)-c cut, Acceptability index, saddle point.
Locally r-compact Spaces Based on Lukasiewicz Logic
O. R. Sayed
Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, EGYPT. E-mail:o_sayed@aum.edu.eg, o_r_sayed@yahoo.com
Abstract:In this paper, some characterizations of fuzzifying r-compactness are given, including characterizations in terms of nets and r-subbases. Several characterizations of locally r-compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.
Key words: Lukasiewicz logic; semantics; fuzzifying topology; fuzzifying compactness; r-compactness; fuzzifying locally compactness; locally r-compactness.
Basic Compactness and Extremal Compactness in Intuitionistic Fuzzy Structure Ring Spaces
R. Narmada Devi, E. Roja and M. K. Uma
Department of Mathematics, Sri Sarada College for Women, Salem, Tamil Nadu, India. Email: : narmadadevi23@gmail.com
Abstract: In this paper, the concepts of an intuitionistic fuzzy rings, intuitionistic fuzzy structure ring spaces, intuitionistic fuzzy G rings, intuitionistic fuzzy compact rings, intuitionistic fuzzy ring basic compact spaces, intuitionistic fuzzy RB-irresolute functions, intuitionistic fuzzy RB-open functions, intuitionistic fuzzy ring extremal compact spaces, intuitionistic fuzzy -irresolute functions and intuitionistic fuzzy RE-open functions. Are studied. In this connection, some interesting properties are established and provided necessary examples.
Key words: Intuitionistic fuzzy rings, intuitionistic fuzzy structure ring spaces, intuitionistic fuzzy G rings, intuitionistic fuzzy compact rings, intuitionistic fuzzy ring basic compact spaces, intuitionistic fuzzy RB-irresolute functions, intuitionistic fuzzy RB-open functions, intuitionistic fuzzy ring extremal compact spaces, intuitionistic fuzzy RE-irresolute functions and intuitionistic fuzzy RE-open functions.
Cyclic Fuzzy Neutrosopic Soft Group
R. Nagarajan
Associate Professor, Department of Mathematics, J. J. College of Engineering and Technology, Tiruchirappalli-09. E-mail: rajenagarajan1970@gmail.com
S. Subramanian
Associate Professor, Department of Mathematics, M. A. M. School of Engineering Tiruchirappalli. E-mail: mathsspmanian@gmail.com
Abstract:
Neutrosophic soft set theory proposed by S. Broumi and F. Samarandach [14] has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, we apply the concept of fuzzy neutrosophic soft set to group theory. The notion of fuzzy neutrosophic soft groups [FNSG] is introduced and their basic properties are presented. Union, intersection and difference operations of fuzzy neutrosophic soft groups are defined. Further we have defined cyclic fuzzy neutrosophic soft group [CFNSG] and studied some related properties with supporting proofs.
Key words:Soft set, Neutrosophic set, Fuzzy neutrosophic set, Fuzzy Neutrosophic soft group, Cyclic group, Characteristic soft group, identity fuzzy neutrosophic soft group.
A fuzzy Mathematical Model to Determine The Non-Alcoholic Steatohepatitis in A Patient
Adam Goodrick, John N. Mordeson, D. S. Malik and S. C. Cheng
Department of Matheamtics Creighton University Omaha Nebraska 68178, USA. E-mail: adamgoodrick@creighton.edu,mordes@creighton.edu,mailk@creighton.edu,scheng@creighton.edu
Abstract:
Six different causal factors of Nonalcoholic Steatohepatits (NSAH) are used to deter-mine the degree of NASH in a patient. The method used involves the determination of a weighted average of these six factors determined by expert opinion. Five linear equations are constructed using the AHP, Guiasu, Yen, Dempster Shafer, and set valued statistical methods.
Key words: Nonalcoholic Steatohepatitis, fatty liver disease; BMI, Gallstone; albumin levels; alk levels, analytical hierarchy process; Guiasu method
Approximation by Fuzzy Perturbed Neural Network Operators
George A. Anastassiou
Department of Mathematical Sciences University of Memphis Memphis, TN38152, U. S. A.E-mail:ganastss@memphis.edu
Abstract: This article deals with the determination of the rate of convergence to the unit of each of three newly introduced here fuzzy perturbed normalized neural network operators of one hidden layer. These are given through the fuzzy modulus of continuity of the involved fuzzy number valued function or its high order fuzzy derivative and that appears in the right-hand side of the associated fuzzy Jackson type inequalities. The activation function is very general, especially it can derive from any sigmoid or bell-shaped function. The right hand sides of our fuzzy convergence inequalities do not depend on the activation function. The sample fuzzy functionals are of Stancu, Kantorovich and Quadrature types. We give applications for the first fuzzy derivative of the involved function.
Key words: Neural network fuzzy approximation, fuzzy derivative, fuzzy modulus of continuity, fuzzy operator.
Fuzzy Fractional Error Function Based Neural Network Approximation
George A. Anastassiou
Department of Mathematical Sciences university of Memphis Memphis, TN 38152, U. S. A.E-mail:ganastss@memphis.edu
Abstract:
Here we treat the univariate fuzzy fractional quantitative approximation of fuzzy real valued functions on a compact interval by quasiinterpolation error function based fuzzy neural network operators. These approximations are derived by establishing fuzzy Jackson type inequalities involving the fuzzy moduli of continuity of the right and left Caputo fuzzy fractional derivatives of the engaged function. The approximations are fuzzy pointwise and fuzzy uniform. The related feed-forward fuzzy neural networks are with one hidden layer. We study also the fuzzy integer derivative and just fuzzy continuous cases. Our fuzzy fractional approximation result using higher order fuzzy differentiation converges better than in the fuzzy just continuous case.
Key words: Error function, neural network fuzzy fractional approximation, fuzzy quasi-interpolation operator, fuzzy modulus of continuity, fuzzy derivative and fuzzy fractional derivative.
Fuzzy Query Processing for Document Retrieval Based on Interval Valued Intuitionistic Fuzzy Concept Networks
P. Dheena and G. Mohanraj
Department of Mathematics, Faculty of Science, Jazan University, Saudi Arabia. E-mail:dheenap@yahoo.com,gmohanraaj@gmail.com
Abstract: In this paper, we present a new method intuitionistic fuzzy query processing for document retrieval based on extended fuzzy concept networks. In an extended fuzzy concept networks, there are two kinds of fuzzy relationship between concepts, i.e., fuzzy relevance association and fuzzy irrelevance association. An extended fuzzy concept network can be modeled by a relevance matrix and a irrelevance matrix where the elements in a relevance matrix indicate the degrees of relevance between concepts and the elements in a irrelevance matrix indicate the degrees of irrelevance between concepts. The implicit degrees of relevance and the implicit degrees of irrelevance between concepts can be inferred by the transitive closure of relevance matrix and the transitive closure of irrelevance matrix respectively. The proposed method is more flexible than the ones presented in [6,7,11] due to the fact that it allows the users to perform relevant queries and irrelevant queries. The proposed method allows the users to perform fuzzy queries in more flexible and more intelligent manner.
Key words:Relevance matrix, irrelevance matrix, relevance query, irrelevance query, document descriptor relevance matrix, document descriptor irrelevance matrix, retrieval status, retrieval threshold value.
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