THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 22, Number 3, September 2014

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Semigroup Compactification in Soft L-fuzzy Convergence Topological Spaces

D. Vidhya, E. Roja and M. K. Uma

Department of Mathematics Sri Sarada College for Women, Salem-16 Tamil Nadu, India.E-mail: vidhya.d85@gmail.com

Abstract: The purpose of this paper is to introduce the concepts of soft L-fuzzy semigroup compactification in soft L-fuzzy convergence topological space and prove that the set of all soft L-fuzzy semigroup compactification of a soft L-fuzzy convergence topological semigroup is an upper complete semi Lattice.

Key words: Soft L-fuzzy convergence topological space, soft L-fuzzy topological semigroup, Bohr soft L-fuzzy compactification, soft L-fuzzy semi-group compactification.

On Intuitionistic Fuzzy Weakly Open Functions

N. Gowrisankar

70/232, Kollupetti Street, M. Chavady, Thanjavur 613001, Tamil-nadu, India.E-mail: gowrisankartnj@gmail.com

N. Rajesh

Department of Mathematics, Rajah Serfoji Govt. College, Thanjavur-613005, Tamilnadu, India.E-mail: nrajesh_topology@yahoo.co.in

Abstract: In this paper, we introduce and characterize a new class of functions called intuitionistic fuzzy weakly open functions in intuitionistic fuzzy topological space.

Key words and phrases: Intuitionistic fuzzy topology, Intuitionistic fuzzy weakly open functions.

Two Simple Characterizations of Open (Homomorphic) Order Homomorphism

Ying Ma, Ling-Qiang Li and Guang-Wu Meng

School of Mathematics Science, Liaocheng University, Liaocheng 252059, China

Abstract: In L-topological spaces, two simple characterizations of open (homomorphic) order homomorphisms are presented by closure operators and interior operators respectively.

Key words: L-topological spaces, open order homomorphism, homomorphic order homomor-phism

Notes on Anti L-fuzzy Subfield of A Field

M. Vasu

Assistant Professor Mathematics Wing, Directorate of Distance Education, Annamalai University, Annamalainagar-608002, Chidambaram, India.E-mail:mvasu1974@gmail.com

D. Sivakumar

Proressor and Head Mathematics Wing, Directorate of Distance Education, Annamalai University, Annamalainagar-608002, Chidambaram, India.

Abstract: In this paper, we made an attempt to study the algebraic nature of anti L-fuzzy subfield of a field.

Key words: L-fuzzy set, anti L-fuzzy subfield.

Folding of Fuzzy Horospheres and Their Retractions

A. E. El-Ahmady

Mathematics Department, Faculty of Science, Taibah University, Madinah, Saudi Arabia Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt.

Abstract: In this paper, we introduce new types for foldings and retractions of fuzzy horospheres in fuzzy Lobachevskian space and spheres in fuzzy Euclidean space . Also new types of the connection between the retraction of fuzzy horospheres and fuzzy Lobachevskian space and its folding. Theorems governing this connection are deduced.

Key words: Folding, Horospheres, Retractions.

Divergence Measure and Its Application to Image Segmentation Using Global Thresholding

Rogi Jacob

Department of Mathematics, U. C. College Aluva, Mahatma Gandhi University, Kerala, India.E-mail: rogijacob@gmail.com

A. Sunny Kuriakose

Principal, B. P. C. College, Piravom. 686664.E-mail: asunnyk@gmail.com

Abstract: Divergence measure is a tool used to quantify the discrimination between any two non empty sets. In this paper, we use a fuzzy divergence measure to find an optimal threshold and to convert a gray scale image into binary image. Gray level of 0 (black) will indicate background and a gray level of 1 (white) will indicate the foreground. The proposed method is proved to be better in terms of the experiment results.

Key words: Divergence measure, Fuzzy membership function, Threshold, Segmentation

Fuzzy Deformation Retract of Fuzzy Spheres in Fuzzy Minkowski Space

A. E. El-Ahmady

Mathematics Department, Faculty of Science, Taibah University, Madinah, Saudi Arabia Mathematics Department, Faculy of Science, Tanta University, Tanta, Egypt

Abstract: In this paper, we introduce a new definition of fuzzy Minkowski space . The relations between fuzzy deformation retracts of and are discussed. Also the fuzzy retractions between and are deduced. Theorems governing this con-nection are presented.

Key words: Fuzzy deformation retract, Fuzzy spheres, Fuzzy Minkowski (n+1)-space.

Tripled Fixed Point for Compatible Mappings in Partially Ordered Fuzzy Metric Spaces

Animesh Gupta

Department of Mathematics, Sagar Institute of Engineering, Technology and Research, Ratibad Bhopal (M. P.), India. E-mail address:animeshgupta10@gmail.com

Rohit Narayan

Department of Electrical Engineering, University of Waterloo, Watarloo, Ontario, Canada-N2L3GL. E-mail address:rohitnarayan@gmail.com, r4narayan@uwatarloo.ca

R. N. Yadava

Director, Environment Management and Human Welfare Council Bhopal-INDIA. Ex. Director, Advance Material Process Research Institute, (AMPRI-CSIR) Bhopal-INDIA. E-mail address:dryadava@gmail.com

Abstract: In this paper we prove a tripled coincidence point theorem for compatible mapping in fuzzy metric space. Our aim of this paper is to improve the result of ¡°A. Roldan, J. M. Moreno, C. Roldan,¡± Tripled fixed point theorem in fuzzy metric spaces and applications¡±, Fixed point theory and applications, doi: 10.1186/1687-1812-2013-29.¡± Our technique for the proof of the theorem is different. We also give an example in support of our theorem.

Key words and phrases: Fuzzy metric space, Tripled Fixed point, Mixed monotone property, g -monotone property.

Handling MADM Problems Based on Ordered Intuitionistic Fuzzy Sets

Sunny Joseph Kalayathankal

Department of Mathematics, K. E. College, Mannanam Kottayam-686561, Kerala, India. .E-mail:sunnyjose2000@yahoo.com

Beena T Balan

Department of Mathematics, S. N. G College of Engineering Kolenchery, Ernakulam, Kerala, India

Abstract: Intuitionistic fuzzy sets (IFSs) proposed by Atanassov, Ordered intuitionistic fuzzy sets (OIFSs) proposed by Sunny Joseph Kalayathanal et al., have gained attention from researchers for applications in various fields. The Multiple Attribute Decision Making (MADM) problem deals with candidate priority alternatives with respect to various attributes. In this paper, similarity measures between ordered intuitionistic fuzzy sets were developed and applied to multiple attribute decision making (MADM) under ordered intuitionistic fuzzy environment.

Key words: Fuzzy set, Intuitionistic fuzzy set, Similarity measure

Some Fixed Point Theorems on F-normed Space

A. Singadurai

Department of Mathematics, T. D. M. N. S. College, T. Kallikulam, TamilNadu, India.E-mail:singadurai_59@yahoo.co.in

Abstract: We study some fixed point theorems on a F-normed space. Also we concentrate on selp maps having 0 as fixed point. Sequence of self maps having the same unique fixed point are also studied.

Key words: F-norm, Fixed point, Self map.

Linear and Quadratic Equations with Applications in Fuzzy Environment

Sanhita Banerjee and Tapan Kumar Roy

Department of Mathematics, India Institute of Engineering Science and Technology Shibpur, Howrah-711103, West Bengal, India Corresponding author-mail: :sanhita.banerjee88@gmail.com

Abstract: In this paper we have considered simple linear and quadratic equations in fuzzy environment. Here coefficients of the equations are taken as Generalized Trapezoidal Fuzzy Numbers. We have used the Strong and Weak solution concept to solve these fuzzy equations. Solution procedures have shown in details. Further some numerical problems have been illustrated in fuzzy environment. Using Defuzzification method we have also calculated their approximated solutions.

Key words: Fuzzy Linear Equations, Fuzzy Quadratic Equations, Generalized Trapezoidal Fuzzy Number (GTrFN), Strong and Weak solutions, Defuzzification.

Separation Axioms of a Soft Fuzzy C-convergence Space

T. Yogalakshmi, E. Roja and M. K. Uma

Department of Mathematics, Sri sarada college for women (autonomous), Salem-16. TamilNadu, India.E-mail: YogaPrithvi_ssp@yahoo.co.in

Abstract: In this paper, a new space, called soft fuzzy C-convergence space is introduced. The concepts of soft fuzzy C-regularity, soft fuzzy weakly C-regularity and soft fuzzy Ti(i=0,1,21/2,3 ) C-convergence spaces are introduced. Characterization of C-regularity in soft fuzzy C-convergence space is established by using the diagonal condition. In this connection, some interesting properties and interrelations among them are discussed.

Key words: Soft fuzzy C-filter, soft fuzzy C-convergence space, soft fuzzy C-convergence product space, soft fuzzy prime C-filter, soft fuzzy C-regular convergence space, soft fuzzy weakly C-regular, soft fuzzy Ti(i=0,1,21/2,3 ) C-convergence space.

Common Fixed Points of Generalized Contractive Mappings in Fuzzy Metric Spaces

Ravindra K. Bisht

Department of Mathematics-Applied Scineces and Humanities, Bipin Triphati Kumaon Institute of Technology, Dwarahat, Almora, 263653, Uttarakhand, India. E-mail: ravindra.bisht@yahoo.com

Abstract: This paper is intended to prove some common fixed point theorems in fuzzy metric space by employing a fuzzy analogue of the (2,d)-contractive condition of Meir and Keeler. Our results fuzzify several well-known fixed point theorems due to Boyd and Wong [On nonlinear contractions, Proc. Amer. Math. Soc., 20, (1969), 458-464], Jungck [Commuting mappings and fixed point, Amer. Math Monthly, 83 (1976), 261-263].

Key words: Fuzzy Metric Space, compatible maps, common Fixed Point, (2,d)contractive condition.

On Fuzzy Ideal of Fuzzy Frames

Rajesh. K. Thumbakara

Department of Mathematics Mar Athanasius College Kothamangalam-686666 Kerala, INDIA.E-mail:rthumbakara@gmail.com

Abstract: Frame theory is the study of topology based on its open set lattice and it was studied extensively by various authors. In this paper we study on quotients of fuzzy ideals of fuzzy frames. The quotients of fuzzy ideals are shown to be ideals of the given fuzzy frame. It is also shown that the collection of all fuzzy frames of a frame and the collection of all fuzzy quotient ideals of a fuzzy ideal are frames.

Key words and phrases: Frame, Subframes, Ideal, Fuzzy ideal.

On Fuzzy Ideals and Fuzzy Filters of A Lattice

M. J. Rani and N. R. Mangalambal

Department of Mathematics St. Joseph¡¯s College, Irinjalakuda, Kerala India-680121. E-mail: krvarghese@rediffmail.com thottuvai@sancharnet.in

Abstract: In this paper the concepts of fuzzy prime ideal, fuzzy prime filter, maximal fuzzy ideal, principal fuzzy ideal and principal fuzzy filter are introduced. The necessary and sufficient conditions for a fuzzy ideal to be a fuzzy prime ideal and necessary condition for a fuzzy ideal to be a maximal fuzzy ideal have been derived. It has also been proved that every convex fuzzy sublattice of a lattice is a unique intersection of a fuzzy ideal and a fuzzy filter and vice versa.

Key words: Fuzzy ideals, fuzzy filter, fuzzy prime ideal, fuzzy prime filter, maximal fuzzy ideal.

Finite Dimensional Quasi-normed Linear Space

G. Rano

Department of Mathematics, Krishnagar Government College Krishnagar, Nadia, Pin-741101, INDIA.E-mail: gobardhanr@gmail.com

T. Bag

Department of Mathematics, Visva-Bharati University West Bengal, INDIA.E-mail: tarapadavb@gmail.com

Abstract: In this paper, some results on finite dimensional quasi-normed linear spaces are established. Idea of equivalent quasi-norm is introduced. Riesz lemma is proved in quasi-normed linear space.

Key words: Quasi-norm, quasi-normed linear space, Compact set, Riesz¡¯s lemma.

Multi-criteria of Bike Purchasing Using Fuzzy Choquet Integral

Ismat Beg

Centre for Mathematics and Statistical Sciences, Lahore School of Economics, Lahore, Pakistan.E-mail: begismat@yahoo.com Phone: 0092-3454161107 FAX:0092-42-36560905

Tabasam Rashid

Department of Science and Humanities, National University of Computer and Emerging Science, Lahore, Pakistan.E-mail: tabasam.rashid@gmail.com

Abstract: A bike purchasing is a multi-criteria decision-making problem including both quantitative and qualitative main and sub-criteria. This paper shows that when these criteria include interactions between each others, Choquet integral presents an excellent tool for the solution of this multi-criteria decision making problem. An example is given to illustrate the proposed model.

Key words: Choquet integral; hierarchy; multi-criteria decision; fuzzy measure.

On IF Weakly Generalized Minimal Closed Set

Sharmistha Bhattacharya (Halder) and Jayanti Tripathi

Department of Mathematics, Tripura University, Suryamaninagar, Tripura-799130

E-mail: halder_731@rediffmail.com

Abstract: The aim of this paper is to construct the concept of IF weakly generalized minimal closed set in IF topological space. Some characterization theorems and properties of this newly constructed set are studied. Also the concept of IF generalized weakly minimal closed set is introduced and some related theorems are studied.

Key words: IF mx structure, IF dense set, IF minimal open set, IF generalized closed set etc.

Intuitionistic Fuzzy Preference Relations and Independence of Irrelevant Alternatives

John N. Mordeson , Terry D. Clark , Mark J. Wierman , Kelly K. Nelson

Department of Mathematics , Department of Political Science , Department of Computer Science , Department of Political Science , Creighton University Omaha, Nebraska 68178, USA

E-mail: mordes@creighton.edu , tclark@creighton.edu , wireman@creighton.edu , kellynelson1@creighton.edu

Karen Albert

Department of Political Science University of Nebraska Lincoln, Nebraska 68588, USA.E-mail:karenalbert@huskers.unl.edu

Abstract: We extend some known Arrowian results involving fuzzy set theory to results involving intuitionistic fuzzy sets. Many of the proofs for intuitionistic fuzzy sets can be obtained from existing results for fuzzy sets in a dual manner. We point out in the conclusion how the use of an involutive fuzzy complement can be used to obtain the results.

Key words: Intuitionistic fuzzy preference relations; Arrow¡¯s theorem; independence of irrelevant alternatives; fuzzy aggregation rules.

Some Fixed Point Theorems in Fuzzy Cone Metric Spaces

Tarapada Bag

Department of Mathematics, Visva-Bharati University, west Bengal, INDIA.E-mail: karenalbert@huskers.unl.edu

Abstract: In this paper, concept of w-distance in fuzzy cone metric space is introduced and by using this concept a fixed point theorem is established. On the other hand, a new order on the subsets of fuzzy cone metric space is defined and prove a fixed point theorem for set-valued contraction mappings.

Key words: Fuzzy cone metric space with w-distance, set-valued mapping.

Existence Theorems for Solutions to Random Fuzzy Volterra Integra-differential Equations

Jong Yeoul Park

Department of Mathematics, Busan Natiioanl University, Busan 609-735, South Korea

Jae Ug Jeong

Department of Mathematics, Dongeui University, Busan 614-714, South Korea.E-mail: jujeong@deu.ac.kr

Abstract: In this paper, we prove the existence and uniqueness of solutions for random fuzzy initial value problems involving integro-differential operators of Volterra type. Some kind of boundedness of the solution is established.

Key words and phrases: Random fuzzy differential equations; fuzzy derivative; fuzzy stochastic process; fuzzy random variables