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THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 26, Number 1, March 2018

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Common Fixed Point of Weakly Compatible Maps without Continuity in Menger Spaces

Rajinder Sharma and Deepti Thakur

Rajinder Sharma and Deepti Thakur Sohar College of Applied Sciences, Sohar.

E-mail: rajind.math@gmail.com

Abstract: In this paper, we prove a common fixed point theorem for six discontinuous non-compatible mappings in a complete Menger space under the condition of weak compatibility. We extend and improve some earlier results. Moreover, a different proof is given. We provide an example in support of our result.

Key words: Weakly compatible maps, Menger space, Common fixed point.

Non-dominated Solution of Fuzzy Maximum-Return Problem

U. M. Pirzada

School of Science and Engineering , Navrachana University Vaodara-391410, India.

E-mail: salmapirzada@yahoo.com

D. C. Vakaskar

Department of Applied Mathematics, Faculty of Tech. and Engg., M. S. University of Baroda,, Vadodara-390001, Gujarat, India, E-mail: dcvakaskar@gmail.com

Abstract: In this paper, we find a non-dominated solution of a fuzzy maximum-return problem (unconstrained single-variable fuzzy optimization problem). We establish Newton method to find the solution of the unconstrained single-variable fuzzy optimization problem using the differentiability of alpha-level functions of a fuzzy-valued function and partial order relation on a set of fuzzy numbers.

Key words: Fuzzy-valued functions, Newton method, Maximum-return problem.

Applications of Soft Sets in Attribute Reduction

G. Sangeetha and V. Renukadevi

Department of Mathematics, Ayya Nadar Janaki Ammal College (Autonomous), Sivakasi - 626 124, Tamilnadu, India.

E-mail: renu_siva2003@yahoo.com , E-mail:geethaphd1990@gmail.com

Abstract: Soft set plays a vital role in all real life problems. Decision making and attribute reductions are the two main concepts in soft set. Attribute reduction is the process of reducing the number of attributes in such a way that the original data of the system will be maintained. The algorithms for attribute reduction given by Kong et. al are based on trial and error method. So, we need a reduction algorithm which is not a manual method. In this paper, we give an algorithm for finding the reduction of attributes using discernibility matrix.

Key words: Soft set, attribute reduction, discernibility matrix, normal parameter reduction, dispensable parameter.

An Application of Transversals of Intuitionistic Fuzzy Directed Hypergraphs

K.K. Myithili and R. Parvathi

Department of Mathematics, Vellalar College for Women, Erode-638 012, Tamilnadu, India, E-mail: myth_maths@rediffmail.com , E-mail:paarvathis@rediffmail.com

Abstract: A transversal is a line that intersects two lines, whereas in intuitionistic fuzzy directed hypergraphs , the transversal is a hyperedge that intersects two or more hyperedges. The concepts of minimal transversal and intuitionistic fuzzy triangular function of hyperedges of are used to decide the hierarchy of substances to be removed in wastewater treatment. In this paper, an attempt has been made to design a mathematical model using transversals of directed hypergraphs for water purification in intuitionistic fuzzy environment. Intuitionistic fuzzy triangular function is used for fuzzification of crisp data. The proposed model is verified with real data to determine a hierarchy of removal of substances in impure water.

Key words: Intuitionistic fuzzy directed hypergraph, intuitionistic fuzzy triangular function, transversals, wastewater treatment plant.

On Fuzzy beta-Baire Spaces

G. Thangaraj

Department of Mathematics Thiruvalluvar University Vellore-632115, Tamilnadu, India.

R. Palani

Research Scholar, Department of Mathematics Thiruvalluvar University Vellore-632115, Tamilnadu, India.

Abstract: In this paper, the concepts of fuzzy beta-nowhere dense set, fuzzy beta-first category set and fuzzy beta-second category set in fuzzy topological spaces, are introduced and studied. By means of fuzzy beta-nowhere dense sets, the concept of fuzzy beta-Baire space is defined and several characterizations of fuzzy beta-Baire spaces are studied.

Key words: Fuzzy open set, fuzzy dense set, fuzzy beta-open set, fuzzy nowhere dense set, fuzzy first category set, fuzzy Baire space.

Adomian Decomposition Method for Solving Initial Value Problem for Fuzzy Integro-differential Equation with An Application in Volterra's Population Model

Suvankar Biswas* and Tapan Kumar Roy

Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711 103, India, E-mail: suvo180591@gamil.com

Abstract: This paper deals with the fuzzy integro-differential equation by using Adomian decomposition method (ADM). Using -cuts of fuzzy numbers we convert a fuzzy integro-differential equation to a system of integro-differential equation in crisp case. We use ADM to find the approximate solution of the system and hence obtain an approximate solution of the fuzzy integro-differential. Moreover some examples have been chosen to illustrate the method and by comparing the numerical solutions with the exacts solution, we have studies their accuracy. We have modified the Volterra's Population Model into new fuzzy Volterra's Population Model. Also application of the proposed method is given in this new fuzzy Volterra's Population Model.

Key words: Fuzzy integral; Fuzzy differential; Adomian decomposition method; Fuzzy integro-differential equation; Fuzzy Volterra¡¯s Population Model.

Fuzzy Soft e-compactness and e-connectedness

V. Chandrasekar

Department of mathematics, Kandaswami Kandar's College, P-velur-638182, Tamil Nadu, India, E-mail:vckkc3895@gmail.com

S. Parimala

Research Scholar (Part Time), Department of Mathematics, Kandaswami Kandar's College, P-velur-638 182, Tamil Nadu, India, E-mail:pspmaths@gmail.com

Abstract: The purpose of this paper is to introduce the concepts of fuzzy soft e-compactness, fuzzy soft e-connectedness, fuzzy soft e-strongly connectedness and fuzzy soft e-C5-connectedness. Some interesting properties of these notions are studied. In this connection, interrelations are discussed. Examples are provided wherever necessary.

Key words: Fuzzy soft e-compactness, fuzzy soft e-connectedness, fuzzy soft e-strongly connectedness and fuzzy soft e-C5-connectedness.

Intuitionisitc Fuzzy Sostak Topology Induced by Distance and Similarity Measures

F. Kutlu

Y¨¹z¨¹nc¨¹ Y?l University, Department of Mathematics. Van, Turkey.

E-mail:fatihkutlu@yyu.edu.tr

A. A. Ramadan

BeniSuef University, Department of Mathematics Ban¨©Suwayf, Beni-Suef, Egypt

E-mail:ramadan58@hotmail.com

T. Bilgin

Y¨¹z¨¹nc¨¹ Y?l University, Department of Mathematics, Van, Turkey.

E-mail:tbilgin@yyu.edu.tr

Abstract: In this study, we define ?ostak¡¯s mean intuitionistic fuzzy topology on intuitionistic fuzzy sets by using distance and measure. Also we compare Chang's mean intuitionistic fuzzy topology defined by the new ?ostak topology and Chang's mean topology defined by distance measure. We define (alpha,beta)-separation axioms in intuitionistic fuzzy ?ostak topology and give some properties of these axioms.

Key words:

Some Results on Fuzzy Soft Banach Algebra

Thangaraj Beaula and M. Merlin Priyanga

Department of Mathematics, TBML College, Porayar, Tamil Nadu, India-609307, E-mail: edwinbeaula@yahoo.co.in

Abstract: In this paper fuzzy soft Banach algebra is introduced and few of its properties are studied. The properties of soft invertible elements and relation among soft invertible elements, fuzzy soft open set and fuzzy soft closed set are emphasized. Fuzzy soft Topological divisors of zero with respect to fuzzy soft norm and alpha-norm of fuzzy soft real numbers are defined and its relations with fuzzy soft closed set are studied.

Key words: Fuzzy soft continuous, invertible soft elements, fuzzy soft Banach algebra, open ball, Topological divisor of zero.

Generalized Common Fixed Point Result in Fuzzy Metric Space

Kanhaiya Jha

School of Science, Kathmandu University P.O. Box No. 6250, Kathmandu, NEPAL.

E-mail:jhaknh(at)yahoo.co.in, E-mail:jhakn(at)ku.edu.np

Abstract: The aim of the paper is to establish a common fixed point theorem for semi-compatible pair of self mappings in a fuzzy metric space which generalizes and improves various well-known comparable results.

Key words: Common fixed point, Fuzzy metric space, Reciprocal continuity, Weakly compatible mappings, Semi-compatible mappings.

Q-soft Subgroups and Anti-Q -soft Subgroups in Universal Algebra

Faysal Hassani

Mathematics Department, Faculty of Science Payame Noor University (PNU), Tehran, Iran, E-mail:Hassani@pnu.ac.ir

Rasul Rasuli

Mathematics Department, Faculty of Science Payame Noor University (PNU), Tehran, Iran, E-mail:rasulirasul@yahoo.com

Abstract: In this paper, We introduce the concept Q-soft subgroups and anti-Q-soft sub-groups and investigate some of their properties and structured characteristics. Also the characterisations Q-soft subgroups and anti-Q-soft subgroups under homomorphism and anti-homomorphism are discussed.

Key words and phrases: Q-soft subsets, group theory, Q-soft subgroups, anti-Q -soft subgroups, homomorphism.

Q-intuitionistic Fuzzy Ordered Filters in Ordered Ternary -semirings

Dr B. Anandh

Assistant Professor of Mathematics PG&Research Department o fMathematics H. H. The Rajahs¡¯ College, Pudukkottai-622001, E-mail: drbalaanandh@gmail.com

R. Jayakumar

Research Scholar, Sudharsan College of Arts & Science, Perumanadu, Pudukkottai-622104, E-mail: thirujaikumar4u@gmail.com

Abstract:

Key words: Q-intuitioistic fuzzy, Q-intuitionistic fuzzy order, Filter, gamma-semirings, Ternary gamma-semirings.

A Study on Probabilistic Banach Space

A. Singadurai

Department of Mathematics, T. D. M. N. S. College, T. Kallikulam, India, E-mail: Singadurai_59@yahoo.co.in

A. Thenmozhi

Department of Mathematics, M. S. University Constituent College, Satankulam, India

Abstract: The aim of this paper is to study the probabilistic Banach spaces. Existence of probabilistic Banach spaces is ensured in the subsequent discussion. We prove closed graph theorem and some results on Banach spaces are established.

Key words: Probabilistic norm, probabilistic Banach space, t-norm, continuous triangle mapping.

New Type of Fuzzy e-open Sets

M. Palanisamy

Assistant professor, Department of Mathematics, Vivekanandha college of Arts and Sciences for women (Autonomous), Tiruchengodu, Tamil Nadu-608 002, E-mail: palaniva26@gamil.com

A. Vadivel

Assistant professor, Department of Mathematics, Annamalai University, Annamalainagar-608 002, E-mail: avmaths@gmail.com

Abstract: The aim of this paper is to introduce and study the notions of fuzzy upper and lower e-limilt sets. Properties and basic relationships among fuzzy upper e-limits set, fuzzy lower e-limits set and fuzzy e-continuity are investigated. Also we introduce fuzzy approximately e-irresolute and fuzzy approximately e-closed functions. Lastly we investigate some basic properties of this concepts.

Key words: Fuzzy e-open sets, Fuzzy upper e-limits set, Fuzzy lower, fuzzy approximately e-irresolute fuzzy approximately e-closed functions and fuzzy e-connected.

Soft Lie Ideals and Anti Soft Lie Ideals

Rasul Rasuli

athematics Department, Faculty of Science Payame Noor University(PNU), Tehran, Iran, E-mail: rasulirasul@yahoo.com

Abstract: The concept of soft Lie ideals and anti soft Lie ideals of a Lie algebra introduced and some fundamental properties of them are given. Also soft Lie ideals and anti soft Lie ideals under Lie homomorphism are discussed.

Key words: Lie algebras, soft sets, soft Lie ideals, anti soft Lie ideals, homomorphisms.

Multidimensional Fixed Point Theorems in Partially Ordered Complete Modified Intuitionistic Fuzzy Metric Spaces

Bhavana Deshpande

Department of Mathematics Govt. P. G. Arts & Science College Ratlam (M. P.) India, E-mail: bhavnadeshpande@yahoo.com

Shamim Ahmad Thoker

Department of Mathematics Govt. P. G. Arts & Science College Ratlam (M. P.) India, E-mail: shamimthoker@gmail.com

Abstract: We prove some existence and uniqueness fixed point theorems for nonlinear mappings satisfying different kinds of contractive conditions in modified intuitionistic fuzzy metric spaces. Our results extend and generalize several known results.

Key words and phrases: Modified intuitionistic fuzzy metric space, theta-coincidence point, theta-fixed point, theta-monotone property, partially ordered set.

On Fuzzy Cone Normed Linear Spaces and alpha-fuzzy Cone Bounded Operators

P. Tamang and T. Bag*

Department of Mathematics, Visva Bharati University, Santiniketan, India, E-mail: haitao641@163.com, E-mail:tarapadavb@gmail.com

Abstract: In this paper, we introduce alpha-fuzzy cone (alpha-FC) bounded linear operator and alpha-fuzzy cone (alpha-FC) continuous linear operator on fuzzy cone normed linear space and investigate some important general properties of them. We also study the alpha-convergence of sequence on fuzzy cone normed linear space. Lastly, we introduce the concept of alpha -equivalent fuzzy cone norm.

Key words: Fuzzy cone norm, alpha-convergent, alpha-fuzzy cone (alpha-FC) bounded linear operator, alpha-fuzzy cone (alpha-FC)continuous linear operator, alpha-equivalent fuzzy cone norm.

Fuzzy Quasi-metric Space

G. Rano*

Department of Mathematics Tehatta Government College, West Bengal, INDIA, E-mail: gobardhanr@gmail.com

T. Bag

Department of Mathematics, Visva-Bharati Unversity Santiniketan 731235, INDIA, E-mail: tarapadavb@gmail.com

Abstract: Following the definition of fuzzy metric space given by Kramosil and Michalek we try to introduce here a totally new concept of fuzzy quasi-metric space. We observe that there is an interrelation between fuzzy quasi-metric and a family of quasi-metrics similar to that of fuzzy metric and a family of metrics. We study these interrelations and analyze the situations. Finally we able to set up a bridge from fuzzy quasi-metric to a family of quasi-metrics in restricted situation and viceversa.

Key words: Quasi-metric, t-norm, fuzzy quasi-metric and decomposition theorem.

Interactive Fuzzy Programming Approach for Vender Selection Problem in Supply Chain with Fuzzy Parameters

H. A. Khalifa

Operations Research Department, Institute of Statistical Studies and Research, Cairo University, Giza, Egypt

Abstract: In this paper, a vendor selection problem with fuzzy parameters both in a price of a unit item, upper limit of the quantity available, and an aggregate demand of the item is studied. These fuzzy parameters are characterized as fuzzy numbers. Through the use of the alpha-level sets of fuzzy numbers, an extended efficiency concept called that alpha-efficient solution is introduced. After converting the fuzzy vender selection problem into an equivalent deterministic vender selection problem, a fuzzy programming approach is applied by defining a membership function. A linear membership function is being used for obtaining alpha-optimal compromise solution. An interactive procedure for obtaining alpha-optimal compromise solution is also presented. An illustrative numerical example is given to clarify the obtained results.

Key words: Multi-objective integer programming; Vender selection problem; Fuzzy parameters; Triangular fuzzy numbers; alpha-level sets; alpha-efficient solution; Linear membership function; Fuzzy programming; Interactive procedure; Supply chain management; alpha-optimal compromise solution