The Journal of Fuzzy Mathematics
Volume 24, Number 1, March 2016
CONTENT
DETAILS
On Exponential Intuitionistic Fuzzy Number
Thangaraj Beaula
Department of Mathematics, T. B. M. L. College, Porayar 609307, TamilNadu, India, E-mail: ghoshpayel86@yahoo.com
V. Vijaya
Department of Mathematics, A. V. C. College of Engineering, Mannampandal, Mayiladuthurai, 609305, India, E-mail: vvijayamanikandan@gmail.com
Abstract:
The methods for finding critical path using exponential fuzzy numbers are inadequate. In this paper, we have introduced the new concept of exponential intuitionistic fuzzy numbers. Also, a method of ranking exponential intuitionistic fuzzy number is proposed and a numerical example is illustrated to find the critical path using the proposed method.
Key words:
Exponential intuitioistic fuzzy number, Ranking, Critical Path.
On Fuzzy Upper and Lower Almost ¦Â-continuous Multifunctions
M. A. Hebeshi and I. M. Taha
Department of Mathematics, Faculty of Science, Sohag University, Egypt. E-mail: mhebeshi@yahoo.com E-mail: imtaha2010@yahoo.com
Abstract:
The aim of this paper is to introduce and study fuzzy upper and fuzzy lower almost ¦Â-continuous and weakly¦Â-continuous multifucntions. Also, several characterizations and properties of the se multifunctions along with their mutual relationahips are established in L-fuzzy topological spaces. Later, composition and union between these multifuctnions are investigated.
Key words and phrases:
L-fuzzy topology, fuzzy multifunction, fuzzy upper and fuzzy lower almost¦Â-continuous, weakly¦Â-continuous, composition and union.
(¡Ê, ¡Ê¡Åq)-fuzzy Ideals of d-algebra
S. R. Barbhuiya
Department of Mathematics, Srikishan Sarda College, Hailakandi, Hailakandi-788151, Assam, India. E-mail: saidurbarbhuiya@gmail.com
Abstract:
The aim of this paper is to introduce the notion of not quasi-coincidence (q) of a fuzzy point and the concept of (¡Ê, ¡Ê¡Åq) -fuzzy ideals in -algebras. The criteria for a fuzzy ideal to be an (¡Ê, ¡Ê¡Åq) -fuzzy ideal is established, (¡Ê, ¡Ê¡Åq) -fuzzy ideal and their Cartesian product and union are discussed. Some properties of (¡Ê, ¡Ê¡Åqk) -fuzzy ideals under homomorphism are also investigated.
Key words:
d-algebra, Fuzzy -ideal, Doubt fuzzy ideal, (¡Ê, ¡Ê¡Åq)-fuzzy ideal, (¡Ê, ¡Ê¡Åq)-fuzzy ideal.
Soft Rough Approach to Lattice-ideal
Susanta Bera and Sankar Kumar Roy
Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University, Midnapore-721102, West Bengal, India. E-mail: sankroy2006@gmail.com
Abstract:
Rough and soft sets are two different mathematical tools for dealing with uncertainties. Soft rough set is the study on roughness through soft set. Soft rough set is a fusion, proposed by Feng et al. [6] between the two mathematical approaches to vagueness. The aim of this paper is to study the lattice theory in the framework of soft rough set. We consider the soft approximation space by means of soft set and define the notions of upper and lower soft rough ideals in a lattice. A numerical example is presented to support of our proposed study.
Key words:
Lattice, Ideal, Soft set, Soft approximation space, Soft rough set.
Application of Generalized Weakly Compatibility in Common Fixed Point Results on Fuzzy Metric Spaces
Bhavana Deshpande and Amrish Handa
Department of Mathematics, Govt. P. G. Arts and Science College, Ratlam-457001 (MP), India. E-mail: bhavnadeshpande@yahoo.com E-mail: amrishhanda83@gmail.com
Abstract:
We introduce the concepts of generalized compatibility and generalized weakly compatibility for the pair {F,G} of mappings F,G:X¡ÁX¡úX in the setting of fuzzy metric space and also introduced the concept of common fixed point of the mappings F,G:X¡ÁX¡úX. We establish a common fixed point theorem for generalized weakly compatible pair F,G:X¡ÁX¡úX, without mixed monotone property of any of the mappings, on a non complete fuzzy metric space, which is not partially ordered. We also given an example to validate our result. Out results generalize some recent comparable results in the literature.
Key words:
Coupled coincidence point, coupled fixed point, common fixed point, fuzzy metric space, generalized compatible mappings, generalized weakly compatible mappings.
On Preserving Intuitionistic Fuzzy g-closed Sets
Jyoti Pandey Bajpai and S. S. Thakur
Department of Applied mathematics, Jabalpur Engineering , Jabalpur (M. P.) 482001 India. E-mail:jyotipbajpai@rediffmail.com E-mail:samajh_singh@rediffmail.com
Abstract:
In this paper we extend the concepts of a-closed and a-continuous mappings due to Baker [5] in intuitionistic fuzzy topological spaces and obtain several results concerning the preservation of intuitioistic fuzzy g-closed sets. Further more we characterize intui-tionistic fuzzy T1/2-spaces due to Thakur and Chaturvedi [16] in terms of intuitionistic fuzzy a-continuous and intuitionistic fuzzy a-closed mappings and obtain some of the basic properties and characterization of these mappings.
Key words:
Intuitionistic fuzzy g-closed sets, Intuitionistic fuzzy g-open sets, Intuitionistic fuzzy g-continuous, Intuitionistic fuzzy a-closed, Intuitionistic fuzzy a-continuous and Intuitionistic fuzzy gc-irresolute mappings.
Intuitionistic Fuzzy Graphs: Weakening and Strengthening Members of A Group
Caravaggio Caniglia
Brownell Talbot E-mail:cacanigl@brownell.edu
Benjamin Cousino
Department of Political Science E-mail:BenjaminCousino@creighton.edu
Shih-Chuan Cheng
E-mail:scheng@creighton.edu
Davender S. Malik
E-mail:malik@creighton.edu
John N. Mordeson
Department of Mathematics Creighton University Omaha, Nebraska 68178 USA E-mail:mordes@creighton.edu
Abstract:
Ross and Harary used graph theory to characterize the role of a members of a group with respect to the member¡¯s presence causing the graph of the group to be more highly connected than that when the member was absent, while a weakening members is one whose presence causes the graph to be more weakly connected. Takeda and Nishida presented an application of a fuzzy graph to the group structure in order to be able to consider situations where the members and edges between members have different strength of membership in the graph. In this paper, we consider intuitionistic fuzzy graphs.
Key words:
Intuitionistic fuzzy graphs; weakening and strengthening members; directed edge; directed path; involutive fuzzy complement; transitive closure.
Multi-fuzzy Vector Space and Multi-fuzzy Linear Transformation over A Finite Dimensional Multi-fuzzy Set
Asit Dey and Madhumangal Pal
Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University, Midnapore-721102, India. E-mail:asitiitk@gmail.com, mmpalvu@gmail.com
Abstract:
The main goal of this article is to introduce and study the multi-fuzzy vector spaces and its properties. Here we present an internal characterization of multi-fuzzy linear transformation and derived fuzzy rank-nullity theorem. The direct sum for multi-fuzzy vector spaces under certain conditions is also characterized. Some properties and characterization for projection operators are established.
Key words:
Multi-fuzzy vector spaces, Multi-fuzzy linear transformation, Direct sum, Projection operator.
Non-commuting Mappings and Common Fixed Points in Fuzzy Metric Spaces
Nanda Ram Das
Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India. E-mail:nrd47@yahoo.co.in
Mintu Lal Saha
Department of Mathematics, Handique Girls¡¯ College, Guwahati 781001, Assam, India. E-mail:mintula13@rediffmail.com
Abstract:
In this paper, we state and prove two common fixed point theorems for non-commuting maps in fuzzy metric spaces in the sense of Kramosil and Michalek, using the notions of compatibility, reciprocal continuity and E. A. property. Our work contains extensions of the fixed point theorems mainly due to R. P. Pant in classical metric spaces and perhaps the first fixed point theorem in fuzzy metric spaces guaranteeing the existence of a common fixed point of a family of maps when all the maps may be discontinuous and even many may not satisfy the compatibility conditions. We deduce some corollaries to our theorems and also illustrate them with suitable examples.
Key words:
Fuzzy metric spaces, compatible maps, reciprocal continuous maps, E. A. property, common fixed points.
Generalized Weakly Compatible Pair of Mappings and Its Application in Common Fixed Point Results on Modified Intuitionistic Fuzzy Metric Spaces
Bhavana Deshpande and Amrish Handa
Department of Mathematics, Govt. P. G. Arts and Science College, Ratlam-457001 (MP), India. E-mail:bhavnadeshpande@yahoo.com E-mail:amrishhanda83@gmail.com
Abstract:
We introduce the concept of generalized compatibility and generalized weakly compatibility for the pair {F,G}, of mappings F,G:X¡ÁX¡úX in the setting of modified intuitionistic fuzzy metric space and also introduce the concept of common fixed point of the mappings F,G:X¡ÁX¡úX. We establish a common fixed point theorem for generalized weakly compatible pair F,G:X¡ÁX¡úX, without mixed monotone property of any of the mappings, on a non complete modified intuitionistic fuzzy metric space, which is not partially ordered. We also give an example to validate our result. Our results generalize some recent comparable results in the literature.
Key words:
Coupled coincidence point, coupled fixed point, common fixed point, modified intuitionistic fuzzy metric space, generalized compatible mappings, generalized weakly compatible mappings.
Cubic Structure of BG-subalgebras of BG-algebras
Tapan Senapati
Department of Mathematics, Padima Janakalyan Banipith, Kukurakhupi 721517, India. E-mail:math.tapan@gmail.com
Abstract:
In this paper, the notion of cubic BG-subalgebras of BG-algebras are introduced. The homomorphic image and inverse image of cubic BG-subalgebras are studied and investigated some related properties.
Key words:
BG-algebra, BG-subalgebra, cubic set, cubic BG-subalgebra.
A Study on Fuzzy Soft gF¦ÒSets
N. Krithika, K. Saranya and Dr. B. Amudhambigai
Department of Mathematics, Sri Sarada College for Women, Salem-16 Tamilnadu, INDIA. E-mail:krithikasureshkumar.idp@gmail.com, saranyamath88@gmail.com, rbamudha@yahoo.co.in
Abstract:
In this paper, the concept of fuzzy soft gF¦Ò sets are introduced and its interrelations with other types of fuzzy soft closed sets are studied with suitable counter examples. Equivalently the interrelations of fuzzy soft gF¦Ò continuous functions with other types of fuzzy soft continuous functions are discussed with necessary counter examples.
Key words:
Fuzzy soft gF¦Òsets, Fuzzy soft gF¦Òcontinuous functions.
Some Observations on Completeness and Compactness in Fuzzy Normed Linear Spaces
T. Bag and S. K. Samanta
Department of Mathematics, Visva-Bharati University, Santiniketan, INDIA. E-mail: tarapadavb@gmail.com E-mail: syamal123@yahoo.com
Abstract:
In this paper, concept of 1-fuzzy convergence sequence, 1-fuzzy closed, 1-fuzzy complete and 1-fuzzy compact sets are introduced in fuzzy normed liner spaces (with general t-norm setting) and some observations are made in our earlier paper [3]. Based on these concepts, we have studied completeness and compactness of finite dimensional fuzzy normed linear spaces and extended the celebrated Riesz Lemma.
Key words:
1-fuzzy convergent, 1-fuzzy closed, 1-fuzzy complete, 1-fuzzy compact, fuzzy normed linear space.
On The Solution of Linear Time-varying Differential Dynamical Systems with Fuzzy Initial Condition and Fuzzy Inputs
Bhaskar Dubey
Department of Mathematics, Indian Institute of Space Science and Technology Thiruvananthapuram, India, PIN-695547. E-mail: bhaskar.dubey@gmail.com
Abstract:
In this paper we investigate the solutions of linear time-varying differential dynamical systems with fuzzy initial condition and fuzzy inputs. We use a complex number representation of the ¦Á-level sets of the fuzzy states to characterize the solutions of such systems by a closed form formula which could be easily used in practical computations. Examples are given to illustrate the results.
Key words:
Fuzzy number; Fuzzy differential equation; Fuzzy initial condition.
¦Ã-connectedness in L-topological Spaces
Baby Bhattacharya and Sunny Biswas
Department of Mathematics, NIT Agartala, Barjala, 799046, Tripura, India.
Abstract:
In this paper, first we study the concept of¦Ã-closed sets in L-topological spaces. Then after a new kind of connectivity called¦Ã-connectedness in L-topological spaces is introduced by help of¦Ã-closed sets in L-topological spaces. Some fundamental properties of¦Ã-connectedness are studied and the inter-relationship between P-connectedness, S-connectedness and connectedness are explained. It is also included that the famous K. Fan¡¯s Theorem can be extended to L-topological spaces for¦Ã-connectedness.
Key words:
¦Ã-open set, ¦Ã-closed set, ¦Ã-separated set, ¦Ã-connectedness, L-topological space.
Uniform Integrability of Set-valued Random Variables on Capacity Spaces
Hongxia Wang
College of Statistics, Henan University of Economics and Law, Zhengzhou, Henan 450046, China.E-mail: xiahongwang@163.com
Abstract:
The article aims at discussing the uniform integrability of the sequence of set-valued random variables on capacity spaces. We investigate the space of the Choquet integrably bounded set-valued random variables, and in this space, we introduce the concepts of uniform integrability.
Key words:
Set-Valued Random Variable; uniformly integrable; Capacity space.
Some Results on G-fuzzy Product Topological Spaces
Ajith S. Kurup
Sree Buddha College of Engineering, Pattoor, Kerala, India.E-mail:ajithskurup@gmail.com
Dr. Mathews M. George
Providence College of Engineering, Chengannur, Kerala, India. E-mail:mathewjas@gmail.com
Abstract:
G-fuzzy topological spaces was introduced by Mathews and Samuel [2008] in their papers titled G-fuzzy topological spaces and fuzzy compactness using two operations sum ¨’ and conjunction &. In this paper, we give a brief introduction to g-Fuzzy Product topological spaces. We make an attempt to motivate g-fuzzy product topological properties.
Key words:
Set-Valued Random Variable; uniformly integrable; Capacity space.
L-fuzzy Ideals with Thresholds-(¦Á, ¦Â] of Lattices
S. H. Dhanani
Department of Mathematics, K. I. T.¡¯s College of Engineering, Kolhapur, Maharashtra, India.E-mail:sachindhanani@rediffmall.com
Y. S. Pawar
Department of Mathematics, Shivaji University, Kolhapur, Maharashtra, India. E-mail: pawar_y_s@yahoo.com
Abstract:
The aim of this paper is to extend the concept of a fuzzy sublattice (ideal) by introducing L-fuzzy sublattice (ideal) with thresholds (¦Á, ¦Â] of a bounded lattice. Some properties of L-fuzzy sublattice (ideal) with thresholds (¦Á, ¦Â] of a bounded lattice are investigated. L-fuzzy convex sublattice with thresholds (¦Á, ¦Â] of a bounded lattice is studied. Finally, we establish a one-one correspondence between L-fuzzy ideals with thresholds (¦Á, ¦Â] of a bounded lattice and their isomorphic images.
Key words:
L-fuzzy sublattice with thresholds (¦Á, ¦Â], L-fuzzy convex sublattice with thresholds (¦Á, ¦Â], L-fuzzy ideal with thresholds (¦Á, ¦Â], and L-fuzzy prime ideal with thresholds (¦Á, ¦Â].
An Introduction of Product Topology in g-fuzzy Topological Spaces
Ajith S. Kurup
Sree Buddha College of Engineering, Pattoor, Kerala, India. E-mail:ajithskurup@gmail.cim
Mathews M. George
Department of Mathematics, Providence College of Engineering, Chengannur, Kerala, India. E-mail:mathewjas@gmail.com
Abstract:
In this paper, we introduce product topology in g-Fuzzy Topological Spaces. We make an attempt to discuss some basic properties.
Key words:
Fuzzy set, g-fuzzy topology, Base for fuzzy topological space, g-fuzzy Subspace Topology, g-fuzzy Compactness, g-fuzzy connectedness and g-fuzzy product topology.
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