The Journal of Fuzzy Mathematics
Volume 26, Number 2, March 2018
CONTENT
DETAILS
Extra Strongly Generalized Closed Soft Sets
Rodyna A. Hosny
Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
Abstract:
In soft topological spaces, we introduce the concept of extra strongly generali- zed closed soft sets as a generalization of the concepts strongly g-closed soft and g-closed soft sets. Some of their basic properties are discussed. Also, the relationships between extra strongly generalized closed soft sets and other existing soft sets are inve- stigated.
Key words:
g-closed soft sets, Strongly g-closed soft sets.
Types of Soft Compactness Via beta-Open Soft Sets and Soft Ideal
Rodyna A. Hosny
Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
Abstract:
This article is devoted to study variant kinds of soft compactness via beta-open soft sets and soft ideal in soft topological spaces which include soft betaI-compact, soft betaI-countably compact, soft betaI-almost compact and soft betaI-lindelof spaces. Some characterizations about them are given. The behaviour of these concepts under various types of soft functions is obtained.
Key words:
beta-open soft sets, Soft betaI-compact spaces, Soft betaI-almost compact spaces, Soft functions.
On Fuzzy Semi-injective Modules
Arbah S. Abdul-Kareem
Department of mathematics-college of sciences-Diyala University
Abstract:
In this work, the notion of fuzzy semi-injective modules has been introduced and studied some of its properties, as: the direct sum of the fuzzy semi-injective modules is again fuzzy semi-injective module and its converse; also we studied the fuzzy semi-injective submodules.
Key words:
semi-injective modules, fuzzy modules.
On Fuzzy Automata p-closed Subsystems in Fuzzy Automata Topological Spaces
B. Amudhambigai and N. Krithika
Department of Mathematics, Sri Sarada College for Women, Salem, Tamilnadu, India, E-mail: rbamudha@yahoo.co.in, E-mail: krithikasureshkumar.idp@gmail.com
Abstract:
The purpose of this paper is to introduce and study the concept of fuzzy automata p-closed subsystems and its relationships with different types of fuzzy automata closed subsystems are investigated. Also, counter examples are given wherever it is necessary. The concept of fuzzy automata p-continuous functions is introduced and its relationships with other forms of fuzzy automata continuous functions are discussed. Moreover, the concept of fuzzy automata p-T spaces is introduced and the interrelation- ships among fuzzy automata p-T spaces, fuzzy automata p-T spaces, fuzzy automata p-T spaces and fuzzy automata spaces are established.
Key words:
Fuzzy automata topological space, fuzzy automata p-closed subsystem, fuzzy automata p-continuous function, fuzzy automata p-T space.
Generalization of L-fuzzy Bitopological Compact Spaces
R. Femina
Keelakkotai Street, Ambalapattu South, Orathanadu, Thanjavur-614626, Tamilnadu, India, E-mail: femina.shankar@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 spacer, using (i,j)-beta-open L-sets and their inequality, a new notion of (i,j)-beta-compactness is introduced in L-bitopological spaces, where L is a complete De Morgan algebra. This notion does not depend on the structure of the basis lattice L and L does not need nay distributivity.
Key words:
L-fuzzy bitopology, (i,j)-beta-open L-set, (i,j)-beta-compactness.
Fuzzy Chaotic Centred Texture Di Structure Spaces
M.K.Uma and R. Malathi
Department of Mathematics, Sri Sarada College for Women, Salem, Tamil Nadu, India,
E-mail: malathymaths90@gmail.com
Abstract:
The focus of this paper is to introduce the concepts of fuzzy orbit open set, fuzzy periodic open set, fuzzy chaotic, fuzzy chaos space, fuzzy chaotic structure space, fuzzy open chaotic set, fuzzy chaotic centred system, fuzzy chaotic centred texture space, fuzzy chaotic centred texture open set, fuzzy chaotic centred texture di-structure space. Some interesting properties of fuzzy chaotic centred texture space, fuzzy chaotic centred texture di-structure space are discussed. Also, the characterization of fuzzy chaotic centred texture maximal difilter, prime cofilter are established.
Key words:
Fuzzy orbit open set, fuzzy periodic open set, fuzzy chaotic, fuzzy chaos space, fuzzy chaotic structure space, fuzzy open chaotic set, fuzzy chaotic centred system, fuzzy chaotic centred texture space, fuzzy chaotic centred texture open set, fuzzy chaotic centred texture di-structure space.
On Fuzzy Automata Hardly betag-open Functions in Fuzzy Automata Topological Spaces
B. Amudhambigai and N. Krithika
Department of Mathematics, Sri Sarada College for Women, Salem, Tamilnadu, India, E-mail: rbamudha@yahoo.co.in;in, E-mail: krithikasureshkumar.idp@gmail.com
Abstract:
In this paper, the concepts of fuzzy automata betag-open, somewhat fuzzy automata betag-open and fuzzy automata hardly betag-open functions are introduced and studied. Some of their characterizations are established. Also the concepts of fuzzy automata betag-connected spaces, fuzzy automata strongly betag-connected spaces and fuzzy automata betag-closed spaces are introduced and their properties are discuss- ed.
Key words:
Fuzzy automata betag-open function, generating fuzzy automata betag-subsystem, somewhat fuzzy automata betag-open function, function automata hardly betag-open function, fuzzy automata betag-connected space, fuzzy automata strongly betag-connected space, fuzzy automata Gbetag-closed space.
Generalization of Cut Sets of 1/(R*R)-intuitionistic Fuzzy Sets
Riyaz Ahmad Padder
Department of Mathematics, Annamalai University, Annamalainagar-608002, India.
E-mail: padderriyaz01@gmail.com
P. Murugadas
Department of Mathematics, Annamalai University, Annamalainagar-608002, India.
E-mail: bodi_muruga@yahoo.com
Abstract:
In this paper, we introduce /(R*R) intuitionistic fuzzy cut sets. We first put forward some properties of intuitionistic fuzzy cut sets. Based on these properties the decomposition and representation theorems are discussed. Moreover, the axiomatic defi-nition of cut set for1/(R*R) intuitionistic fuzzy set is given and also, discuss its properties.
Key words: Intuitionistic Fuzzy Sets, Cut sets, Representation theorems, Decom-position theorems.
On -connectedness in (i,j)-beta-bitopological Spaces
R. Femina
Keelakkotai Street, Ambalapattu South, Orathanadu, Thanjavur-614626, Tamilnadu, India, E-mail: femina.shankar@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 spaper, a certain new connectedness of L-fuzzy subsets in L-bitopological spaces is introduced and studied by means of (i,j)-beta-closed sets. It presr- rves some fundamental properties of connected set in general topology. Especially the famous K. Fan's Theorem holds.
Key words:
L-bitopological space, (i,j)-beta-closed set, (i,j)-beta-connected set, (i,j)-beta-connected set.
Some Extended Quality Measures Concerning Fuzzy Association Rules
Thanuja T S
Research Scholar Dept of Mathematics, Mar Ivanios College, Trivandrum, E-mail: thanuja963@gmail.com
Dr Mary George
Associate Professor and Head Dept of Mathematics, Mar Ivanios College, Trivandrum,
E-mail: marygeo@rediffmail.com
Abstract:
Association rules are initially discovered in the market basket analysis [1] to identify frequently purchased items by customers. It gives certain regularities and depen- dencies within a data by finding frequent co-occurrence of items with a set of transacti- ons. Usually support and confidence are the two important quality measures used to assess the quality of association rules. In fuzzy association rule mining, fuzzy support and confidence are used, which are based on -norm operators. In addition to this opposition measures are also defined using -norm operators. These measures were arised during the categorisation of transactions into positive and negative examples [5, 6]. Here we tried to extend these quality measures using averaging operators and studied their properties.
Key words:
Fuzzy association rules, Support, Opposition, Averaging operators, fuzzy average support, fuzzy average opposition.
Measure of Fuzzy (i,j)-beta-compactness in L-fuzzy Topological Spaces
G. Balaji
Department of Mathematics, Thangavelu Engineering College, Chennai, Tamilnadu, India
R. Femina
Keelakkotai Street, Ambalapattu South, Orathanadu, Thanjavur-614626, Tamilnadu, India, E-mail: femina.shankar@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, the notion of fuzzy (i,j)-beta-compactness degrees is introduced in L-fuzzy topological spaces by means of the implication operation of L. Characterizatio- ns of fuzzy (i,j)-beta-compactness degrees in L-fuzzy topological spaces are obtained, and some properties of fuzzy (i,j)-beta-compactness degrees are researched.
Key words:
L-bitopological spaces, fuzzy (i,j)-beta-compactness, Fuzzy (i,j)-beta-compact- ness degree.
A Fuzzy Based Decision Support System Framework for Open and Distance Learning Institutions
Pankaj Khanna
Planning and Development Division, Indira Gandhi National Open University (IGNOU), Maidangarhi,
New Delhi 11068, India,
E-mail: khanna.delhi@gmail.com; pk@ignou.ac.in
P. C. Basak
Professor (Ex.) of Management, Indira Gandhi National Open University (IGNOU) Maidangarhi,
New Delhi 110068, India, E-mail: parimalbasak1@gmail.com
Abstract:A fuzzy based decision support system ( ) is developed for problem solving and decision making in Open and Distance Learning Institutions ( ). Such a system is designed primarily for solving problems involving imprecision and/or uncertainty in their data values. A fuzzy model framework is designed in which multi criteria decision making approach consisting of fuzzy along with fuzzy scale and weighting priority technique have been adopted for assessing the performance of the programmes involved. In this model the performance scores obtained under different criteria, are aggregated into an overall performance score for each programme. Thereafter ranking of the programmes under study is undertaken. The overall process of performance evaluation and decision making is mainly involved in defining the problem, creating programme criteria and generating programme reports. Subsequently the management can recommend about the future strategies to be adopted for the improvement of the programme concerned..
This study would help the management to quickly identify the programmes/activities that need immediate attention. As a result this would improve the quality of education delivery as well as teaching and learning systems in the concerned .
Key words:
Fuzzy systems; analytic hierarchy process; triangular fuzzy number; decision support system; decision making; performance evaluation.
On Q1 and Q2 Fuzzy Ideals in Ordered Semigroups
P. Nandakumar
Perunthalaivar Kamarajar Institute of Engineering and Technology,
Karaikal -609 603, U.T.of Puducherry, India, E-mail: drpnandakumar@gmail.com
B. Sambathkumar
Research and Development Centre, Bharathiyar University, Coimbatore, India, E-mail: sambathkumarbu@gmail.com
P. Dheena
Professor of Mathematics(Rtd.), Annamalai University Annamalainagar-608 002, Tamilnadu, India, E-mail: dheenap@yahoo.com
Abstract:
In this paper, we first introduce the new idea of Q1 and Q2 fuzzy ideals and Q1 and Q2 fuzzy bi-ideals of an ordered semigroup , when Q is a semigroup.
Key words:
Q fuzzy set, Q fuzzy ideals, ordered semigroup, ordered Q fuzzy point.
On Solutions of Linear Fractional Programming Problems with Rough-interval Coefficients in The Objective Function
H. A. Khalifa
Department of Operations Research, Institute of Statistical
Studies and Research, Cairo University, Giza, Egypt,
Abstract:
In this paper, a rough interval linear fractional programming (RILFP) problem is introduced. The RILFP problem is considered by incorporating rough intervals in the objective function coefficients. It is shown that the RILFP problem may be converted into an optimization problem with rough intervals objective function which it's upper and lower approximation intervals are interval-valued linear fractional programming (IVLFPP) problem. Also, the IVLFPP problem can be converted into an optimization problem with interval-valued objective function whose bounds are linear fractional functions. Also, we show that the IVLFPP problem can be resolved into a series of LFP problems under assumptions. The solutions of these kind of optimization problems will be discussed through illustrative numerical examples.
Key words:
Rough interval; Linear fractional programming; Rough interval linear fractional programming.
Share Functions for Cooperative Games with Fuzzy Coalitions
Rajib Biswakarma
Department of Mathematics, Dibrugarh University, India, E-mail: rajib01101987@gmail. com
Surajit Borkotokey
Department of Mathematics, Dibrugarh University, India, E-mail: surajitbor@yahoo.com Chunqiao Tan
Department of Management Science and Information Management,
School of Business; Central South University, China, E-mail: chunqiaot@sina.com
Abstract:
In this paper, we introduce the notion of Share functions for fuzzy games. A set of axioms to characterize the Share function is proposed. Some interesting results pertaining to a special class of fuzzy games, namely the fuzzy games in multilinear form are obtained. The Shapley share and Banzhaf share functions for this class are derived.
Key words:
Fuzzy cooperative game, Multilinear extension, share function, Shapley share function, Banzhaf share function.
Soft Almost Pre-continuous Mappings
S. S. Thakur
Department of Applied Mathematics, Jabalpur Engineering College ,
Jabalpur (M. P.) 482011 India, E-mail: samajh_singh@rediffmail.com
Alpa Singh Rajput
Department of Applied Mathematics, Jabalpur Engineering College ,
Jabalpur (M. P.) 482011 India, E-mail: alpasinghrajput09@gmail.com
Abstract:
In the present paper the concept of soft almost pre-continuous mappings and soft almost preopen mappings in soft topological spaces have been introduced and studied.
Key words:
Soft regular open set, Soft pre-open set, Soft almost continuous mappings, Soft pre-continuous mappings, Soft almost pre-continuous mappings and Soft almost pre-open mappings.
Fuzzy Almost e-continuous Mappings and Fuzzy e-compactness
A. Vadivel
Department of Mathematics, Annamalai University, Annamalainagar, Tamil Nadu-608002, E-mail: avmaths@gmail.com
B. Vijayalakshmi
Mathematics section, FEAT, Annamalai University, Annamalainagar, Tamil Nadu-608002, E-mail: mathvijaya2006au@gmail.com
Abstract:
In this paper, we introduce the concept of fuzzy almost e-continuous, r-fuzzy e-compact, r-fuzzy almost e-compactness and r-fuzzy near e-compactness in Sostak¡¯s fuzzy topological spaces. We study some properties of them under several types of fuzzy e-continuous mappings and fuzzy e-regular spaces.
Key words:
fuzzy (almost, weakly)-e-continuous, fuzzy e-regular spaces, r-fuzzy (almost, near) e-compactness.
Doubt Fuzzy Ideals of BE-algebra
Fengxiao Wang
College of Mathematics and Statistics, Kashigar University, Kashi, 844000, China, E-mail: fxw-hz@126.com
Abstract:
The aim of this paper is to introduce the notion of doubt fuzzy ideal in BE-algebra and to investigate some of their properties. Characterizations of a doubt fuzzy ideal are provided. It is shown that the union and Cartesian product of doubt fuzzy ideals are also doubt fuzzy ideals. Finally, the homomorphism properties of doubt fuzzy ideal in BE-algebra are present.
Key words:
BE-algebra; doubt fuzzy ideal; Cartesian product; homomorphism..
On Fuzzy Random Multi-objective Linear Programming with Application to Multi-item Solid Transportation Problem
H. A. Khalifa
Operations Research Department, Institute of Statistical Studies and Research,
Cairo University, Giza, Egypt
Abstract:
In this paper, a multi-objective linear programming (FR-MOLP) problem with fuzzy random objective functions coefficients and fuzzy random constraints parameters is studied. At the first, the results show that a fuzzy random efficient solution of a fuzzy random multi-objective linear programming may be resolved into a series of pseudorand- om optimal solutions of relative random linear programming problems. Secondly, some theorems with proofs to find the optimal solutions of the relative linear programming problems are presented. Also, an application fuzzy multi-objective multi- item solid transportation problem is discussed and an acceptable solution of such problem is given. Finally, numerical examples are given in the sake of the paper to clarify the obtained results.
Key words:
Multi-objective linear programming; Fuzzy numbers; Fuzzy efficient solution; Fuzzy random variables; Interval analysis; Random multi-objective linear programming; Fuzzy random multi-objective linear programming; Weighting method; Fuzzy random optimal solution; Multi- item solid transportation problem.
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