The Journal of Fuzzy Mathematics
Volume 23, Number 1, March 2015
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On (enriched) L-fuzzy Topologies: Decomposition Theorem
Guopeng Wang, Lingqiang Li, GuangwuMeng and Qingxue Su
School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China. E-mail: happywgp2008@163.com
Abstract:
To our knowledge, the existed decomposition theorems for L-fuzzy topologies are only available in the case that the lattices to be completely distributive complete lattice. In this paper, considering L to be an arbitrary complete Heyting algebra, a decomposition theorem for (enriched) L-fuzzy topologies is presented. Said precisely, it is proved that an (enriched) L-fuzzy topology can be represented as a family of (stratified) L-topologies with some left-continuous condition.
Key words:
Enriched L-fuzzy topology, stratified L-topology, decomposition theorem
On Pairwise Intuitionistic Fuzzy Resolvable(Irresolvable) Spaces
K. Biljana
Institute of Mathematics, Faculty of Mathematics and Natural Sciences, University St. Cyril and Methodius, P. O. 162, 1000 Skopje, Macedonia. E-mail: madob2006@yahoo.com
N. Rajesh
Department of Mathematics, Rajah Serfoji Govt. College, Thanjavur-613005, Tamilnadu, India. E-mail: nrajesh_topology@yahoo.co.in
V. Vijayabharathi
Department of Mathematics, National Institute of Technology, Tiruchi-Rappalli, Tamilnadu, India.
E-mail: vijayabharathi_v@yahoo.com
Abstract: In this paper, we introduce and study the concepts of intuitionistic fuzzy resolvability, intuitionistic fuzzy irresolvability and intuitionistic fuzzy open hereditarily irresolvability in intuitionistic fuzzy bitopological spaces.
Key words and phrases:
Intuitionistic fuzzy bitopology, pairwise intuitionistic fuzzy resolvable spaces.
On Generalized Intuitionistic Fuzzy Topology
N. Gowrisankar
70/232 6B, Kollupettai 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
V. Vijayabharathi
Department of Mathematics, National Institute of Technology, Tiruchi-Rapalli, Tamilnadu, India.E-mail: vijayabharathi_v@yahoo.com
Abstract:
The aim of this paper is to present a common approach allowing to obtain familes of intuitionistic fuzzy sets in an intuitionistic fuzzy topological space.
Key words: Generalzied Intuitionistic fuzzy topology, g-intuitionistic fuzzy open set.
More on Generalized Intuitionistic Fuzzy Topology
N. Gowrisankar
70/232 6B, Kollupettai 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
V. Vijayabharathi
Department of Mathematics, National Institute of Technology, Tiruchi-Rapalli, Tamilnadu, India.E-mail: vijayabharathi_v@yahoo.com
Abstract:
The purpose of the paper is to investigate some results concering particular monotonic functions in generalized intuitionistic fuzzy topology.
Key words:
Generalized intuitionistic fuzzy topology
Characterization of Connectedness and Surroundness in An Intuitionistic Fuzzy Digital Topology
R. Narmada Devi, E. Roja and M. K. Uma
Department of Mathematics, Sri Sarada College for Women, Salem, Tamil Nadu, India.E-mail:narmadadevi23@gmail.com
Abstract:
Topological relationships among parts of a digital picture, such as connectedness and surroundedness, play an important role in picture analysis and description. This paper generalizes these concepts to an intuitionistic fuzzy sets and discussed some of their basic properties.
Key words:
Intuitionistic fuzzy strength of a path, intuitionistic fuzzy connectedness, intuitionistic fuzzy components like intuitionistic fuzzy plateau, intuitionistic fuzzy top, intuitionistic fuzzy bottom and intuitionistic fuzzy surroundness.
Generalization of An Intuitionistic Fuzzy &str Open Sets in An Intuitionistic Fuzzy Grill Structure Spaces
R. Narmada Devi, E. Roja and M. K. Uma
Department of Mathematics, Sri Sarada College for Women, Salem, Tamil Nadu, India.E-mail:narmadadevi23@gmail.com
Abstract:
The purpose of this paper is to introduce the concepts of an intuitionistic fuzzy grill, intuitionistic fuzzy & strucute space, intuitionistic fuzzy d&str set and intuitionistic fuzzy a&str open set. The concepts of an intuitionistic fuzzy Ea&str continuous function, intuit-tionistic fuzzy a&str -Ti space, i=0,1,2 and intuitionistic fuzzy a&str -co-closed graphs are defined. Some interesting properties are established.
Key words:Intuitionistic fuzzy grill, intuitionistic fuzzy & structure space, intuitionistic fuzzy d&str set and intuitionistic fuzzy a&str (resp. a&str, semi&str, pre&str, regular&str and b&str) open set, intuitioistic fuzzy a&str exterior, intuitionistic fuzzy Ea&str continuous function, intuitionistic fuzzy a&str -Ti space, i=0,1,2 and intuitionistic fuzzy a&str -co-closed graphs.
A Note on Fuzzy Continuum on Mixed Fuzzy Topological Spaces
N. R. Das
Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India.
Brojen Das
Department of Mathematics, M. C. College, Barpeta, Assam, India.E-mail: brojen.das@rediffmail.com
Abstract:
This paper deals with the study of H-continuum and N-continuum in Mixed Fuzzy Topological Spaces. We have already given the H-continuum and N-continuum structure to Fuzzy topological spaces in our papers ¡°A note on H-continuum¡± and ¡°Some Aspects of Fuzzy N-continuum¡±,and Prof. N. R. Das and P. C. Baishya has given the Mixed Topological structure in Fuzzy setting. We have tried to study the continuum structure in Mixed Fuzzy Topology. Hence in this paper we also see that the presence of H-closed and N-closed sets with Mixed Fuzzy topology give arise some new properties which are also be studied. Our perspective is to explore more results in this direction.
Key words: q-connectedness, d-connectedness, H-closed, N-closed, H-continuum, N-continuum, q-continuous, d-continuous.
Fuzzy Reliability Optimization Based on Fuzzy Geometric Programming Method Using Different Operators
A. K. Shaw and T. K. Roy
Department of Mathematics, Bengal Engineering and Science University, Shibpur Howrah-711103, West Bengal, India. E-mail address:ashokshaw2001@yahoo.co.in
Abstract: In this paper, we summarize the fundamentals of fuzzy GP and present the problem of optimal reliability for a series system subject to a cost constraint. In real life, it is necessary to improve the reliability of the system under limited available cost of reliability component. Practically some desired system reliability level subject to constraint on cost has always been imprecise and vague in nature. It may be formulated as a fuzzy geometric programming problem. Numerical examples are given to illustrate the model through fuzzy geometric programming by max-min, max-additive and max-product operators.
Key words and phrases: Fuzzy GP, reliability, posynomial, signomial.
Concept Analysis with Interior and Closure Operators
Subrata Bhowmik
Department of Mathematics, Tripura University Suryamaninagar, Tripura, INDIA-799022. E-mail:subrata_bhowmik_math@rediffmail.com
Abstract: The study of concept analysis is done within the lattice structure. In this paper we are interested to study concept analysis in some different way. Here we will introduce some algebraic operators and study some algebra. Also we will study different types of Information-System and the rules of decision making using this new type of concept analysis.
Key words:Formal Concept Analysis, Semi-Lattices, Fuzzy Set, Information System.
On Somewhat Fuzzy Nearly Continuous Functions
G. Thangaraj
Department of Mathematics Thiruvalluvar University Vellore-632115, Tamilnadu, India.
S. Anjalmose
Research Scholar, Department of Mathematics Thiruvalluvar University Vellore-632115, Tamilnadu, India.
Abstract:In this paper the concept of somewhat fuzzy nearly continuous functions, somewhat fuzzy nearly open functions are introduced and studied. Besides giving characterizations of these functions, several interesting properties of these functions are also given. Several examples are given to illustrate the concepts introduced in this paper.
Key words: Somewhat fuzzy continuous, somewhat fuzzy nearly continuous, somewhat fuzzy open, somewhat fuzzy nearly open, fuzzy irresolute, fuzzy pre semi-open, fuzzy dense, fuzzy nowhere dense, fuzzy Baire space.
Some Fixed Point Results in Fuzzy Metric Spaces under Common Limit Range Property
Sunny Chauhan
Near Nehru Training Centre H. No.274, Nai Basti B-14, Bijnor-246701, Uttar Pradesh, India. Email: : sun.gkv@gmail.com
Mujahid Abbas
Dept. of Mathematics and Applied Mathematics, University of Preteria,Lynvvood Road, Pradesh, InPretoria, 002, South Africa. Email: : mujahid@lums.edu.pk
Ishak Altun
Dept. of Mathematics, Fuculty of Science and Arts, Kirikkale University71450 Yahsihan, Kirikkale, Turkey. Email: : ialtun@kku.edu.tr
Jelena Vujakovic
University of Pristina, Faculty of Sciences and Mathematics Lole Ribara 29 38 200, Kosovska Mitrovica, Serbia. Email: : jelena.vujakovic@pr.ac.rs
Abstract: In this paper, some new common fixed point theorems under certain strict contractive conditions for mappings sharing the (CLRST) property in fuzzy metric spaces are proved. Examples in support of our results are also given. A fixed point theorem for four finite families of self mappings in fuzzy metric space is also obtained. Our results improve and extend the results of Sedghi and Shobe [Common fixed point theorems under strict contractive conditions in fuzzy metric spaces using property (E.A). Commun. Korean Math. Soc. 27 (2), 399-410 (2012)].
Key words: Fuzzy metric space; weakly compatible mappings; property (E. A); common property (E. A); common limit range property; fixed point.
Some Fixed Point Theorems on Generalized M-fuzzy Metric Space
A. Singadurai and G. Pushpalakshmi
Department of Mathematics, TDMNS college, T. Kallikulam-627117 Tamilnadu, India.E-mail: singadurai_59@yahoo.co.in
Abstract: We define compatibility and weak compatibility of a collection of self maps on generalized -fuzzy metric space. This concept motivates us to establish a unique fixed point for a collection of self maps. Also we study a fixed point theorem for multivalued maps on generalized -fuzzy metric space.
Key words:Generalized M-fuzzy metric space, self map, compatiblemaps and weakly compatible maps, multivalued map.
Fuzzy Implication Groupoids
Ravi Kumar Bandaru
Department of Engineering Mathematics, GITAM University, Hyderabad Campus, Andhra Pradesh, India-502329.E-mail: ravimaths83@gmail.com
Bijan Davvaz
Department of Mathematics, Yazd University, Yazd, IRAN.E-mail: bdavvaz@yahoo.com
Abstract: In this paper, we fuzzify the concept of implication groupoids and investigate some of their properties. We give a characterization of fuzzy implication groupoid, and discuss a characterization of fuzzy implication groupoids in terms of level subalgebras of fuzzy implication groupoids.
Key words: Implication groupoid, distributive implication groupiod, level subalgebra, normal fuzzy implication groupoid.
Some Results on D*-fuzzy Cone Metric Spaces and Fixed Point Theorems in Such Spaces
T. Bag
Department of Mathematics, Visva-Bharati University West Bengal, India.E-mail:tarapadavb@gmail.com
Abstract: In this paper, an idea of D*-fuzzy cone metric space is introduced. Some basic definitions viz. convergence of sequence, Cauchy sequence, closedness, completeness etc are given and study some related properties. Some fixed point theorems are established in such spaces.
Key words: D*-fuzzy cone metric space, weakly compatible mapping.
New Distance and Similarity Measures for Soft Sets
Wang Ling, Qin Keyun and Liu Yaya
College of Mathematics, Southwest Jiaotong University, Sichuan, Chengdu, 610031, China.E-mail:wling.1989@qq.com, keyunqin@263.net, 1109731034@qq.com
Abstract:
In this paper, we will show that some results presented in [3] may be unreasonable and proper results will be introduced. Meanwhile new distance measure and similarity measures for oft sets will be proposed. Furthermore, some application examples about soft sets are also given.
Key words: Soft set, Distance measure, Similarity measure.
On Fuzzy Upper and Lower b-irresolute Multifunctions
S. E. Abbas
Department of Mathematics, Faculty of Science, Jazan University, Saudi Arabia
M. A. Hebeshi and I. M. Taha
Department of Mathematics, Faculty of Science, Sohag University, Egypt.E-mail:imtaha2010@yahoo.com
Abstract: The main purpose of this paper is to introduce and study fuzzy upper and fuzzy lower b-irresolute, b-continuous and strongly semi b-irresolute multifunctions. Also, several characterizations and properties of these multifunctions along with their mutual relationships are established in fuzzy topological spaces.
Key words:Fuzzy topology, fuzzy multifunction, graph multifunction, upper and lower b-continuous, b-irresolute, strongly semi b-irresolute, composition, union and compactness.
Rough Prime Bi-ideals in G-semigroups
N. Thillaigovindan
Veltech Ranga Sanku Arts College, Avadi , Chennai-600 062, India.E-mail: thillaigovindan.natesan@gmail.com
V. S. Subha
Department of Mathematics Annamalai University Annamalainagar-608002, India.E-mail: surandsub@yahoo.com
Abstract: In this paper we introduce the notions rough prime bi-ideals, strongly rough prime bi-ideals, rough semiprime bi-ideals, strongly rough irreducible and rough irreducible bi-ideals of -semigroups. We have shown that the lower and upper approximation of a prime bi-ideal are also prime bi-ideals.
Key words:Prime bi-ideals, Strongly rough prime bi-ideals, Irreducible bi-ideals, Rough semiprime bi-ideals, Strongly rough irreducible bi-ideals, Rough irreducible bi-ideals.
Compatible 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: mintulal3@rediffmail.com
Abstract:In this paper, we state and prove some common fixed point Theorems in fuzzy metric spaces in the sense of Kramosil and Michalek, using the notions of compatibility and reciprocal continuity of maps. Our work contains proper generalizations of many important Theorems mainly due to Murthy, Jungck and Cho. We deduce some Corollaries to our Theorems and also illustrate them with suitable examples.
Key words:Fuzzy metric spaces, compatible maps, reciprocal continuous maps, common fixed points.
Bipolar Fuzzy Structure of BG-subalgebras
Tapan Senapati
Department of Mathematics, Padima Janakalyan Banipith Kukrakhupi, Paschim Medinipur-721517, India.
E-mail: math.tapan@gmail.com
Abstract:Based on the concept of bipolar fuzzy set, a theoretical approach of the BG-subalgebras is established. Some characterizations of bipolar fuzzy BG-subalgebras of BG-algebras are given.
Key words:BG-algebra, BG-subalgebra, bipolar fuzzy BG-subalgebra.
Singular Fuzzy Submodules
Mrinal C. Kalita
Department of Mathematics, Pandu College, Guwahati-781012 INDIA.
E-mail: mckbamundi@yahoo.co.in
Helen K. Saikia
Department of Mathematics, Gauhati University, Guwahati-781014 INDIA
E-mail: hsaikia@yahoo.com
Abstract:In this paper we introduce the notion of singular fuzzy submodules of modules in terms of fuzzy essentiality. We investigate various characteristics of such submodules.
Key words:Fuzzy submodule, essential fuzzy submodule, fuzzy annihilators, singular submodule
Generalized Regular Fuzzy Closed Sets and Their Applications
B. Bhattacharya
Department of Mathematics, NIT Agartala, Tripura, 799055, India
E-mail: babybhatt75@gmail.com
J. Chakraborty
Department of Mathematics, NIT Agartala, Tripura, 799055, India.
E-mail: chakrabortyjayasree1@gmail.com
Abstract:This paper introduces a new class of sets called generalized regular fuzzy closed sets which is a stronger form of generalized fuzzy closed sets. Basic properties of generalized regular fuzzy closed sets are analyzed. Generalized fuzzy closed sets lie between generalized regular fuzzy closed sets and regular generalized fuzzy closed sets. Generally fuzzy closed set is not a generalized regular fuzzy closed set. But in this paper it is shown that closure of any fuzzy open set is always a generalized regular fuzzy closed set. With the help of generalized regular fuzzy closed sets, the concept of generalized regular fuzzy continuity and fuzzy generalized regular closed irresolute mapping are introduced. Latter on the interrelationship between generalized regular fuzzy continuity, generalized fuzzy continuity and regular generalized fuzzy continuity are also discussed. Different kinds of contra continuity based on fuzzy closed set, regular generalized fuzzy closed set, generalized regular fuzzy closed set are defined and few related results are shown. The decomposition of fuzzy homeomorphism is discussed via generalized fuzzy homeomorphism, generalized regular fuzzy homeomorphism and regular generalized fuzzy homeomorphism.
Key words:Generalized regular fuzzy closed set, generalized regular fuzzy open set, generalized regular fuzzy continuous function, generalized regular fuzzy contra continuity, generalized regular fuzzy homeomorphism.
(E,E,q) -fuzzy Subalgebras of Lattice Implication Algebras
Peng Deng and Yang Xu
School of Mathematics, Southwest Jiaotong University, Sichuan, Chengdu 610031, China.
E-mail: 871845567@qq.com; xuyang@home.swjtu.edu.cn
Abstract:In this paper we propose the concept of (E,E,q)-fuzzy subalgebras of lattice implication algebras (LIAs), and discuss its equivalent characterization. Then, some related properties are investigated, such as the properties about lattice implication homomorphism of (E,E,q)-fuzzy subalgebras of LIAs are given. Finally, new operations of (E,E,q)-fuzzy subalgebras of are introduced and also discuss its related properties.
Key words:Lattice implication algebra, (E,E,q)-fuzzy subalgebra, homomorphism.
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