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THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 26, Number 3, September 2018

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Commuting Fuzzy Congruences on A Lattice

M. J. Rani

Department of Mathematics, Sahrdaya college of advanced studies, Kodakara, Kerala, India, E-mail:krvarghese@rediffmail.com

Abstract: The notion of fuzzy congruences on a nonempty lattice X has been discussed in previous papers by the author. It has been proved that the collection FC(X) of all fuzzy congruences on X under suitably defined meet and join is obtained as a complete distributive lattice. In this paper the operation of product of two fuzzy congruences is derived. The equivalent conditions which imply that the product of any two fuzzy congruences become equal to their join have been derived. The condition under which any two fuzzy congruences commute under the product is also verified.

Key words: Fuzzy equivalence relation, fuzzy congruences, join of fuzzy congruences, meet of fuzzy congruences, product of fuzzy congruences.

On Some Characterizations of Fuzzy Rough Lindelof Automata Subsystem Spaces via !6s Structure Spaces

D. Vidhya

Department of Mathematics Lady Doak College, Madurai Tamil Nadu, India, E-mail: vidhya.d85@gmail.com

Kalasaiagam Deomed University, Krishnanroil, Tamilnadu, India,

Abstract: In this paper, the concepts of fuzzy rough nearly Lindel?f automata subsystem spaces, fuzzy rough almost Lindel?f automata subsystem spaces, fuzzy rough weakly Lindelof automata subsystem spaces and fuzzy rough almost regular Lindel?f automata subsystem spaces are introduced. Also, some interesting properties and characterizations are discussed.

Key words: Fuzzy rough nearly Lindelof automata subsystem spaces, fuzzy rough almost Lindelof automata subsystem spaces, fuzzy rough weakly Lindelof automata subsystem spaces and fuzzy rough almost regular Lindel?f automata subsystem spaces.

Derivations of Fuzzy BCI-ideals p-ideals and H-ideals

Tamadhur Faham Alsolami

Department of Mathematics Faculty of Science King Abdulaziz University Jeddah, Saudi Arabia, E-mail: talsolami0036@stu.kau.edu.sa

Department of Mathematics Faculty of Science Adham College Umm Al-Qura University Makkah, Saudi Arabia, E-mail:tfsolami@uqu.edu.sa

Sabah Ahmad Bashammakh

Department of Mathematics Faculty of Science Al-Faisaliah Campus King Abdulaziz University Jeddah, Saudi Arabia, E-mail:sbashammakh@kau.edu.sa

Abstract: We present the notion of fuzzy left-right (resp. right-left) derivation on -ideals and inves-tigate many related properties. In addition, we introduce the same concept of fuzzy left-right (resp. right-left) derivation on p-ideals and H-ideals of BCI-algebra and discuss new properties.

Key words: Derivation, fuzzy derivation, BCI-ideals, p-ideals, H-ideals.

On Some (BVa)F.S Sequence Spaces of Fuzzy Soft Real Numbers Defined by Modulus Function

Thangaraj Beaula and M. Merlin Priyanga

Department of Mathematics, TBML College, Porayar, Tamil Nadu, India-609 307, E-mail:edwinbeaula@yahoo.co.in

Abstract: In this paper, the sequence spaces of fuzzy soft real numbers are defined using modulus function. Different properties viz: convergence, null and boundedness on sequence spaces of fuzzy soft real numbers are discussed. Further properties like solid, symmetric, canonical pre-image, monotone and convergence free are defined.

Key words: Fuzzy soft real number sequences, bounded variation a-bounded variation, modulus function, normal, symmetric, convergence free, k-step space, canonical pre image, monotone.

Fixed Point Theorems in Fuzzy Quasi-metric Spaces

Dr. Gobardhan Rano

Department of Mathematics Tehatta Government College Tehatta-741160, West Bengal, INDIA, E-mail:gobardhanr@gmail.com

Abstract: We introduce here the notions of convergence of sequences, Cauchyness, completeness and compactness in fuzzy quasi-metric spaces. The definitions of different kinds of contracting mappings are given here and finally we able to prove some most important basic fixed point theorems of functional analysis such as Banach, Kannan, Edelstein and Caristi in this setting.

Key words: Quasi-metric, t-norm, fuzzy quasi-metric, contracting mappings, fixed point theorems.

A Study on Relational based Image Clustering

Sharmistha Bhattacharya (Halder) and Amarjit Chanda

Dept of Mathematics, Tripura University, Tripura,

Abstract: The goal of clustering is to group similar objects in one cluster and dissimilar objects in different clusters. Cluster analysis or clustering plays an important role in data analysis, web mining, image processing, bioinformatics etc. Many Researchers has done works on several field using fuzzy clustering. Our target is to form a new fuzzy relation which is not a fuzzy equivalence relation but can be transformed into fuzzy transitive closure. It can be partitioned into fuzzy equivalence classes and hence a new fuzzy cluster is formed. This fuzzy clustering helps to cluster images of similar and different types. Using MATLAB 7.9 software the relational based image clustering is shown.

Key words: Fuzzy Equivalence Relations, Clustering Based on Fuzzy Relations.

Certain Single-valued Neutrosophic Graphs

Muhammad Akram and Saba Siddique

Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan, E-mail: m.akram@pucit.edu.pk, E-mail:sabasabiha6@gmail.com

Abstract: Neutrosophic sets are the generalization of the concept of fuzzy sets and intuitionistic fuzzy sets. Neutrosophic models give more flexibility, precisions and compatibility to the system as compared to the classical, fuzzy and intuitionistic fuzzy models. In this research paper, we present certain types of single-valued neutrosophic graphs, including regular single-valued neutrosophic graphs, totally regular single-valued neutrosophic graphs, edge regular single-valued neutrosophic graphs and totally edge regular single-valued neutrosophic graphs. We also investigate some of their related properties.

Key words: Edge regular single-valued neutrosophic graphs, Totally edge regular single-valued neutrosophic graphs.

A Bell Shaped Fuzzy Economic Order Quantity (EOQ)Model with Constant Demand, Shortages under Fully Backlogged

Wasim Akram Mandal

Beldanga D.H.Sr.Madrasah, Beldanga-742189, Murshidabad , WB, India, E-mail: wasim0018@gmail.com

Sahidul Islam

Department of mathematics, University of kalyani, kalyani, W.B, India, E-mail: sahidul.math@gmail.com

Abstract: In this paper, we have proposed a fuzzy inventory model with shortage under fully backlogging with constant demand, in a fuzzy environment. Here we use Bell shaped fuzzy membership function. In this paper we have developed the concept of possibility theory and possibilistic moment generating function. Three type of possibilistic mean values as Lower possibilistic (EL(A)), Upper possibilistic (ER(A)) and Crisp possibilisitc (E(A)) of total average cost function developed here. Also some necessary theorems have been derived here. Finally, these are illustrated by numerical examples and applications.

Key words: Inventory model, fuzzy numbers, Bell shape , Possibility. Variance.

On Fuzzy Multigroups and Fuzzy Submultigroups

P. A. Ejegwa

Department of Mathematics/Statistics/Computer Science, University of Agriculture, P.M.B. 2373, Makurdi, Nigeria, E-mail: ocholohi@gmail.com

Abstract: The concept of fuzzy multigroups is the algebraic structure of fuzzy multisets and hence the extension of the notion of fuzzy groups. This paper studies fuzzy multigroups and proposes the idea of fuzzy multigroupoids. It is shown that the level set of a fuzzy multigroup is a subgroup of a group. The notion of fuzzy submultigroups is introduced and some related results are established.

Key words: Fuzzy multisets, Fuzzy submultisets, Fuzzy multigroups, Fuzzy submultigroups, Fuzzy multigroupoids.

On Abelian Fuzzy Multigroups

P. A. Ejegwa

Department of Mathematics/Statistics/Computer Science, University of Agriculture, P.M.B. 2373, Makurdi, Nigeria , E-mail: ocholohi@gmail.com

Abstract: In this paper, we study some properties of abelian fuzzy multigroups and propose the notion of fuzzy semi multigroups. The concepts of center and centralizer in fuzzy multigroups context are proposed and some results are established. Homomorphic images and homomorphic preimages of abelian fuzzy multigroups are presented.

Key words: Abelian fuzzy multigroups, Centralizer, fuzzy multisets, fuzzy multigroups, Fuzzy semi multigroups.

On Fuzzy Real-valued Triple Sequence Space

Sangita Saha, Ayhan Esi and Santanu Roy

Department of Mathematics/Statistics/Computer Science, University of Agriculture, P.M.B. 2373, Makurdi, Nigeria, E-mail:ocholohi@gmail.com

Abstract: The concept of fuzzy multigroups is the algebraic structure of fuzzy multisets and hence the extension of the notion of fuzzy groups. This paper studies fuzzy multigroups and proposes the idea of fuzzy multigroupoids. It is shown that the level set of a fuzzy multigroup is a subgroup of a group. The notion of fuzzy submultigroups is introduced and some related results are established.

Key words: Fuzzy multisets, Fuzzy submultisets, Fuzzy multigroups, Fuzzy submultigroups, Fuzzy multigroupoids.

Pairwise Separation Axioms via Fuzzifying Beta-open Sets

R. Femina

Keelakotai street, ambalapattu south, orathananu, 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, we introduce and study the concepts of fuzzifying pairwise separation axioms in fuzzifying bitopological spaces.

Key words: Lukasiewicz logic, fuzzifying bitopology, fuzzifying pair-wise Beta-open sets.

Convergence of Nets and Filters in Fuzzifying Bitopology

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 theory of (i,j)-Beta-convergence on nets and filters is established in fuzzifying bitopology. Some important and interesting results in fuzzifying bitopology are obtained by means of the theory.

Key words: Fuzzy logic; fuzzifying bitopology; convergence, fuzzifying Beta-open sets.

Fuzzy Almost Contra m-continuous Multifunction

Anjana Bhattacharyya

Department of Mathematics, Victoria Institution (College) 78 B, A.P.C. Road, Kolkata, India, E-mail: anjanabhattacharyya@hotmail.com

Abstract: This paper deals with a new type of fuzzy multifunction between a set having minimal structure and a fuzzy topological space. Several characterizations and properties are established here. We also prove that the m-compact space [14, 15] has fuzzy strongly compact [18] image under surjective fuzzy upper almost contra m-continuous multifunction provided that some natural conditions are satisfied. Lastly, we have shown that this concept unifies fuzzy upper (lower) almost contra continuous multifunction [6].

Key words: m-open set, m-compact space, fuzzy regular closed set, fuzzy Theta-semiclosed set, m-space, m-frontier of a set.

Study of The Fuzzy Algebra Induced by An Arbitrary Semilattice without Zero (1)

Armand Fotso Tatuene

Department of Mathematics, University of Yaounde 1, P.O.Box 812 Yaounde, Cameroon, E-mail: f.armando2001@gmail.com

Marcel Tonga

Department of Mathematics, University of Yaounde 1, P.O.Box 812 Yaounde, Cameroon, E-mail: tongamarcel@yahoo.fr

Abstract: For a semilattice A=(A;*)(* belongs to{conjunction, disjunction}), a Brouwerian lattice L=(L;conjunction, disjunction,0,1), the set Fu(A)=A power of L of all fuzzy subsets of A induces an algebra A bend=(Fu(A);* bend)which is called the fuzzy algebra associated to the semilattice A. In this paper, first of all, we characterize semilattices for which associated fuzzy algebras are also semilattices and we prove that there is at least one subalgebra of A bend which is a semilattice as A in the others cases. After that, we construct some subuniverses of A bend and we specify all of them which are semilattices. We give respectively some ways to generate easily tables of A power of 2, FuPt(A) (the set of fuzzy points of A) and FuCt(A) (the set of constant fuzzy subsets of A) in Fu(A) . Later, we show that there are many ways to embed A in A bend , L in Fu(A)=(Fu(A);conjunction, disjunction,c0,c1) , L in (FuSub(A);conjunction,t,c0,c1) ( FuSub(A) is the set of all fuzzy subsemilattices of A); and we give some relationships between * and operations of Fu(A). After that, we evaluate images of some subuniverses of A bend by Zadeh¡¯s extension. Finally, the notion of T-fuzzy subsemilatices is introduced as a generalization of the notion of fuzzy subsemilattices, some of their properties are investigated.

Key words: Semilattice; Brouwerian lattice; Fuzzy subsemilattice; Fuzzy algebra; Subuniverse; Zadeh¡¯s extension.

The d-approximate Equivalence Method of Changing Fuzzy Set into Rough Set

Liu Feng

Institute of Systems Science, Northeastern University, Shenyang 110004,China; Dalian Survey Group Of The National Statistics Bureau, Dalian , 116021,China ,

Fan Chuan-qiang

Institute of Systems Science, Northeastern University, Shenyang 110004,China; School of Sciences, Liaoning University of Petroleum & Chemical Technology,

Abstract: Rough set theory provides a method of data analysis and automatic extraction of rules, and has been successfully applied to industrial control. The biggest feature of rough set controller is simple structure, and easy realization, and fast speed. But just because the rough fuzzy control is used to generate the membership function, and rough membership function are used for fuzzy logic reasoning, while rough membership function is the ladder shaped, thus the control is still not accurate enough. The key to solve the problem is that the membership function of rough set can be accurately transformed into the membership function of fuzzy set. In this paper, by discussing the relations of fuzzy set membership and the membership function of rough set relationship, the d-approximation equivalence method of changing fuzzy set into rough set is proposed. The method ensures that the fuzzy membership degree and the membership function of rough set that is generated are illimitably closed, and in the range of the value of , they can be considered entirely equal, thus fuzzy set can be completely changed into rough set and membership function of fuzzy set almost is unchanged. The method of this paper fully proved that rough set is much larger than the fuzzy set. So the accuracy of rough fuzzy control can be improved, and the application scope of rough fuzzy control can be expanded.

Key words: Fuzzy set; Rough set; Rough control; Fuzzy control; Rough fuzzy control; membership function; d-approximation equivalence method