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THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 26, Number 4, September 2018

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Fuzzy Soft Regular Semiopen Sets and Maps in Fuzzy Soft Topological Spaces

E. Elavarasan

Department of Mathematics, Annamalai University, Annamalainagar, Tamil Nadu-608 002, E-mail:maths.aras@gmail.com

Abstract: This paper introduces fuzzy soft regular semiopen (fuzzy soft regular semiclosed) sets in fuzzy soft topological spaces. Some basic properties of them and their relationship with different types of fuzzy soft open sets are discussed. Also, the concept of fuzzy soft regular semi continuous (open and closed) functions is presented. Finally, fuzzy soft regular semi homeomorphisms and fuzzy soft regular semi C-homeomorphisms are given with the help of fuzzy soft regular semi continuity.

Key words: Fuzzy soft sets, fuzzy soft topological spaces, fuzzy soft regular semiopen (closed) sets, fuzzy soft regular semi continuous (open and closed) functions, fuzzy soft regular semi homeomorphisms.

An Intuitionistic Fuzzy Soft Set Based Triple I method

Binbin Xue and Keyun Qin

College of Mathematics, Southwest Jiao tong University, Chengdu, Sichuan 610031, china, E-mail: xuebinbin@yeah.net, E-mail:keyunqin@263.net

Abstract: Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool for dealing with uncertainties. This paper is devoted to the discussion of intuitionistic fuzzy soft set based approximate reasoning. Triple methods for intuitionistic fuzzy soft modus ponens (IFSMP) and intuitionistic fuzzy soft modus tollens (IFSMT) are investigated. Computational formulas for both IFSMT and IFSMP with respect to left-continuous intuitionistic t-norms and its residual intuitionistic implication are presented. Besides, the reversibility property of Triple 1 methods of IFSMP are analyzed.

Key words: Intuitionistic fuzzy set, Intuitionistic fuzzy soft set, Triple I method, left-continuous intuitionistic t-norm, Reversibility

Upper(Lower) Contra -Irresolute Intuitionistic Fuzzy Multifunctions

S. S. Thakur

Department of Applied Mathematics, Jabalpur Engineering College, Jabalpur-48201 1, M.P., India, E-mail:samajh_singh@rediffmail.com

Swantantra Tripathi

Department of Applied Mathematics, Jabalpur Engineering college, Jabalpur-48201 1, M.P., India, E-mail:tripathiswatantra74@gmail.com

Abstract: In this paper we introduce the concepts of upper and lower contra -irresolute intuitionistic fuzzy multifunctions from a topological space to an intuitionistic fuzzy topological space and obtain some of their properties and characterization.

Key words: Intuitionistic fuzzy sets, Intiitionistic fuzzy topology, Intuitionistic fuzzy multifunctions, lower contra a-irresolute and upper contra a-irresolute Intutionistic fuzzy multifunctions.

An Interactive Fuzzy Judgment Aggregation Model for Consensus with Partially Undecided Judges

Ismat Beg and Ayesha Syed

Lahore School of Economics, Lahore 53200, Pakistan Corresponding author, E-mail :ibeg@lahoreschool.edu.pk

Abstract: New requirements and challenges arise in judgment aggregation, due to the complexity of judgment making process and the necessity of dealing with huge amounts of vague and uncertain information and alternatives. In this paper we propose an interactive fuzzy judgment aggregation method for consensus to deal with the situation where judges are partially undecided.

Key words: Judgment aggregation; fuzzy; consensus decision.

On The Determinant of A Square Bifuzzy Matrix

E. G. Emam

Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt, E-mail:eg_emom@yahoo.com

M. A. Fndh

Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt, E-mail:m.fndh@yahoo.com

Abstract: In this paper, we prove several properties of the determinant of a bifuzzy matrix. Also, we define the adjoint matrix of a square bifuzzy matrix and prove some important results on this matrix. However, we show that many properties of a square bifuzzy matrix ( such as t-reflexive, symmetric and transitive) are carried out to its adjoint. Finally, we show how to construct a transitive bifuzzy matrix from any given one through its adjoint.

Key words: Intuitionistic fuzzy matrices, bifuzzy matrices, determinant of a square bifuzzy matrix, adjoint of a square bifuzzy matrix.

Study of The Fuzzy Algebra Induced by An Arbitrary Semilattice without Zero (2)

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

A View on Generalized Fuzzy *F Structure Compactification and Generalized Fuzzy *Convergence Structure in Generalized Fuzzy *Matroids

M. Sudha and J. Mahalakshmi

Department of Mathematics, Sri Sarada College for Women, Salem-636016 Tamil Nadu, India, E-mail:paapumaha13@gmail.com

Abstract: In this paper, the concepts of generalized fuzzy *prefilters in generalized fuzzy *matroids, generalized fuzzy *ultrafilter and generalized fuzzy prime *prefilter, gen-eralized fuzzy *normal family and generalized fuzzy *Frechet matroid are introduced and studied. Further, the process of generalized fuzzy *F structure compactification for a generalized fuzzy *matroid is established. The concepts of generalized fuzzy *convergence structure are introduced and studied.

Key words: Generalized fuzzy *prefilter; generalized fuzzy *ultrafilter; generalized fuzzy prime *prefilter; generalized fuzzy *Frechet matroid; generalized fuzzy *F structure compactification; generalized fuzzy *convergence structure.

The Fuzzy Topological Semigroups and Fuzzy Topological Ideals

Cheng-Fu Yang

School of Mathematics and Statistics of Hexi University, Zhangye Gansu,734000, P. R. China, E-mail: ycfgszy@126.com

Abstract: This paper gives the concepts of the fuzzy topological semigroups, fuzzy topological left ideals (right ideals, intrinsic ideals and double ideals) and discusses the homomorphic image and inverse image of them.

Key words: Fuzzy topological space; Fuzzy topological semigroup; Fuzzy topological ideal, homomor-phic image and inverse image.

Some New Fixed Fuzzy Point Theorems in Hausdorff Fuzzy Metric Spaces

J. Jeyachristy

Department of Mathematics, Karunya University, Coimbatore, Tamil Nadu, India-641114, E-mail: jeyachristypriskillal@gmail.com

P. Thangavelu

Ramanujam Centre for Mathematical Sciences, Thiruppuvanam, Tamil Nadu, India-630611, E-mail: ptvelu12@gmail.com

Abstract: In this paper, we introduce fuzzy ¦×-contractive fuzzy mapping and extend some fixed point theorems in Hausdorff fuzzy metric spaces.

Key words: Fuzzy metric space, Fuzzy mapping, Fixed fuzzy point.

Fuzzy Programming with Mirror Image of S Shaped Membership Function Approach to Multiobjective Solid Transportation Problem

A. K. Bit

Department of Mathematics, Faculty of Civil Engineering, College of Military Engineering, Pune-411031 (M. S.), India , E-mail: amalkbit@yahoo.com

Abstract: The linear multiobjective solid transportation problem in which the supply, demand and capacity constraints are all equality type and the objectives are equally important, non commensurable and conflicting in nature. The fuzzy programming with Mirror image of shaped (nonlinear) membership functions for obtaining efficient solutions as well as the best compromise solution of a multiobjective solid transportation problem has been presented in this paper. An example is included to illustrate the methodology. Also this method is compared with one existing fuzzy programming algorithm with linear membership function and nonlinear membership functions. It may be noted that the necessity of the multiobjective solid transportation problem arises when there are heterogeneous conveyances available for the shipment of goods. The multiobjective solid transportation problem is of much use in public distribution systems.

Key words: Multiobjective decision making, multiobjective solid transportation problem, fuzzy programming, efficient solution, compromise solution, Mirror image of S shaped membership function, nonlinear membership function.

Double Fuzzy [¦Á, ¦Â, ¦È, ¦Ä, (I, I*)]-continuity

S. E. Abbas

Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt, E-mail: saahmed@jazanu.edu.sa

I. Ibedou

Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt., E-mail: iibedou@jazanu.edu.sa

Abstract: In this paper, we introduce the concept of double fuzzy [¦Á, ¦Â, ¦È, ¦Ä, (I, I*)]-continuous functions. In order to unify several characterizations and properties of some kinds of modifications of double fuzzy continuous and double fuzzy open functions. We introduce and explore a generalized form of double fuzzy continuous and double fuzzy open functions, namely double fuzzy (¦Æ¦Æ*, ¦Ç¦Ç*)-continuous functions and double fuzzy Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt-open functions.

Key words: Double fuzzy continuous; double fuzzy (¦Æ¦Æ*, ¦Ç¦Ç*)-continuous; double fuzzy ideal.

The Triple Sequence Spaces of ¦Ö3I(F)¦¤mf¦Ë of Fuzzy Numbers Defined by A Sequence of Musielak-orlicz Functions

A. Esi and A. Esi

Department of Mathematics, Adiyaman University, 02040, Adiyaman, Turkey, E-mail: aesi23@hotmail.com, E-mail:aytenesi@yahoo.com

M. Aiyub

Department o fMathematics, College of Science University of Bahrain, P. O. Box-32038 Manam, Kingdom of Bahrain., E-mail:majyub2002@gmail.com

N. Subramanian

Department of Mathematics, Sastra University, Thanajavur-613401, India, E-mail:nsmaths@yahoo.com

Abstract: We introduce certain new triple sequence spaces of ¦Ö3 of fuzzy numbers defined by 1-convergence using sequences of Musielak-Orlicz functions and a difference operator of order and also study some basic topological and algebraic properties of these spaces, investigate the inclusion relations between these spaces.

Key words: Analytic sequence, triple sequences, difference sequence space, Musielak-Orlicz function, -metric space, Ideal, -convergent, fuzzy number.

A View on ¦Á-¦×*-FRi(i=0,1) Spaces in Fuzzy Topological Systems on B-algebra

M. Rowthri and Dr. B. Amudhambigai

Department of Mathematics, Sri Sarada College for Women, Salem-636016 Tamilnadu, India, E-mail: femina.shankar@gmail.com, E-mail:rowth3.m@gmail.com

Abstract: In this paper the notion of fuzzy topological systems on B-algebra is introduced. The concept of ¦×* operator on a family of fuzzy a-open sets in a fuzzy topological system is introduced. Then the notions of fuzzy ¦Á-¦×*-open sets and fuzzy ¦Á-¦×* -closed sets are studied with necessary examples. In terms of the operator ¦×* , as initialted by Csaszar, the unified definitions of ¦Á-¦×*-FRi(i=0,1) spaces on fuzzy topological system are introduced and some of their properties are studied. Also some equivalent statements of ¦Á-¦×*-FRi(i=0,1) spaces on fuzzy topological systems are discussed.

Key words: B -fuzzy topological system, fuzzy operator ¦×* on a family of fuzzy ¦Á-open sets, fuzzy ¦Á-¦×* -open set, fuzzy ¦Á-¦×* -closed set, ¦Á-¦×* -kernal of a fuzzy set, ¦Á-¦×*-FT0-system, ¦Á-¦×*-FT1-system, ¦Á-¦×*-FT2-system, ¦Á-¦×*-FR0-system, ¦Á-¦×*-FR1-system.

More on Pairwise Fuzzy Volterra Spaces G. Thangaraj and V. Chandiran

G. Thangaraj

Department of Mathematics, Thiruvalluvar University Serkkadu, Vellore-632115, Tamil Nadu, India.

V. Chandiran

Research Scholar, Thiruvalluvar University Serkkadu, Vellore-632115, Tamil Nadu, India.

Abstract: In this paper we investigate several characterizations of pairwise fuzzy Volterra spaces and study the conditions under which a fuzzy bitopological space is a pairwise fuzzy Volterra space.

Key words: Pairwise fuzzy dense set, pairwise fuzzy nowhere dense set, pairwise fuzzy G¦Ä-set, pairwise fuzzy F¦Ò-set, pairwise fuzzy first category set, pairwise fuzzy second category space, pairwise fuzzy Baire space, pairwise fuzzy strongly irresolvable space, pairwise fuzzy Volterra space and pairwise fuzzy weakly Volterra space.

¦Á-B-Finitisticness of Fuzzy Bitopological Spaces

Shakeel Ahmed

Govt.Degree College, Thanna Mandi,

Rohini Jamwal

Department of Mathematics, University of Jammu, E-mail: rohinijamwal121@gmail.com

Abstract: In this paper, we have introduced the concept of ¦Á-B-finitistic fuzzy bitopological spaces and studied some of their basic properties.

Key words: Covering Dimension, Finitisticness, Fuzzy Bitopological Space, Open Refinement.

Generalized Version of Fuzzy ¦Ä-preclosed Set

Anjana Bhattacharyya

Department of Mathematics, Victoria Institution (College) 78 B, A. P. C. Road Kolkata-700009, India , E-mail:anjanabhattacharyya@hotmail.com

Abstract: This paper deals with generalized versions of fuzzy ¦Ä-set preclosed et, viz., fg¦Äp -closed [5] and f¦Äpg-closed sets. Then the mutual relationships between these two sets and with other generlazied versions of fuzzy closed sets are established. Afterwards, we discuss about fg¦Äp-closed and f¦Äpg-closed functions. Fuzzy ¦Äp -normality is introduce in [5]. Here we introduced and study fuzzy ¦Äpg-normality and establish that fuzzy ¦Äp-normality remains invariant under fg¦Äp-closed function. We also introduce fg¦Äp (resp., f¦Äpg-closure operator and establish some properties of these two operators. Then we introduce and study fg¦Äp (resp., f¦Äpg )-continuous functions and establish mutual relationships of these two functions with other generalized versions of fuzzy continuous like functions. In Section 6, we introduce and characterize fg¦Äp (resp., f¦Äpg )-regular and fg¦Äp (resp. f¦Äpg )-normal spaces. It is shown fg¦Äp (resp.,f¦Äpg )-normal space remains invariant under fg¦Äp (resp., f¦Äpg )-irresolute function. In the last section we first introduce fg¦Äp (resp., f¦Äpg )- T2-space. Then some different types of fuzzy continuous-like functions are introduced and show that the inverse image of fg¦Äp (resp., f¦Äpg )-T2 space under these functions are fuzzy T2-space.

Key words: fg¦Äp (resp., f¦Äpg )-closed set, fg¦Äp (resp., f¦Äpg )-closed function, fg¦Äp (resp., f¦Äpg )-continuous function, fg¦Äp (resp., f¦Äpg )-regular space, fuzzy ¦Äp -normal space, fg¦Äp (resp., f¦Äpg )-normal space, fuzzy strongly fg¦Äp (resp., f¦Äpg )-continuous function.