THE JOURNAL OF FUZZY MATHEMATICS
  Introduction of The Journal   Instructions to Authors   Archive

The Journal of Fuzzy Mathematics

Volume 25, Number 1, March 2017

CONTENT

DETAILS

 

New Soft Metric Applications

G¨¹zide Senel

Department of Mathematics, Faculty of Arts and Science, Amasya University, 05100 Amasya, Turkey. E-mail: g.senel@amasya.edu.tr

Abstract: The problem of not to analyse the distance between two soft points encountered in many practical applications such as soft distance that can not be defined in soft topological spaces [3, 8, 18, 22, 23, 24, 28]. To figure it out, in this study, we generate the soft metric spaces whose structure is represented by soft distance function shown by d~. The description of d~ provides an exact method to analyse the distance between two soft points. By using this method, we studied new classes of soft mappings. We presented different definitions of d~, in the sense that we provided soft metric spaces that were not described before.

Key words: Soft set, soft open set, soft closed set, soft point, soft distance, soft real set, soft metric space.

On Common Fixed Point of Multivalued Mappings under R-weak Commutative Condition

Deepti Thakur

College of Applied Sciences, PO Box 135, PC 311, Sohar, Sultanate of Oman. E-mail: thakurdeepti@yahoo.com

Rajinder Sharma

College of Applied Sciences, PO Box 135, PC 311, Sohar, Sultanate of Oman. E-mail: rajind.math@gmail.com

Abstract: The objective of this paper is to prove some common fixed point theorems for multi-valued mappings under R-weak commutative condition. By dropping condition of continuity and employing R-weak commutativity we improve, generalize and extend several known results in this field.

Key words and phrases: Fixed Point, R-weak commutativity, Contraction, Multivalued mappings.

Basic Arithmetic Operation on Triangular Intuitionistic Fuzzy Numbers Based on ??-level Sets

Shyamal Debnath

Department of Mathematics, Tripura University, Suryamaninagar -799022, India. E-mail: shyamalnitamath@gamil.com

Jayanta Debnath

Department of Mathematics, National Institute of Technology, Agartala-799055, India. E-mail: mailme_jdebnath@rediffmail.com

Bimal Chandra Das

Department of Mathematics, Tripura University, Suryamaninagar -799022, India. E-mail: bcdas3744@gmail.com

Abstract: Addition, subtraction, multiplication, inverse, division of fuzzy numbers already established in terms of ??-level sets. In this paper we have introduced some basic arithmetic operation on intuitionistic fuzzy numbers (IFNs) in terms of ??-level sets viz. addition, subtraction, multiplication, inverse, division etc. and also investigate associative, commutative, distributive properties. A new distance between two IFN also introduced.

Key words: Fuzzy set, IFN, TIFN, ??-level sets, arithmetic operation.

Intuitionistic Fuzzy BCK-submodules

L. B. Badhurays and S. A. Bashammakh

Department of mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah, Saudi Arabia. E-mail: lbadhurays@stu.kau.edu.sa E-mail: Sbashammakh@kau.edu.sa

Abstract: We introduce the notion of intuitionistic fuzzy submodules of BCK-algebra and investigate some of their properties. We define some operations on the intuitionistic fuzzy submodules of a BCK-algebra and investigate some related properties.

Key words: Intuitionistic fuzzy set, Fuzzy set, BCK-modules, Intuitionistic fuzzy BCK-submodules.

An Innovative Approach for Solving Transportation Problem Involving Pentagon Fuzzy Numbers

R. Helen

Department of Mathematics, Poompuhar College (autonomous), Melaiyur-609107, India. E-mail: helenranjan@gmail.com

G. Uma

Department of Mathematics, Bharathiyar College of Engineering and Technology, karaikal-609609, India. E-mail: Uma.gramesh@gmail.com

Abstract: The main objective of this paper is to discuss the maximum flow approach model in the fuzzy transportation problem. A numerical example is also given to demonstrate our proposed approach.

Key words: Fuzzy transportation problem, Pentagon fuzzy number, Ranking using Incenter of centroids.

Fuzzy Matrix ?? -semiring and Fuzzy Matrix Incline M. Murali Krishna Rao and B. Venkateswarlu

M. Murali Krishna Rao and B. Venkateswarlu

Department of Mathematics, GIT, GITAM University Visakhapatnam-530045, A. P., India. E-mail:mmkr@gitam.eduE-mail:bvlmaths@gmail.com

Abstract: In this paper, we introduce the notion of fuzzy ??-semiring, fuzzy matrix ??-semiring and study the properties of fuzzy matrix ??-semiring and fuzzy matrix incline. We prove that F_m,n is a regular incline if and only if F is a regular incline and every nonzero element in fuzzy matrix ??-semiring F_n(??) is invertible if and only if F is a fuzzy field ??-semiring.

Key words: ??-semiring, field ??-semiring, fuzzy ??-semiring, fuzzy matrix ??-semiring, incline, fuzzy matrix incline.

On Some Generalizations of Fuzzy Open and Closed Sets in A Fuzzy Topological Space

B. Davvaz and M. Haddadzadeh

Department of Mathematics, Yazd University, Yazd, Iran. E-mail:bdavvaz@yahoo.com E-mail: davvaz@yazd.ac.ir

Abstract: The purpose of this paper is to study several concepts of fuzzy sets called fuzzy semiopen, ??-open, preopen, ??-open, ????-open sets in fuzzy topological spaces and investigate certain basic properties of these fuzzy sets. Among many other results it is investigated the relations between their closures and interior sets.

Key words: Fuzzy set, fuzzy topology, fuzzy topological space, fuzzy open set, fuzzy closed set.

Intuitionistic Fuzzy P-connectedness

Mahima Thakur and S. S. Thakur

Department of Applied Mathematics Jabalpur Engineering College, Jabalpur, (M. P.) 482011 India. E-mail:mahimavthakur@gmail.comE-mail:samajh_singh@rediffmail.com

Abstract: The aim of this paper is to introduce and discuss the concepts of intuitionistic fuzzy P-Connectedness and intuitionistic fuzzy P-Connectedness between intuitionistic fuzzy sets in intuitionistic fuzzy topological spaces.

Key words: Intuitionistic fuzzy sets, Intuitionistic fuzzy topology, Intuitionistic fuzzy pre open sets, Intuitionistic fuzzy pre closed sets intuitionistic fuzzy P-connectedness, intuitionistic fuzzy P-connectedness between intuitionistic fuzzy sets.

Menger Probabilistic Normed Linear Spaces and Its Topological Structure

I. Sadeqi, F. Solaty Kia and F. Yaqub Azari

Department of Mathematics, Sahand University of Technology, Tabriz-Iran. E-mail:esadeqi@sut.ac.irE-mail:solaty-f@yahoo.comE-mail:fyaqubazari@gmail.com

Abstract: In this paper the concept of Menger probabilistic normed linear space is given and it is shown that a probabilistic normed linear space is a topological vector space in classical sence. Therefore, all results can be translated in probabilistic normed linear spaces. Moreover, by an example we show that the category of probabilistic normed linear spaces is broader than the classical case.

Key words: Menger probabilistic normed space, Probabilistic seminormed spaces, Topological vector space.

On Fuzzy Simply Continuous Functions

G. Thangaraj

Department of Mathematics Thiruvalluvar University Vellor-632115, Tamilnadu, India.

K. Dinakaran

Research Scholar Department of Mathematics Thiruvalluvar University Vellor-632115, Tamilnadu, India.

Abstract: In this paper, the concept of fuzzy simply open set sets by means of fuzzy boundary sets in fuzzy topological spaces, are introduced and studied. The characterization of fuzzy strongly irresolvable space, is established by means of fuzzy simply open sets. Several characterizations of fuzzy simply continuous function, fuzzy simply open function, fuzzy simply irresolute function and fuzzy strongly simply continuous function, are established in this paper.

Key words: Fuzzy dense set, fuzzy nowhere dense set, fuzzy boundary set, fuzzy semi-open set, fuzzy pre-open sets, fuzzy G?? set, fuzzy strongly irresolvable space, fuzzy contra-continuous function, fuzzy semi-continuous function.

Fuzzy Programming with Exponential Membership Function and Some Other Nonlinear Membership Functions 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 exponential membership function and some other 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 hyperbolic membership function. 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, exponential membership function, nonlinear membership function.

(2,(p1,p2,...,p_m))-regularity in m-polar Fuzzy Graphs

Muhammad Akram and Arooj Adeel

Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan. E-mail:m.akram@pucit.edu.pkE-mail:arooj_adeel@ymail.com

Abstract: In this paper, we introduce the concept of d2-degree of a vertex in m-polar fuzzy graphs. We present the concepts of (2,(p1,p2,...,p_m))-regular, totally (2,(p1,p2,...,p_m))-regular m-polar fuzzy graphs and investigate some of their properties. We compute the d2 -degrees of alpha product, beta product and gamma product of m-polar fuzzy graphs. We also study an application of polar fuzzy graphs and compute its d2-degrees.

Key words: d2-degree of m-polar fuzzy graphs, (2,(p1,p2,...,p_m))-regular m-polar fuzzy graph, d2-degrees of alpha, beta and gamma products of m-polar fuzzy graph.

On Fuzzy Automata Hypermanifolds

K. Saranya and B. Amudhambigai

Department of Mathematics, Sri Sarada College for Women, Salem, Tamilnadu, India. E-mail: saranyamath88@gmail.comE-mail:rbamudha@yahoo.co.in

Abstract: In this paper, the concepts of fuzzy automata topological space and fuzzy automata manifolds of higher dimension are introduced. Some interesting properties of fuzzy automata retractions and fuzzy automata topological foldings of the fuzzy automata hypermanifolds are established.

Key words: Fuzzy automata topological space, fuzzy automata topological vector space, fuzzy automata diffeomorphism, fuzzy automata atlas, fuzzy automata hypermanifold, fuzzy automata retraction and fuzzy automata topological folding.

On Dimensions of A Fuzzy Topological Space

B. Amudhambigai, K. Saranya

Department of Mathematics, Sri Sarada College for Women, Salem, Tamilnadu, India. E-mail:rbamudha@yahoo.co.in E-mail:saranyamath88@gmail.com

R. Dhavaseelan

Department of Mathematics, Sona College of Technology, Salem, Tamilnadu, India. E-mail:dhavaseelan.r@gmail.com

Abstract: In this paper, the concepts of large inductive dimension of a fuzzy topological space, fuzzy g~-open sets, local dimension and local inductive dimension of a fuzzy topological space are introduced and some interesting properties are studied.

Key words: Large inductive dimension, fuzzy g~-open sets, local dimension and local inductive dimension of a fuzzy topological space.

On Fuzzy Filters of Hoop-algebras

R. A. Borzooei and M. Aaly Kologani

Department of Mathematics, Shahid Beheshti University, Tehran, Iran. E-mail:borzooei@sbu.ac.irE-mail: mona4011@gmail.com

Abstract: In this paper, we defined the concepts of fuzzy filters, fuzzy (positive) implicative and fuzzy fantastic filters of hoop algebras and discussed the properties of them. Then we define a congruence relation on hoop algebras by a fuzzy filter and proved that the quotient structure of this relation is a hoop algebra. Finally, we investigate that under what conditions that quotient structure will be Brouwerian semilattice, Heyting algebra and Wajesberg hoop.

Key words: Hoop algebra, fuzzy filter, fuzzy implicative (positive implicative, fantastic) filter, Brouwerian semilattice, Heyting algebra, Wajesberg hoop.

Some I(??_r)-convergence Sequence Classes of Fuzzy Real Numbers Defined By Sequence of Modulus Functions

Manmohan Das

Deptt. of Mathematics, Bajali College (Gauhati University), Assam, India.E-mail: mdas.bajali@gmail.com

Abstract: In this article our aim to introduce some new I(??_r)-sequence classes of fuzzy real numbers defined by sequence of modulus functions and studies some topological and algebraic properties. Also we establish some inclusion relations.

Key words: Fuzzy real number, I-convergence, modulus function, difference sequence, admissible ideal.

Properties of ??-open Sets and ??-continuity 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, we introduce and study the concepts of fuzzifying (i,j)-??-open sets in fuzzifying bitopological spaces.

Key words: Lukasiewicz logic, fuzzifying bitopology, fuzzifying (i,j)-??-open sets.

Fuzzy Non-associative Algebras I

Jo?o Carlos da Motta Ferreira and Maria das Gra?as Bruno Marietto

Center of Mathematics, Computation and Cognition, Federal University of ABC, Avenida dos Estados, 5001, 09210-580, Santo Andr?, Brazil.E-mail: joao.cmferreira@ufabc.edu.brE-mail:graca.marietto@ufabc.edu.br

Abstract: In this paper we apply the concepts of fuzzy sets to non-associative algebras in order to introduce and to study the notions of solvable and Amistur (Behrens) nil fuzzy radicals. We obtain similar results with respect to the crisp theory.

Key words: Fuzzy non-associative algebras, fuzzy radicals.

Fuzzy Non-asocaitive Algebras II

Jo?o Carlos da Motta Ferreira and Maria das Gra?as Bruno Marietto

Center of Mathematics, Computation and Cognition, Federal University of ABC, Avenida dos Estados, 5001, 09210-580, Santo Andr?, Brazil.E-mail: joao.cmferreira@ufabc.edu.brE-mail:graca.marietto@ufabc.edu.br

Abstract: This paper is the continuation of a precedent one (cf [1]). We generalize two general structure theorems of classes of alternative, Jordan and Lie algebras to a class of fuzzy non-associative algebras, namely the structure theorems for semisimple algebras and the Wedderburn and Levi¡¯s decomposition theorems.

Key words: Simple fuzzy non-associative ideals, semisimple fuzzy non-associative ideals, Levi-Wedderburn fuzzy decomposition.

An Improved Tsukamoto Method to Solve The Max-Min Fuzzy Relation Equations

Wu Xiaorui

School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China.

Song Zhenming

Inteligent Control Development Center, Southwest Jiaotong University, Chengdu 610031, China

Abstract: In this paper we studied the max-min fuzzy relation equation A*X=B aiming at solving solution set faster than tsukamoto method. By the Tsukamoto method, we made some improvements-Firstly, matrix B satisfies the following inequalities: 1¡Ýb1¡Ýb2¡Ý...¡Ý0; Secondly, if it exists a_ij< b1 in A, then we get a_ij=0 , so that we reduce the number of nonzero elements and also simplify the matrix A. In the process of transformation, we avoid the solutions as empty sets or repeat solutions, and reduce useless calculations and time, so it makes calculation simpler and faster than Tsukamoto method.

Key words: Max-min fuzzy relation equations, Tsukamoto method, fuzzy matrix.

A Novel-Goal-directed Strategy for Based on The Similarity Between Clauses

Xinran Ning, Yang Xu and Xingxing He

National-Local Joint Engineering Laboratory of System Credibility Automatic Verification, Southwest Jiaotong University, Chengdu 610031, China.E-mail: joao.cmferreira@ufabc.edu.brE-mail:xinxinran@my.swjtu,edu.cn

Abstract: Along with the increase of the requirement of making large theory reasoning, it has become a research direction finding useful axioms from a large axiom sets. No matter on the aspect of preprocessing for large theory sets or the aspect of designing optimized strategies during the reasoning process for large theory sets, there have been plenty of methods come up with to deal with the problem. The majority of methods are goal-directed, choosing clauses relevant to the goal clauses to participate in reasoning. However, those methods are simple and rough, describing the relevance between general clauses with goal clauses roughly. In this paper, a novel goal-directed Strategy for ATP based on the similarity between clauses is come up with. The goal clauses are considered as center and the predicate, function and constants symbols, maximum items and atoms of a clause are treated as the dimensions to describe a clause. Compared with the previous methods, it describe the clauses specifically and profoundly, as a result, it can capture the relevance among clauses more precisely. The relevance among clauses is called the similarity among clauses. Considering the similarity among clauses, connecting goal clauses with useful axioms can be a good strategy for reasoning.

Key words: goal-directed strategy, ATP, similarity