THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 18, Number 1, March 2010

CONTENT

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Discussion for Fuzzy Automation and Its Language

QingE Wu, Tuo Wang, Yong Xuan Huang and JiSheng Li

School of Electronic and Information Engineering Xi¡¯an Jiao Tong University , Xi¡¯an, Shaanxi, 710049, P.R.China E-mail: wqe969699@163.com

Abstract: For processing and recognizing better different fuzzy automatic language, it requires an equal device. So, this paper presents the different fuzzy automata, and describes the relationship of the different fuzzy automata and fuzzy language. However, with the brand-new theory methods, the fuzzy pushdown automation and their corresponding fuzzy grammar that generate the appropriate fuzzy language are mainly discussed. These researches will not only impulse further the development of the theories of the fuzzy automata. Thus, the development of theories in this paper in turn can quicken the applications of the fuzzy automata in various fields. It will also be a theoretic base for extraction and application of the fuzzy automata. Finally, some problems on the fuzzy automata and their language to be solved and development trends are discussed.

Keyword: Guage; finite-state deterministic fuzzy automation; fuzzy pushdown automation; fuzzy Turing machine.

The Linguistic Computational Models Based on Index of Linguistic Label

Dan Meng

School of Economics Information Engineering, Southwestern University of Finance and Economics, Chengdu, Sichuan 610074, China E-mail: mengd_t@swufe.edu.cn

Zheng Pei

School of Mathematic and Computer, Xihua Univercity, Chengdu, Sichuan 610039, China E-mail: pqyz@263.net

Abstract: Index of object is pervasive in mathematics, e.g., using natural number as index of variable to identify between and ,where and .From practical point of view, it is not always possible for the user to define a fuzzy set for each linguistic label. In such situation, index of linguistic label is an alternative method for dealing with linguistic information directly. In this paper, the relationship between linguistic labels and their indexes is analyzed. Then, linguistic computational model based on fuzzy number index of linguistic label are reviewed. For linguistic computational model based on fuzzy number index of linguistic label, Arithmetic mean and linguistic weighted average operators are defined.

Keyword: Computing with words, Aggregation operation, fuzzy number

An EPQModel under Fuzzy Chance Constraint: A Geometric Programming Approach

Soumen Bag

Department of mathematics, Indian Institute of technology Kharagpur-721302, India E-mail: soumen@maths.iitkgp.ernet.in

Abstract: An economic production quantity ( EPQ ) model with fuzzy demand, imprecise inventory costs incorporating flexibility and reliability of the production process is developed. The model involves one constraint on store house capacity which is assumed as fuzzy in nature. Then, the model is formulated as fuzzy chance constraint is satisfied with some predefined degree of necessity. As optimization of fuzzy objective is not well defined a necessity based return of objective is optimized under the constraint. Finally, the model is transferred to a crisp one using fuzzy extension principle and solved using geometric programming ( GP ).

Keyword: Necessity, Fuzzy Chance Constraint, Geometric Programming.

Fuzzy Locally Uniform Spaces

D.Hazarika and D.K.Mitra

Department of Mathematics Sciences, Tezpur University, Nappam-784028, India

Abstract: In this paper , we localize fuzzy uniformity following the approach of James. Fuzzy locally uniform spaces are shown to be fuzzy regular. With countable base they are shown to be fuzzy pseudo-metrizable. Different types of Cauchy filters are used to develop generalizations of completeness in fuzzy locally uniform spaces.

Keyword: Fuzzy local uniformity, fuzzy pseudo-metrizable, fuzzy Cauchy filter

Random Walks with Intuitionistic Fuzzy Random Variable

J.Earnest Lazarus Piriyakumar and J. Daniel Department of Mathematics, Tranquebar Bishop Manickam

Department College, Porayar-609307, South India. E-mail: jelpriyakumar@yahoo.com

Abstract: In this paper based on the works of Kwakernaak , a general theory of intuitionistic fuzzy random variables is introduced. Random walk for intuitionistic fuzzy random variables is discussed. Walds equation and Spitzer¡¯s identity are proved using intuitionistic fuzzy random variables.

Keyword: Intuitionistic fuzzy random variables, Intuitionistic fuzzy numbers and Random walk.

On Quotient Space of Fuzzified Topology

Tazid Ali

Department of Mathematics, Dibrugarh University Dibrugarh, Assam, India

Sampa Das

Department of Mathematics, Dibrugarh Polytechnic Dibrugarh, Assam, India

Abstract: In this paper we introduce the concept of quotient space of a fuzzified topology. We will study some of the classical results of topology in this setting.

Keyword: Fzzified topology, subspace, continuity, quotient space.

On Interval Valued and Fuzzy Number Valued Possibility Distributions Possibility Distributions

Gigi Georeg

Department of Mathematics, Mar Thoma college for Woman, Perumbavoor Perumbavoor P. O. Ernakulam District Kerala, S. India PIN 683542 E-mail:frpraise@yahoo.com

A.Sunny Kuriakose

Department of Mathematics, Union Christian College Aluva Ernakulam District Kerala, S. India

Abstract: In this paper we give a characterization for interval valued and fuzzy number valued possibility distributions in terms of crisp possibility distributions. Possibility and necessity measures induced by these distributions are determined and their properties are studied. The concepts of ordered interval valued and ordered fuzzy number valued possibility distributions are also introduced. A one to one correspondence is established between ordered fuzzy number valued possibility distributions and consonant fuzzy number valued basic distributions.

Keyword: Interval valued possibility distributions, ordered interval valued possibility distributions, fuzzy number valued possibility distributions, ordered fuzzy number valued possibility distributions.

Common Fixed Point of Uniformly R-subweakly Commuting Mappings in Fuzzy Banach Spaces

Ismat Beg

Department of Mathematics and Centre for Advanced Studies in Mathematics Lahore University of Mangement Sciences, 54792- Lahore,PAKISTAN E-mail:ibeg@lums.edu.pk

Shaban Sedghi

Department of Mathematics, Islamic Azad University Ghaemshahr Branch, Ghaemshahr P. O. Box 163, Iran E-mail: sedghi_gh@yahoo.com

Nabi Shobe

Department of Mathematics, Islamic Azad University-babol branch, Iran E-mail: nabi_shobe@yahoo.com

Abstract: We prove a common fixed point theorem for uniformly R-subweakly commuting mappings in fuzzy banach spaces.

Keyword: Fuzzy normed space, uniformly R-subweakly commuting mappings, common fixed point.

¦Á-order of an Element

Shakeel Ahmed

Department of Mathematics, Govt. Degree College Thanna Mandi, Thanna Mandi-185212(J&K,India) E-mail: shakeelar2002yahoo.co.in

Abstract: In this paper, we have introduced the concept of ¦Á-order of an element in fuzzy topological spaces and studied its various properties.

Keyword: ¦Á-finitistic space, sum space, homeomorphism, good extension property.

Common Fixed Point Theorems for Hybrid Mappings in Fuzzy Meric Spaces

H. M. Abu-donia

Department of Mathematics, Faculty of science, Zagazig University, Egypt

Kh.Abd-Rabou

Department of Mathematics, Faculty of science, Tanta University, Egypt

Abstract: The purpose of this paper is to study common fixed point theorems for set-valued and single-valued mappings in fuzzy metric, fuzzy 2-metric and fuzzy 3-metric spaces. We extend new definitions in fuzzy metric, fuzzy 2-metric and fuzzy 3-metricspaces. Also, We extend results of Fisher [6], Sharma and Tiwari [17]. We proved common fixed point theorems for hybrid mappings in fuzzy metric, fuzzy 2-metric and fuzzy 3-metric spaces.

Keyword: Fuzzy metric, fuzzy 2-metric and fuzzy 3-metric spaces, weakly compatible mappings, common fixed point.

A Note on Fuzzy Matroid

Shiny Philip Department of Mathematics, Govt. Model Engineering College, Thrikkakkara P. O. Cochin-682021, India E-mail: shinyphilip@mec.ac.in

Abstract: In this paper we introduce fuzzy matroid and show that a fuzzy matroid is preserved under fuzzy convexity preserving ( FCP ) and fuzzy convex to convex ( FCC ) functions

Keyword: fuzzy matroid, fuzzy convexity preserving function, fuzzy convex to convex functions, *- fuzzy convexity, fuzzy exchange law.

H-fuzzy Topological Spaces

Sunil C. Mathew

Department of Mathematics, St. Thomas College Palai, Arunapuram P. O. -686574,Kottayam(dist.). Kerala, India E-mail: sunil@stcp.ac.in, sunilmathew@rediffmail.com

Anjaly Jose

Department of Mathematics, St. Thomas College Palai, Centre for Mathematical Science (Pala Campus) Arunapuram P. O. , Kottayam(Dt), Kerala 686574, India

Abstract: In this paper we introduce the concept of -fuzzy topological spaces and study its relationship with nice fuzzy topological spaces and homogeneous topological spaces. This notion is then generalized to -fuzzy topological spaces of degree. The sums, subspaces and simple extensions of those fuzzy topological spaces have also been investigated.

Keyword: Homeomorphism, H-fts, Nice fts, Homogeneous fts.

On ¦Á-induced Bifuzzy Supra Topological Spaces and Its Associated ¦Á-initial Bitopological Spaces

Anjan Mukherjee

Department of Mathematics, Tripura University, Suryamaninagar, Agartala-799130, Tripura, India. E-mail: anjan2002_m@yahoo.co.in

Abstract: Let be a bitopological space and be the set of all -lower semi-continuous functions, defined from X into the closed unit interval . In this paper the concept of -induced fuzzy supra topology due to A. Mukherjee has been gene-ralized to the bifuzzy supra topological setting and some of its basic properties are discussed. It is seen that the study of - induced fuzzy supra topological space turns out to be the study of a special kind induced fuzzy supra topological space. Some applications and connections betweens some separation properties of the bitopological space and that of a - induced fuzzy supra topological space are shown. Finally the concept of -initial bitopological space associated with a - induced bifuzzy supra topological space is introduced and some of its properties are investigated.

Keyword: Fuzzy topology, - induced fuzzy supra topology, -lower semi-continuous functions, Strong (weak) -cut, Bifuzzy supra topological spaces, -compactness, Fuzzy supra- compactness.

Single Period Inventory Model with Continuous Fuzzy Random Variable Demand

Oshmita Dey and Debjani Chakraborty

Department of Mathematics, Indian Institute of Technology , Kharagpur-721302,India E-mail: debjani@maths.iitkgp.ernet.in

Abstract: In this paper, a single period single item inventory model, otherwise popularly known as the newsboy problem, is considered in a mixed fuzzy stochastic environment. The imprecision and random which is very often encountered in the real world is incorporated into the model by means of the customer demand which is assumed to be a continuous fuzzy random variable. Since, in real life situations, decision makers may wish to achieve a target profit instead of tying to maximize it, a methodology has been developed here keeping this argument in mind. This target level, also been a subjective managerial decision is modeled by fuzzy numbers. Instead of defuzzification, the comparison of two fuzzy number based on the concept of fuzzy inequality relation is used to determined the required order quantity such that the target profit is achieved.

Keyword: Single item inventory, continuous fuzzy random variable, fuzzy target level, fuzzy inequality relation

The Theory of Approximate Reasoning in Intuitionistic Fuzzy Environment

Lisy Cherian Mar Thoma

College for Women, Perumbavoor, Kerala, India, Pin-683542. E-mail: thomaspt46@yahoo.co.in

Sunny Kuriakose A. Union Christian College, Aluva, Kerala, India

Abstract: The purpose of this paper is to interpret the intuitionistic fuzzy linear programming problems as intuitionistic fuzzy multiple reasoning schemes. This is an extension to the work of Robert Fuller and C. Carlsson on fuzzy reasoning for solving problems, into environment in which the degree of non-membership or vagueness of objective(s) and constraints are considered together with the degree of membership or satisfaction. This reslut will clearly show the superiority of approach over the solutions of analogous fuzzy and crisp problems. Also the solution process coincide with those suggested by Plamen Angelov.

Keyword: Intuitionistic fuzzy sets , Intuitionistic fuzzy linear programming , Multi-objective Intuitionistic fuzzy linear programming , Multiple reasoning schemes .

Unique Common Fixed Point Theorem for Four Weakly Compatible Mappinga in Complete Fuzzy Metric Spaces

Shaban Sedghi

Department of mathematics, Islamic Azad University-Ghaemshahr Branch, Ghaemshahr P. O. Box 163.Iran E-mail: sedhgi_gh@yahoo.com

Binayak S Chowdhury

Department of mathematics, Bengal Engineering and Science University Shibpur, Howrah-711103,West Bengal, India E-mail:binayakl12@yahoo.co.in

Nabi Shobe

Department of mathematics, Islamic Azad University-Ghaemshahr Branch, Iran E-mail: nabi_shobe@yahoo.com

Abstract: In this paper, we establish a common fixed point theorem in complete fuzzy metric spaces for four weakly compatible mappings.

Keywords: Fuzzy contractive mapping,; Complete fuzzy metric space; Common fixed point theorem.

On ¦Á-fuzzy Orders

Abdelkader Stouti

UFR and Laboratory of Mathematics and Applications, Faculty of Sciences and Techniques, University Sultan Moulay Slimane, P. O. Box 523,23000 Beni-Mellal, MOROCCO E-mail: stouti@yahoo.com

Lemnaouar Zedam

Laboratory of Pure and Applied Mathematics, M¡¯sila University, P. O. Box 166 Ichbilia , M¡¯sila 28105,Algeria E-mail: L.zedam@yahoo.fr

Abstract: In this paper we study ¦Á-fuzzy orders. First, we establish some results which enable us to build new ¦Á-fuzzy orders from crisp order relations. Secondly, we give a result concerning compatible ¦Á-fuzzy orders defined on real vector spaces. Also, we characterize a subcategory of totally ¦Á-fuzzy orders which are compatible with the usual addition and multiplication on real line.

Keyword: Fuzzy set theorem, fuzzy relations, partial order, ordered linear spaces, ¦Á-fuzzy orders.

Fuzzy Semihypergroup Associated with Fuzzy Relation

M. K. Sen and G. Chowdhury

Department of Pure Mathematics ,University of Calcutta, 35,Ballygunge Circular Road, Kolkata-700019, India E-mail: senmk6@eth.net

Abstract: In this paper we study a semihypergroup associated with a relation R on a nonempty set H and also study semihypergroup , fuzzy hypergroup associated with a fuzzy relation on a nonempty set H.

Keyword: Hyperoperation, Fuzzy hyperoperation, Fuzzy relation, Outer element, Fuzzy semihypergroup, Fuzzy hypergroup, Fuzzy Regular Hypergroup.

On Weakly Fuzzy ¦Ä-semi Precontinuous Mapping and Weakly Fuzzy ¦Ä-semi Pre irresolute Mapping

Anjan Mukherjee

Department of Mathematics, Tripura University; Surjyamaniagar, Agartala-799130, TRIPURE, INDIA E-mail: anjan2002_m@yahoo.co.in

Runu Dhar

Department of Mathematics, R. K. Mahavidyalaya; Kailashshar-799177, TRIPURE, INDIA E-mail: mr.runu@rediffmail.com

Abstract: The aim of this paper is to induce weakly fuzzy ¦Ä-semi pre continuous mapping and weakly fuzzy ¦Ä-semi pre irresolute mapping in fuzzy topological space (ftspace, for short) and study their properties and their relationships with other fuzzy functions. Lastly some applications are shown with the help of above concept.

Keyword: fuzzy topological space, fuzzy pre open set, fuzzy ¦Ä-semi pre open set, weakly fuzzy ¦Ä-semi pre continuous and weakly fuzzy ¦Ä-semi pre irresolute mappings.

Strongly Generalized Closed Fuzzy Sets in Fuzzy Sets in Fuzzy Topological Spaces and New Separation Axioms

A. H. Zakari

Girls¡¯ Education College, Jazan University, Kingdom of Saudi Aria

H. S. Ai-Saadi

Girls¡¯ Education College in Makkah, Umm Al-Qura University, Kingdom of Saudi Aria

Abstract: In this paper, we introduce the concept of strongly generalized closed (open) fuzzy sets, which are generalized of closed (open) fuzzy sets in fuzzy topological spaces. Further, we introduce a new fuzzy closure operator and obtain a new fuzzy topology , then we study some of their properties. Also, we introduce the concept of fuzzy -regular space, -space, -space and fuzzy -normal space and obtain some of new and important properties.

Keyword: Topological spaces, strongly generalized closed fuzzy sets, strongly generalized open fuzzy sets, -spaces, fuzzy -regular spaces, -spaces, -spaces, fuzzy -normal spaces.

Fuzzy T-neighborhood Ordered Spaces

Khaled A. Hashem

Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt

Abstract: The concept of fuzzy T- neighborhood spaces were introduced by Hashem and Morisi in [2002], where T stand for any triangular norm, in this paper we introduce the notion of fuzzy T- neighborhood ordered spaces. We study the continuity of functions between fuzzy T- neighborhood ordered spaces. Also, we introduce definitions and results of some separation axioms in fuzzy T- neighborhood ordered spaces. Some characterization properties with fundamental results are deduce.

Keyword: Fuzzy topology, fuzzy T- neighborhood ordered spaces, ordered set.

On Some Fuzzy Mappings-¢ò

A. Kharal and B. Ahmad

College of Aeronautical Enginees, National University of Science & Technology PAM Academy, Risalpur 24090, PAKISTAN Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, 60800, Pakistan E-mail: atharkharal@gmail.com, drbashir9@gmail.com

Abstract: In continuation of early work [1] we further investigate several properties and characterizations of fuzzy semi-open (fuzzy semi-closed), fuzzy semi-preopen (fuzzy emi-preclosed), fuzzy semi-precontinuous and fuzzy pre-semi-preopen (fuzzy pre-semi-preclosed) mapping.

Keyword: Fuzzy semi-open, Fuzzy semi-closed, Fuzzy semi-preopen, Fuzzy emi-preclosed, Fuzzy pre-semi-preopen, Fuzzy pre-semi-preclosed.

On Fuzzy Approximately Semi-pre-irresolute and Fuzzy Approximately Semi-pre-closed Functions

Anjan Mukherjee

Department of Mathematics, Tripura University, Suryamaninagar, Agartala-799130, Tripura, India. E-mail: anjan2002_m@yahoo.co.in

Snigdhendu bikas chakraborty

Department of Mathematics, Tripura University, Suryamaninagar, Agartala-799130, Tripura, India. E-mail: snighendu2007@yahoo.co.in

Abstract: The aim of this paper is to introduce and study two new concepts called fuzzy approximately semi pre irresolute and fuzzy approximately semi pre closed functions. We also investigate some basic properties of those concepts.

Keyword: Fuzzy topology, fuzzy generalized semi pre closed sets, fuzzy semi pre open sets.