THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 20, Number 3, Septerber 2012

CONTENT

DETAILS

Uncertain Demand in (Q,R) Inventory Systems£ºA Fuzzy Optimization

Approach Pankaj Dutta

SJM School of Management, Indian Institute of Technology. Bombay, Mumbai-400076,India

Debjani Chakraborty and A.R.Roy

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

Abstract: This paper presents an approach for solving continuous review (Q , r) inventory syatems with imprecise customer demand. Traditionally to describe uncertainty probability density functions are being used. In this paper we present an alternative approach considering imprecise, uniform annual demand rate. Viewing the lead-time demand as a triangular fuzzy number, we present an iterative algorithm to determine the optimal order quantity and reorder point simultaneously. In addition, a distinct characteristic of this study is to incorporate the level-weighted average of a fuzzy number using possibilistic mean value approach in which the total expected annual cost in the fuzzy sense has a minimum value .After defuzzification, an estimate interval of total annual cost is also determined. Numerical illustration is performed to investigate the result of the proposed fuzzy model.

Keyword: Inventory, continous review, fuzzy demands, fuzzy total cost, possibilistic mean value

New Operations On Intuitionistic Fuzzy Soft Sets

Pabitra Kumar Maji

Department of Mathematics B. C. College, Asansol

Akhil Ranjan Roy

Department of Mathematics I. I. Kharagpur West Bengal,India. E-mail: arroy@maths.iitkgp. ernet. in

Abstract: In this paper we have introduced some new operations on intuitionistic fuzzy soft sets. Some properties on these new operations have also been investigated. An example has also been given as an application of these operation s.

Keyword: Soft Set, Fuzzy Soft Sets, Intuitionistic Fuzzy Soft Sets, Similarity Measurement.

On G -Covering Dimension of L-Topological Spaces

Dalip Singh Jamwal and Renu Gupta

Department of Mathematics, University of Jammu, jammu-180006, INDIA E-mail: dalipsj@yahoo. com, E-mail: renu_ju@yahoo. com

Abstract: In this paper, the concept of G -covering dimension of L -topological spaces is introduced and a characterization of G -covering dimension is obtained. Also a relationship betweeen G -covering dimension covering dimension of L -topological spaces is established and various properties of G -covering dimension are studied.

Keyword and phrase: Fuzzy grill, G ¨Corder, G -covering dimension, L -topological spaces.

Some Properties of Fuzzy Hilbert Spaces and Fixed Point Theorems in Such Spaces

S.Mukherjee

Department of Mathematics, Visva Bharati Santiniketan-732135, W.Bengal, India

T.Bag

Department of Mathematics, Visva Bharati Santiniketan-732135, W.Bengal, India E-mail address:tarapadavb@gmail.com

Abstarct: In this paper we establish some theorems in fuzzy Hibert spaces viz. Bessel¡¯s inequality,Riesz represention theorem. Some fixed point theorems are proved in such spaces.

Keyword: Hilbert spaces, Bessel¡¯s inequality, Riesz represention theorem, fixed point.

Soft Real Sets, Soft Real Numbers and Their Properties

Sujoy Das

Department of Mathematics, Bidhan Chandra College, Asansol-4, W. B., India

S.K.Samanta

Department of Mathematics, Visva Bharati, Santiniketan, W. B., India Email: symal 123@yahoo.co.in and syamal.samanta@visva-bharati.ac.in

Abstarct: Combining the existing and the the resent revised definitions of fuzzy real numbers proposed by Dubios and Prade [3] and the idea of soft set introduced by Molodtsov [9], we inteoduce, in this paper, a definition of soft real set and soft real number and study some of their basic properties.

Keyword: Soft set, soft real set, soft real number, fuzzy real number, fuzzy set, gradual set, gradual number, fuzzy element, similarity measure.

Strictly Convex Fuzzy Normed (Felbin¡¯s Type) Linear spaces

D. Halder

Research scholar department of mathematics Visva-Bharati University, West bengal, INDIA

T. Bag

Reader, Department of Mathematics Visva-Bharati University, West bengal, INDIA E-mail: tarapadav@gmail.com

S. K. Samanta Prof.Department of mathematics Visva-Bharati University, West bengal, INDIA

Abstract: In this paper,the concept of Strict convexity of a fuzzy norm in a normed linear space is introduced. Relation between ¡®uniform convexity¡¯ and ¡®strict convexity¡¯ of fuzzy normed linear spaces are studied and Taylor-Foguel theorem is established in fuzzy setting.

Keywod: Fuzzy normed linear space, strictly convex fuzzy normed linear space, uniformly convex fuzzy normed linear space, fuzzy closed set.

On Level Fuzzy and Valuation Fuzzy Ideals of Rings

Souriar Sebastian

Dept of Mathematics, St. Albert¡¯s College, Ernakulam,Kochi-682018,Kerala,India E-mail: souriasebastian@gmail.com

George Mathew

Dept of Mathematics, B. C. M college, Kottayam-686001, kerala, india E-mail: gmathew5616x@gmail.com

Abstract: In [13] we have introduced, the notion of level fuzzy ideals and derived some of their basic properties. Also, we have obtained some necessary and sufficient conditions for the existence of level fuzzy ideals. Another class of fuzzy ideals called valuation fuzzy ideals was introduced in [14] and the conditions required for the existence of such ideals were derived. We also established an order preserving correspondence between such ideals and valuations of a valuation ring. In this paper we continue this investigation. Here we prove that a valuation ring with a real valuation always possesses a valuation fuzzy ideal. We also differentiate between level fuzzy ideals and valuation fuzzy ideals. We further prove that these notions are identical in a DVR. We also construct a valuation fuzzy ideal on a NDVR which is not a level fuzzy ideal.

Keyword: Valuation, Valuation rings, discrete valuation rings (DVR), non-discrete valuation rings (NDVR), absolute value, fuzzy ideals, level fuzzy ideals, valuation fuzzy ideals.

On Quasi Continuous Intuitionistic Fuzzy Multifunctions

S. S. Thakur

Department of Applied mathematics, government Engineering College,Jabalpur (M.P) 482011 India E-mail: samajh- singh@rediffmail.com

Kush Bohre

Department of Applied Mathematics, Gyan Gangga college of technology, jabalpur (M. P.) -482001 India. E-mail: kushbohre@yahoo.co.in

Abstract: The aim of this paper is introduce the concepts of upper and lower intuitionistic fuzzy quasi-continuous intuitionistic fuzzy multisfunctions and obtain some of their properties.

Keyword: Intuitionistic fuzzy sets, Intuitionistic fuzz topology, Intuitionistic fuzz multisfunctions, lowe r quasi continuous and upper quasi continuous Intuitionistic fuzzy multifunctions.

Study of Some Aspects of Mixed -pre Fuzzy Topological Spaces

N. R. Das

Dept.of mathematics, Gauhati University Guwahati 781014, Assam, India

Jonali Sharma Laban Assamse Girl' Secondary school,Laban Shillong 793004, Meghalaya,Indian E-mail: jonalisharma2007@rediffmail.com

Abstrct: This paper deals with the construction of a fuzzy topological space, from two different topologies and is named 'Mixed -pre Fuzzy Topological Space'. Some result of fuzzy continuity are proved in this newly constructed fuzzy topological space. Attempts are also made to study separation axioms and also open and closed maps in this newly constructed fuzzy topological space.

Keyword: Fuzzy -preopen set, fuzzy -preclosed set, fuzzy -pre-q-nbd, fuzzy -precluster point , fuzzy -preclosure, fuzzy -preregular, fuzzy -preopen map, fuzzy -preclosed map, fuzzy M -precontinuous function, product topology, bitopological space.

Fixed Point for Mappings Satisfying An Implicit Relation in Ordered Fuzzy Metric spaces

Ismat Beg and Asma Rashid Butt

Centre for Advanced Studies in Mathematics, Lahore University of Management Sciences, Lahore -54792, Pakistan. E-mail: ibeg@lums.edu.pk

Abstract: Let (X, M, T, ¡Ü) be a partially ordered fuzzy metric space and f , g be two self mappings on X .we obtained sufficient conditions for existence of common fixed point of f , g satisfying an implicit relation in X .

Keywords and phrases: Fixed point; ordered fuzzy metric space; implicit relation.

On Preserving Intuitionistic Fuzzy W-closed Sets

S.S.thakur Department of Applied Mathematics Jabalpur engineering college Jabalpur (M. P.) 482011 India E-mail: samajh_singh@rediffmail.com

Jyoti Pandey Bajpai

Department of Applied Mathematics Jabalpur engineering college Jabalpur (M. P.) 482011 India E-mail: ygshbajpai@yahoo.com

Abstract: In this paper we introduced the concept of aw-closed and aw-continuous mappings in intuitonistic fuzzy topological spaces and obtain several results concerning the preservation of intuitionistic fuzzy w -closed sets. Further more we characterize intuitionistic fuzzy -spaces due to Thakur and Bajpai [18] in terms of intuitionistic fuzzy aw-continuous and intuitionistic fuzzy aw-closed mapping and obtain some of the basic properties and characterization of these mappings.

Key word: Intuitionistic fuzzy w -closed sets, intuitionistic fuzzy w -open sets, Intuitionistic fuzzy w -continuous, Intuitionistic fuzzy aw-closed, Intuitionistic fuzzy aw-continuous and Intuitionistic fuzzy w-irresolute mapping.

Approximations in F-normed Spaces

A. Singadurai

Department of Mathematics, TDMNS College, T. Kallikulam 627113 Tamilnadu, INDIA E-mail: singadurai_59@yahoo.co.in

Abstract: In this paper we investigate some properties of the t -best approximations and p -best approximations in F -normed spaces.

Keyword: F -norm, t -best approximation, t -limit point, p -approximately compact, t -boundedly compact.

Fuzzy -S-closed and Fuzzy -s -closed Fuzzy Bitopological spaces

Subrata Bhowmik

Department of Mathematics Tripura University Suryamaninagar, Tripura-799130 (INDIA) E-mail: subrata _bhowmik_math@rediffinail.com

Abstract: Coker and Hydar [3] studied fuzzy S -closed spaces, Sinha and Malakar [11] studied fuzzy s-closed spaces and Mukherjee and Bhowmik [9] introduce the closed and closed bitopological spaces. In this paper we are interested to generalize these concepts for fuzzy bitopological spaces with the concepts of [3], [11] and [9]. In this context we introduce and study fuzzy closed, fuzzy closed fuzzy bitiopological spaces with the notion of i j -fuzzy semi open sets [12] in the fuzzy bitopological spaces. Lastly we will try to find if any kind of relationship that can be set up between the notions of fuzzy closed fuzzy closed concepts in fuzzy bitopological spaces and fuzzy S-closed and fuzzy s-closed concepts in fuzzy topological spaces.

Keywords: Fuzzy bitopological space, ij -fuzzy semi open sets in fuzzy bitopological space£¬fuzzy filterbase, net.

Intuitionistic Fuzzy Equivalences and Congruences in A Lattice

K. V. Thomas

Bharata Mata College Thrikkakara Kochi Kerala E-mail: tkapiarumala@yahoo.co.in

Latha S. Nair

Mar Athanasius College Kothamamgalam Kochi Kerala E-mail: lathavichattu@gmail.com

Abstract: The definition of reflexivity of a intuitionistic fuzzy relation R on a set S is generalized by defining R(x,x)=(t,k). Intuitionistic fuzzy equivalence relations and intuitionistic fuzzy congruence relation on a lattice are studied under this generalized setting. Certain characterization of (t,k) equivalence relations in terms of their level subsets are given. Also we study the relationship between intuitionistic fuzzy ideals and intuitionistic fuzzy congruence and their lattice isomorphism with the help of upper and lower level subsets. Finally we study intuitionistic fuzzy quotient lattice and defined the quotient of an IFL relative to congruence and the intuitionistic fuzzy analog of the fundamental theorem of homomorphism is provided.

Keywords: Lattice, intuitionistic fuzzy lattice (IFL), intuitionistic fuzzy ideals (IFI), intuitionistic fuzzy relation (IFR), intuitionistic fuzzy equivalence relations, intuitionistic fuzzy congruence relations. Level subsets.

Intuitionistic Fuzzy Soft Flood Index Model

Sunny Joseph Kalayathankal

Department of Matheamtics, K.E.College, Mannanam, Kottayam, 686561, India Email address: sunnyjose 2000@yahoo.com

G.Suresh Singh

Department of Mathematics, University of Kerala, Trivandrum, 695581, India

Sabu Joseph

Department of Environment Sciences, University of Kerala, Trivandrum, 695581, India

Abstract: Rainfall being the dominant component in most hydrological systems, reliable quantification of rainfall is absolutely essential for various ecological, meteorological, geo-morphological and disaster management studies. This paper investigates the potential of intuitionistic fuzzy soft set theory in real-time flood warning and is applied to five selected sites of Kerala, India to predict potential flood.

Keywords: Rainfall; Intuitionistic Fuzzy soft set; Flood;Simulation

A Fuzzy Network Flood Alarm Model

Sunbny Joseph Kalayathankal

Department of Mathematics, K. E. College, Mannanam, Kottayam, 686561, India Email address: sunnyjose2000@yahoo.com

G. Suresh Singh Department of Mathematics, University of Kerala, Trivandrum, 695581, India

Sabu Josepah and Jobin Thomas

Department of Environmental Science, University of Kerala, Trivandrum, 695581, India

Abstract: A flood warning system is a non-structural measure for flood mitigation. Several parameters are responsible for flood related disasters and a quick-responding flood warning system is required for effective flood mitigation measures. This work illustrates a fuzzy network analysis that has the capability to simulate the unknown relations between a set of meteorological, hydrological and morphometric parameters. A fuzzy network approach to flood alarm prediction based on intuitionistic set theory is applied to five selected sites of Kerala, India to predict potential flood.

Keyword: Rainfall; Network; Intuitionistic fuzzy set; Simulation

Interval-valued Intuitionistic Fuzzy BG-subalgebras

Tapan Senapati , Monoranjan Bhowmik and Madhumangal Pal

Department of Matheamtics, V.T.TCollege, Midnapore, Paschim Medinipur-721101, India. E-mail: mbvttc@gmail.com

Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University, Midnapore-721102, India. E-mail: mmpalvu@gmail.com

Abstract: In this paper, we introduce the notion of interval-valued intuitionistic fuzzy subalgebras of BG -algebra. Also defines homomorphism of interval-valued intuitionistic fuzzy BG -subalgebras and Investigate some of their properties.

Keyword and phrases: BG -algebras, BG -subalgebras, interval-valued intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy BG -subalgebras, homomorphism.

Fuzzy Boundaries and Their Generalizations

Dibyajyoti Hazarika and Debajit Hazarika

Department of Mathematical Sciences, Tezpur University, Napam-784028, Assam INDIA

Abstract: A comparative analysis of the three notions of fuzzy boundaries due to Warren, Pu and Liu as well as duo to Cuchillo-Ibanez and Tarres has been presented in this paper. Several important identities have been proved and various counter-examples have been provided to support the inequalities. Further, two generalized forms of fuzzy boundaries have been introduced in this paper.

Keywords: Fuzzy boundary, fuzzy semi-boundary

Ordered Ideal Intuitionistic Fuzzy Flood Index Model

Sunny Joseph Kalayathankal

Department of Mathematics, K. E. College, Mannanam Kottayam-686561, Kerala, India E-mail:sunnyjose2000@yahoo.com

G. Suresh Singh

Department of Mathematics, University of Kerala, Kariavattom Thiruvananthapuram-695581, Kerala, India

Sabu Joseph

Department of Environment Science, University of Kerala, Kariavattom Thiruvananthapuram-695581, Kerala, India

Abstract: Over the last few decade, fuzzy technology (FT) has been increasingly used in hydrological forecasting. Their computational speed in simulating and forecasting has become highly relevant in real time operations. In this paper, we first define ordered ideal intuitionistic fuzzy sets and establish some results on them. Then, we define three types of similarity measures between ordered ideal intuitionistic fuzzy sets (OIIFS) and apply these similarity measures to five selected sites of Kerala, India to predict flood index under ordered ideal intuitionistic fuzzy environment.

Keywords: Rainfall, Ordered intuitionistic fuzzy set, Flood, Simulation.

Similarity Measures of Ordered Ideal Intuitionistic Fuzzy Sets

Sunny Joseph Kalayathankal

Department of Mathematics, K. E. College, Mannanam Kottayam-686561, Kerala, India E-mail: sunnyjose2000@yahoo.com

G.Suresh Singh

Department of Mathematics, University of Kerala, Kariavattom Thiruvananthapuram-695581, Kerala, India

Sabu Joseph

Department of Environmental Science, University of Kerala, Kariavattom Thiruvananthapuram-695581, Kerala, India

Abstract: The Multiple Attribute Decision Making (MADM) problem deals with candidate priority alternatives with respect to various attributes. Several approaches have been developed for assessing the weights of MADM problems. Anew approach is proposed to solve the MADM problem, where the decision maker gives his/her preference on alternatives in a fuzzy environment. In this paper, we first define ordered ideal intuitionistic fuzzy (OIIF) sets and establish some results on them. Then, we define some similarity measures of ordered ideal intuitionistic fuzzy sets and apply these similarity measures to multiple attribute decision making under ordered ideal intuitionistic fuzzy environment.

Keywords: Fuzzy set, Ordered intuitionistic fuzzy set, Similarity measure