Interval-valued intuitionistic fuzzy linear transformation

R. Santhi; N. Udhayarani

doi:10.26637/mjm1003/004

Abstract

In this paper we introduce the concept of interval-valued intuitionistic fuzzy relations(in biefly IVIFR) and composition of IVIFR-equations. Then we continued it to interval-valued intuitionistic fuzzy linear transformation(in brief IVIFL-transformation) and discussed its properties. Also introduced the concept of composition of IVIFL-transformations.

Keywords:

Composition of IVIF-Relations, $IV IF_0L$ -transformations, $IV IF_I L$ - transformations, $IVIFL$-transformations, $IVIF$-Relations

Mathematics Subject Classification:

03E72, 15A03

Authors Imprint References Funding Related Articles Downloads

R. Santhi PG and Research Department of Mathematics, Nallamuthu Gounder Mahalingam College, Pollachi-642001, Tamil Nadu, India.
N. Udhayarani PG and Research Department of Mathematics, Nallamuthu Gounder Mahalingam College, Pollachi-642001, Tamil Nadu, India. https://orcid.org/0009-0006-1004-333X

Pages: 216-223
Date Published: 01-07-2022
Vol. 10 No. 03 (2022): Malaya Journal of Matematik (MJM)

K.T. A TANASSOV , Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1)(1986), 87–96.

K.T. A TANASSOV AND G. G ARGOV , Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems,

(1989), 343–349.

K.T. Atanassov, Operations over interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64(1994), 159-174.

M. Bhowmik And M. Pal, Intuitionistic fuzzy linear transformations, Ann. Pure and Appl. Math., 1(1)(2012), 57-68.

H.L. Huang, $(T, S)$ - based interval-valued intuitionistic fuzzy composition matrix and its application For clustering, Iranian J Fuzzy Systems, 9(5)(2012), 7-19.

A.K. Katsaras And D.B. LiU, Fuzzy vector spaces and Fuzzy topological vector vpaces, Far-East J Math. Sci., 58(1977), 135-146.

K.H. Kim And F.W. Roush, Generalized fuzzy matrices, Fuzzy Sets and Systems, 4(1980), 293-315.

M.L. Lin And H.L. Huang, $(T, S)$-based intuitionistic fuzzy composite matrix and its application, Int. J Appl. Math. Stat., 23(2011), 54-63.

M. Pal, S.K. Khan and A.K. Shyamal, Intuitionistic Fuzzy Matrices, Notes on Intuitionistic Fuzzy sets, $mathbf{8 ( 2 ) ( 2 0 0 2 ) , ~ 5 1 - 6 2 . ~}$

Madhumangal Pal and Susanta K.Khan, Interval-Valued Intuitionistic Fuzzy Matrices, Notes on Intuitionistic Fuzzy Sets, 11(1)(2005), 16-27.

A. R. Meenakshi and T. Gandhimathi, Intuitionistic fuzzy linear Transformations, Int. J Compu. Sci. Math., 3(1)(2011), 99-108.

Moumita Chiney and S.K. Samanta, Intuitionistic Fuzzy Basis of an Intuitionistic Fuzzy Vector Space Notes on Intuitionistic Fuzzy Sets, 23(4)(2017),62-74.

A. Narayanan, S. Vijayabalaji and N. Thillaigovindhan, Intuitionistic Fuzzy Linear Operators, Iranian J. Fuzzy Sys., 4(2007), 89-101.

Rajkumar Pradhan and Madhumangal Pal, Intuitionistic fuzzy linear Transformations Ann. Pure Appl. Math., 1(1)(2012), 57-68.

R. Santhi and N. Udhayarani, Properties of Interval-Valued Intuitionistic Fuzzy Vector Space, Notes on Intuitionistic Fuzzy Sets, 25(1)(2019),12-20.

S.K. Shyamal and M. Pal, Interval-Valued Fuzzy Matrices, J Fuzzy Math., 14(3)(2006),583-604.

Y. Terao and N. Kitsunezaki, Fuzzy Sets and Linear Mappings on Vector Spaces, Mathematica Japonica, 39(1)(1994), 61-68.

Z.S. XU AND R.R. Yager, Intuitionistic and Interval-Valued Intuitionistic Fuzzy Preference Relations and Their Measures of Similarity for the Evaluation of Agreeement within a Group, Fuzzy Opti. Decision Making, 8(2009), 123139.

L.A. ZADEH, Fuzzy Sets, Info. Cont., 8(1965), 338-353.

ZE-Shui XU AND JIAN ChEn, Approach to Group Decision Making Based on Interval-Valued Intuitionistic Judgement Matrices, Sys. Engi.: Theory and Practices, 27(2007), 126-133.