On Starshaped Intuitionistic Fuzzy Sets

Weihua Xu, Yufeng Liu, Wenxin Sun

.

DOI: 10.4236/am.2011.28146                

Abstract

Intuitionistic fuzzy starshaped sets (i.f.s.) is a generalized model of fuzzy starshaped set. By the definition of i.f.s., the intuitionistic fuzzy general starshaped sets (i.f.g.s.), intuitionistic fuzzy quasi-starshaped sets (i.f.q-s.) and intuitionistic fuzzy pseudo-starshaped sets (i.f.p-s.) are proposed and the relationships among them are studied. The equivalent discrimination conditions of i.f.q-s. and i.f.p-s. are presented on the basis of their properties which are meaningful for the research of the generalized fuzzy starshaped sets. Moreover, the invariance of the two given fuzzy sets under the translation transformation and linear reversible transformation are discussed.

Keywords

Intuitionistic Fuzzy Starshaped Sets, Cut Sets, Starshapedness, Convex Sets

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	K. Atanassov, “Intuitionistic Fuzzy Sets,” Fuzzy Sets and Systems, Vol. 20, No. 1, 1986, pp. 87-96. doi:10.1016/S0165-0114(86)80034-3
[2]	S. Manro, “Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces,” Applied Mathematics, No. 1, 2010, pp. 510-514. doi:10.4236/am.2010.16067
[3]	G. Deschrijive and E. E. Kerre, “On the Position of Intuitionistic Fuzzy Set Theory in the Framework of Theories Modelling Imprecision,” Information Sciences, Vol. 177, No. 8, 2007, pp. 1860-1866. doi:10.1016/j.ins.2006.11.005
[4]	L. Lin, X. H. Yuan and Z. Q. Xia, “Multicriteria Fuzzy Decision-Making Methods Based on Intuitionistic Fuzzy Sets,” Journal of Computer and System Science, Vol. 73, No. 1, 2007, pp. 84-88. doi:10.1016/j.jcss.2006.03.004
[5]	L. K. Vlachos and G. D. Sergiadis, “Intuitionistic Fuzzy Information—Applications to Pattern Recognition,” Pattern Recognition Letters, Vol. 28, No. 2, 2007, pp. 197-206. doi:10.1016/j.patrec.2006.07.004
[6]	H. Bustince and P. Burillo, “Structures on Intuitionistic Fuzzy Relations,” Fuzzy Sets and Systems, Vol. 78, No. 3, 1996, pp. 293-303. doi:10.1016/0165-0114(96)84610-0
[7]	M. D. Cock, C. Cornelis and E. E. Kerre, “Intuitionistic Fuzzy Relational Images,” Studies in Computational Intelligence, Vol. 2, 2005, pp. 129-145.
[8]	D. Coker, “An Introduction to Intuitionistic Fuzzy Topological Spaces,” Fuzzy Sets and Systems, Vol. 88, No. 1, 1997, pp. 81-89. doi:10.1016/S0165-0114(96)00076-0
[9]	G. Deschrijive and E. E. Kerre, “On the Composition of Intuitionistic Fuzzy Relations,” Fuzzy Sets and Systems, Vol. 136, No. 3, 2003, pp. 333-361. doi:10.1016/S0165-0114(02)00269-5
[10]	D. Qiu, L. Shu and Zh. W. Mo, “On Starshaped Fuzzy Sets,” Fuzzy Sets and Systems, Vol. 160, No. 11, 2009, pp. 1563-1577. doi:10.1016/j.fss.2008.11.005
[11]	M. Li, “Cut Sets of Intuitionistic Fuzzy Sets,” Journal of Liaoning Normal University Vol. 30, No. 2, 2007, pp. 152-154.
[12]	Y. R. Syau, “Closed and Convex Fuzzy Sets,” Fuzzy Sets and Systems, Vol. 110, No. 2, 2000, pp. 287-291. doi:10.1016/S0165-0114(98)00082-7
[13]	J. G. Brown, “A Note on Fuzzy Set,” Information and Control, Vol. 18, No. 1, 1971, pp. 32-39. doi:10.1016/S0019-9958(71)90288-9