Generalized Semistrongly Convex Fuzzy Sets

Authors

  • Pishtiwan O. Sabir Department of Mathematics, Faculty of Science and Education Sciences, University of Sulaimani, Kurdistan Region, Iraq. Author

DOI:

https://doi.org/10.17656/jzs.10553

Keywords:

Fuzzy sets, Fuzzy convex sets, Semistrongly convex fuzzy sets

Abstract

The intention of this work is to study various aspects on the concepts of generalized convex fuzzy sets, generalized strongly convex fuzzy sets, and generalized semistrongly convex fuzzy sets. Precisely has investigated the properties and relations among them.

References

Zadeh, L. A., Fuzzy sets, Inform. & Control Vol.8, pp 338–353, (1965). DOI: https://doi.org/10.1016/S0019-9958(65)90241-X

Dubois, D. and Prade, H., Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York (1980).

Klir, G. J., and Yuan, B., Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice-Hall, Upper Saddle River, N.J. (1997).

Lee, K. H., First Course on Fuzzy Theory and Applications, Springer Berlin Heidelberg, NY (2005).

Zimmermann, H. J., Fuzzy Set Theory and Its Applications, 2nd Revised Ed., Kluwer Academic Publishers, Boston, London (1991). DOI: https://doi.org/10.1007/978-94-015-7949-0

Chalco-Cano, Y., and Rojas-Medar, S-convex fuzzy processes, Computer and Mathematics with Applications, Vol.47, pp 1411-1418, (2004). DOI: https://doi.org/10.1016/S0898-1221(04)90133-2

Chen, J., Syau, Y., and Tnig, C.-J., Convexity and semicontinuity of fuzzy sets, Fuzzy Sets and Systems, Vol.143, pp 459-469, (2004). DOI: https://doi.org/10.1016/S0165-0114(03)00159-3

Delhi, I., Convex and concave soft sets and some properties, arXiv:1307.4960v1.

Drewniak, J., Convex and strongly convex fuzzy sets, Journal of Mathematical Analysis and Applications, Vol.126, pp 292-300, (1987). DOI: https://doi.org/10.1016/0022-247X(87)90093-X

Kaiqi, Y.Z., A note on convex fuzzy sets, BUSEFAL, Vol.77, pp 72-74, (1999).

Matloka, M., A note on (ΦE1, ΦE2) -Convex fuzzy processes, Advances in Fuzzy Systems, Vol 2012, pp 1-4. DOI: https://doi.org/10.1155/2012/290845

Peng, Z.-Y., Long, X.-J., Lin, Z., Some new properties of strongly convex fuzzy sets, Fuzzy Information and Engineering, Vol.62, pp 687–693, (2009). DOI: https://doi.org/10.1007/978-3-642-03664-4_75

Syau, Y., Closed and convex fuzzy sets, Fuzzy Sets and Systems, Vol.110, pp 287-291, (2000). DOI: https://doi.org/10.1016/S0165-0114(98)00082-7

Wu, S., and Cheng, W., A note on fuzzy convexity, Applied Mathematics Letters, Vol.17, pp 1127-1133, (2004). DOI: https://doi.org/10.1016/j.aml.2003.11.003

Yang, X., Some properties of convex fuzzy sets, Fuzzy Sets and Systems, Vol.7, pp 129-132, (1995). DOI: https://doi.org/10.1016/0165-0114(94)00285-F

Yang, X.-M., and Yang, F.-M., A property on convex fuzzy sets, Fuzzy Sets and Systems, Vol.126, 269-271, (2002). DOI: https://doi.org/10.1016/S0165-0114(01)00075-6

Zadeh, L. A., The Concept of a Linguistic Variable and its Application to Approximate Reasoning. Memorandum ERL-M 411, Berkeley, Ca. (1973). DOI: https://doi.org/10.1007/978-1-4684-2106-4_1

Zadeh, L. A., The Concept of a Linguistic Variable and its Application to Approximate Reasoning (I), (II), and (III), Inf. Sci. Vol.8, pp 199–249, pp 301–357, (1975) and Vol.9, pp 43–80, (1975). DOI: https://doi.org/10.1016/0020-0255(75)90046-8

Gorzalczany, B., Approximate inference with interval-valued fuzzy sets – an outline, in: proceedings of the polish symposium on interval and fuzzy mathematics, Poznan, Poland, pp 89-95, (1983).

Turksen, B., Interval valued fuzzy sets based on normal forms, Fuzzy Sets and Systems, Vol.20, pp 191- 210, (1986). DOI: https://doi.org/10.1016/0165-0114(86)90077-1

Hong, D.H., and Lee, S., Some algebraic properties and a distance measure for interval-valued fuzzy numbers, Information Sciences, Vol.148, pp 1-10, (2002). DOI: https://doi.org/10.1016/S0020-0255(02)00265-7

Published

2016-09-20

How to Cite

Generalized Semistrongly Convex Fuzzy Sets. (2016). Journal of Zankoy Sulaimani - Part A, 18(3), 241-248. https://doi.org/10.17656/jzs.10553

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