Properties of invertible elements in complete intuitionistic fuzzy pseudo normed algebra

Year 2021, , 34 - 45, 31.12.2021

Bivas Dinda , Santanu Kumar Ghosh , Tapas Samanta

https://doi.org/10.54187/jnrs.979984

Abstract

In this paper, we deal with the invertible elements in a complete intuitionistic fuzzy pseudo normed algebra (in short, IFPNA) with respect to Archimedean t-norm and Archimedean t-conorm. It is done by studying the continuity of algebraic operations in a complete IFPNA and investigating the condition for existence of inverse of an element in a complete IFPNA. Also some properties of invertible elements are studied. It is observed that the set of invertible elements in a complete IFPNA is an open set.

Keywords

IFPNA, Invertible element, Intuitionistic fuzzy continuity

References

• L. A. Zadeh, Fuzzy sets, Information and control, 8(3), (1965) 338–353.
• K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), (1986) 87–96.
• A. K. Katsaras, Fuzzy topological vector spaces i, Fuzzy sets and systems, 6(1), (1981) 85–95.
• A. K. Katsaras, Fuzzy topological vector spaces ii, Fuzzy sets and systems, 12(2), (1984) 143–154.
• C. Felbin, Finite dimensional fuzzy normed linear space, Fuzzy sets and Systems, 48(2), (1992) 239–248.
• S. C. Cheng, J. N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bulletin of the Calcutta Mathematical Society, 86, (1994) 429–436.
• T. Bag, S. K. Samanta, Finite dimensional fuzzy normed linear spaces, Journal of Fuzzy Mathematics, 11(3), (2003) 687–706.
• R. Saadati, S. Vaezpour, Some results on fuzzy banach spaces, Journal of Applied Mathematics and Computing, 17(1), (2005) 475–484.
• I. Gole¸t, On generalized fuzzy normed spaces and coincidence point theorems, Fuzzy sets and Systems, 161(8), (2010) 1138–1144.
• B. Dinda, T. K. Samanta, Intuitionistic fuzzy continuity and uniform convergence, International Journal of Open Problems in Computer Science and Mathematics, 3(1), (2010) 8–26.
• R. Saadati, J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos, Solitons & Fractals, 27(2), (2006) 331–344.
• I. Sadeqi, F. S. Kia, Fuzzy normed linear space and its topological structure, Chaos, Solitons & Fractals, 40(5), (2009) 2576–2589.
• B. Dinda, T. K. Samanta, I. H. Jebril, Fuzzy anti-norm and fuzzy α-anti-convergence, Demonstratio Mathematica, 45(4), (2012) 739–754.
• A. K. Mirmostafaee, Perturbation of generalized derivations in fuzzy menger normed algebras, Fuzzy sets and systems, 195, (2012) 109–117.
• T. Bınzar, F. Pater, S. Nadaban, On fuzzy normed algebras, Journal of Nonlinear Sciences and Applications, 9(9), (2016) 5488–5496.
• N. Konwar, P. Debnath, Intuitionistic fuzzy n-normed algebra and continuous product, Proyecciones (Antofagasta), 37(1), (2018) 68–83.
• J. R. Kider, A. H. Ali, Properties of a complete fuzzy normed algebra, Baghdad Science Journal, 16(2), (2019) 382–388.
• S. Nǎdǎban, Fuzzy pseudo-norms and fuzzy f-spaces, Fuzzy Sets and Systems, 282, (2016) 99–114.
• T. Bag, S. K. Samanta, Fuzzy bounded linear operators, Fuzzy sets and Systems, 151(3), (2005) pp. 513–547.
• B. Dinda, S. K. Ghosh, T. K. Samanta, Intuitionistic fuzzy pseudo-normed linear spaces, New Mathematics and Natural Computation, 15(1), (2019) 113–127.
• B.Dinda, S. K.Ghosh, T. K. Samanta, On w-convergence and s-convergence in intuitionistic fuzzy pseudo normed spaces, New Mathematics and Natural Computation, 17(3), (2021) 623–632.
• B. Dinda, S. K. Ghosh, T. K. Samanta, Relations on continuities and boundedness in intuitionistic fuzzy pseudo normed linear spaces, arXiv preprint, arXiv:2102.06519, 2021.
• B. Dinda, S. K. Ghosh, T. K. Samanta, An introduction to spectral theory of bounded linear operators in intuitionistic fuzzy pseudo normed linear space, Sahand Communications in Mathematical Analysis, (2021) 12 pages (accepted), doi:10.22130/SCMA.2021.531698.942.
• B. Schweizer, A. Sklar, Statistical metric spaces, Pacific Journal of Mathematics, 10(1), (1960) 313 – 334.
• M. M. Gupta, J. Qi, Theory of t-norms and fuzzy inference methods, Fuzzy sets and systems, 40(3), (1991) 431–450.