Kumar V, Kumar K, On the ideal convergence of sequences of fuzzy numbers, Information Sciences, 2008, 178(24):4670-4678.$$\def \C $ is a decreasing sequence. Khan VA, Rababah RKA, Esi A, Sameera Ameen Ali Abdullah, and Kamal Mohammed Ali Suleiman Alshlool, Some new spaces of ideal convergent double sequences by using compact operator, Journal of Applied Sciences, 2017, 17(9):467-474. Khan VA, Kara EE, Altaf H, Ahmad M, Intuitionistic fuzzy I-convergent Fibonacci difference sequence spaces, Journal of Inequalities and Applications, 2019, Vol.(2019)(1), 1-7 Khan VA, Ahmad M, Fatima F, Khna MF, On some results in intuitionistic fuzzy ideal convergence double sequence spaces, Advances in Difference Equations, 2019, vol.(2019): 1-10. Nanda S, On sequences of fuzzy numbers, Fuzzy sets and systems, 1989, 33(1):123-126. Kostyrko P, Wilczynski W, Salat T, I-convergence, Real Analysis Ex-change, 2000, 26(2):669-686.
Matloka M, Sequences of fuzzy numbers, Busefal, 1986, 28(1):28-37. Fast H, Sur la convergence statistique Colloquium Math., 1951, (2), 241-244. Nuray F, Savas E, Statistical convergence of sequences of fuzzy numbers, Mathematica Slovaca, 1995, 45(3):269-273. Hazarika B, Fuzzy real valued lacunary I-convergent sequences, Applied Mathematics Letters, 2012, 25(3):466-470. Alaba BA, Norahun WZ, Fuzzy Ideals and Fuzzy Filters of Pseudocomplemented Semilattices, Advances in Fuzzy Systems, 2019, Vol. Esi A, Mehmet Acikgoz, On almost λ-statistical convergence of fuzzy numbers, Acta Scientiarum.Technology, 2014, vol. In Section 4, we state the conclusion of this chapter. In Section 3, we introduce the spaces of fuzzy valued lacunary ideal convergence of sequence with the help of a compact operator and prove our maim results. In Section 2, we recall some basic definitions related to the fuzzy number, ideal convergent, monotonic sequence and compact operator. The intervals are determined by θ and defined by I r = k r − 1 k r. Where a lacunary sequence is an increasing integer sequence θ = k r such that k 0 = 0 and h r = k r − k r − 1 → ∞ as r → ∞. Subsequently, Hazarika studied the concept of lacunary ideal convergent sequence of fuzzy real numbers. studied the notion of J-convergence in intuitionistic fuzzy normed spaces. Kumar and Kumar extended the theory of ideal convergence to apply to sequences of fuzzy numbers. introduced ideal J −convergence which is based on the natural density of the subsets of positive integers.
Esi and Acikgoz examined almost λ-statistical convergence of fuzzy numbers.
Furthermore, it was examined from the sequence space point of view and linked with summability theory. After that, and under different names, statistical convergence has been discussed in the ergodic theory, Fourier analysis and number theory. Alaba and Norahun studied fuzzy Ideals and fuzzy filters of pseudocomplemented semilattices Moreover, Nuray and Savas extended the notion of convergence of the sequence of fuzzy real numbers to the notion of statistical convergence.įast introduced the theory of statistical convergence. Nanda investigated some basic properties for these sequences and showed that the set of all convergent sequences of fuzzy real numbers form a complete metric space. Matloka initiated the notion of ordinary convergence of a sequence of fuzzy real numbers and studied convergent and bounded sequences of fuzzy numbers and some of their properties, and proved that every convergent sequence of fuzzy numbers is bounded. The concepts of fuzzy sets were initiated by Zadeh, since then it has become an active area of researchers.
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