Lacunary bounded variation sequence of fuzzy real numbers

Tripathy, Binod Chandra; Dutta, Amar Jyoti

doi:10.3233/ifs-2012-0544

Cited by 38 publications

(10 citation statements)

References 13 publications

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“…The strongly almost summable sequence spaces were introduced and studied by Maddox [18], Nanda [21], Güngör et al, [12], Esi [7], Gungor and Et [15] and many authors. For matrix maps on sequence spaces we refer to [23] and for difference sequence spaces we refer to [28][29][30][31] and references therein.…”

Section: Classes Of Lacunary Orlicz Difference Sequencesmentioning

confidence: 99%

New type of Lacunary Orlicz difference sequence spaces generated by infinite matrices

Esi

Hazarika

Eşi

2016

Filomat

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The main purpose of this paper is to introduce the spaces w o θ A, M, ∆, p , w θ A, M, ∆, p and w ∞ θ A, M, ∆, p generated by infinite matrices defined by Orlicz functions. Some properties of these spaces are discussed. Also we introduce the concept of S θ [A, ∆] −statistical convergence and derive some results between the spaces S θ [A, ∆] and w θ [A, ∆]. Further, we study some geometrical properties such as order continuous, the Fatou property and the Banach-Saks property of the new space w ∞ θα A, ∆, p. Finally, we introduce the notion of S θ [A, ∆] −statistical convergence of order α of real number sequences and obtain some inclusion relations between the set of S [A, ∆] −statistical convergence of order α.

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Section: Classes Of Lacunary Orlicz Difference Sequencesmentioning

confidence: 99%

New type of Lacunary Orlicz difference sequence spaces generated by infinite matrices

Esi

Hazarika

Eşi

2016

Filomat

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“…In recent past different classes of sequences of fuzzy real numbers have been introduced and studied by Altinok, Altin and Et [1], Dutta [3], Savas [12], Mursaleen and Başarir [11], Esi [6], Tripathy and Dutta ([14], [15], [16]), Tripathy and Sarma ( [17], [18]) and others.…”

Section: Clearlyd Define a Metric On R(i)mentioning

confidence: 99%

Statistically pre-Cauchy Fuzzy real-valued sequences defined by Orlicz function

Dutta¹,

Tripathy

2014

Proyecciones (Antofagasta)

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“…Several methods of computational intelligence and soft computing have been widely used for chaotic signals prediction and identification. Neuro-fuzzy systems is one of the interesting soft computing approaches utilized in various application such as modelling, classification, and prediction [1][2][3][4][5][6][7][8]. Turksen introduced another type of fuzzy structure, called Fuzzy Functions (FFs) [9,10] which has a simpler structure compared a local and global method, the interactively recurrent 73 self-evolving fuzzy neural network (IRSFNN) [21] has 74 been introduced which its recurrent structure is formed 75 as an external loops and internal feedback.…”

Section: Introductionmentioning

confidence: 99%

Interactively recurrent fuzzy functions with multi objective learning and its application to chaotic time series prediction

Goudarzi

Khodabakhshi

Moradi

2016

IFS

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Fuzzy functions (FFs) models were introduced as an alternate representation of the fuzzy rule based approaches. This paper presents novel Interactively Recurrent Fuzzy Functions (IRFFs) for nonlinear chaotic time series prediction. Chaotic sequences are strongly dependent on their initial conditions as well as past states, therefore feed forward FFs models cannot perform properly. To overcome this weakness, recurrent structure of FFs is proposed by placing local and global feedbacks in the output parts of multidimensional subspaces. IRFFs' optimized parameters should minimize the output error and maximize clusters density. To achieve these contradictory goals, Non-dominated Sorting Genetic Algorithm II (NSGAII) is applied for simultaneously optimizing the objectives. Also, feedback loop parameters are tuned by utilizing gradient descent algorithm with line search strategy based on the strong Wolfe condition. The experimental setup includes comparative studies on prediction of benchmark chaotic sequences and real lung sound data. Further simulations demonstrate that our proposed approach effectively learns complex temporal sequences and outperforms fuzzy rule based approaches and feed forward FFs.

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Lacunary bounded variation sequence of fuzzy real numbers

Cited by 38 publications

References 13 publications

New type of Lacunary Orlicz difference sequence spaces generated by infinite matrices

New type of Lacunary Orlicz difference sequence spaces generated by infinite matrices

Statistically pre-Cauchy Fuzzy real-valued sequences defined by Orlicz function

Interactively recurrent fuzzy functions with multi objective learning and its application to chaotic time series prediction

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