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Synergies in Analysis, Discrete Mathematics, Soft Computing and ModellingНазвание: Synergies in Analysis, Discrete Mathematics, Soft Computing and Modelling
Автор: P.V. Subrahmanyam, V. Antony Vijesh, Balasubramaniam Jayaram, Prakash Veeraraghavan
Издательство: Springer
Серия: Forum for Interdisciplinary Mathematics
Год: 2023
Страниц: 225
Язык: английский
Формат: pdf (true), epub
Размер: 35.3 MB

In real-life situations, we come across problems that comprise imprecise or uncertain, simple or complex information that needs to be analyzed for various requirements. To tackle this situation, Zadeh in 1965 formulated the concept of a fuzzy set, which in an imprecise environment that captured the inexactness present in a system. Later, Zadeh elucidated the concept of linguistic variables to handle situations that involved less preciseness in humanistic systems. This was further studied by several researchers using appropriate quantification of fuzziness on kinds of fuzzy numbers. To process and analyze the features connected with entities in such a scenario, fuzzy information systems were studied in the literature.

On the other hand, the concept of a soft set as a mathematical tool for dealing with uncertainty was introduced by Molodtsov in 1999. In soft set theory, the parameterization tool involved in the concepts played a major role and had drawn the attention of many researchers over the years which led to the rapid development of the theory. A combination of soft sets with fuzzy sets was noticed by some researchers as more rewarding to capture the nature of entities in the problem in hand viewed as an information system.

Optical Flow estimation is one of the most challenging problems in Computer Vision. Optical flow is defined as the per-pixel motion between two consecutive digital images. Optical flow has many applications, such as video post-production, particle velocimetry, video compression, control of autonomous vehicles, and many others. Since the seminal work of "Determining optical flow", many contributions have been made in order to improve the optical flow estimation. In that work, the authors proposed a variational model to estimate the optical flow. The proposal is an energy model to estimate the optical flow estimation error, and the argument that minimizes that energy is the optical flow of the sequence of images. The proposal is a model that uses a quadratic error, and it means that the model is susceptible to outliers and the presence of noise. Zach et al. proposed another model based on the absolute value of the error. All those models in an iterative way minimize the energy error model. In each iteration, some of them filter the optical estimation to eliminate noise or outliers, avoiding noise and outliers propagating across the iterations.

L.A. Zadeh in 1965 set forth the exceptional concept of fuzzy sets, that have Brobdingnagian applications in several fields of study. In 1986, a generalization of fuzzy sets was created by Atanassov, which is understood as Intuitionistic fuzzy sets (IFS). In IFS, in addition to one membership grade, there will additionally be another grade called non-membership grade that’s hooked up to every part. To boot, there’s a restriction that the total of those two grades at most be unity. A new theory was introduced by Smarandache in 1999, called neutrosophic sets and logic. Uncertainty describes a lack of knowledge in one’s knowledge but whereas ambiguity describes the ability to entertain more than in one interpretation. Thus, Neutrosophic set is used to deal with incomplete, indeterminate, and inconsistent information present in the real world. A neutrosophic set (NS) is employed to tackle uncertainty using the truth membership, indeterminacy membership, and falsity membership grades which are considered to be independent. The generalization of IFS is the neutrosophic sets since there is no restriction between the degree of truth, indeterminacy, falsity. Applications of Neutrosophic set can be found in the field of medicine, information technology, information system, decision support system, etc.

Both the invited articles and submitted papers were broadly grouped under three heads: Part 1 on analysis and modeling (six chapters), Part 2 on discrete mathematics and applications (six chapters), and Part 3 on fuzzy sets and soft computing (three chapters):

1. The Second- and Third-Order Hermitian Toeplitz Determinants for Some Subclasses of Analytic Functions Associated with Exponential Function
2. Some Results on a Starlike Class with Respect to (j, m)-Symmetric Functions
3. Experimental Evaluation of Four Intermediate Filters to Improve the Motion Field Estimation
4. On the Derivative of a Polynomial
5. On the Problem of Pricing a Double Barrier Option in a Modified Black-Scholes Environment
6. Caputo Sequential Fractional Differential Equations with Applications
7. Herscovici’s Conjecture on Product of Some Complete Bipartite Graphs
8. On Fault-Tolerant Metric Dimension of Heptagonal Circular Ladder and Its Related Graphs
9. BKS Fuzzy Inference Employing h-Implications
10. Note on Distributivity of Different String Operations Over Language Sets
11. A Generalization of -Binding Functions
12. A Short Proof of Ore’s f-Factor Theorem Using Flows
13. A Decision-Making Problem Involving Soft Fuzzy Number Valued Information System: Energy-Efficient Light-Emitting Diode Blubs
14. Role of Single Valued Linear Octagonal Neutrosophic Numbers in Multi-attribute Decision-Making Problems

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