On the fixed point theory of soft metric spaces

[EN] The aim of this paper is to show that a soft metric induces a compatible metric on the collection of all soft points of the absolute soft set, when the set of parameters is a finite set. We then show that soft metric extensions of several important fixed point theorems for metric spaces can be directly deduced from comparable existing results. We also present some examples to validate and illustrate our approach.Salvador Romaguera thanks the support of Ministry of Economy and Competitiveness of Spain, Grant MTM2012-37894-C02-01.Abbas, M.; Murtaza, G.; Romaguera Bonilla, S. (2016). On the fixed point theory of soft metric spaces. Fixed Point Theory and Applications. 2016(17):1-11. https://doi.org/10.1186/s13663-016-0502-yS111201617Zadeh, LA: Fuzzy sets. Inf. Control 8, 103-112 (1965)Molodtsov, D: Soft set theory - first results. Comput. Math. Appl. 37, 19-31 (1999)Aktaş, H, Çağman, N: Soft sets and soft groups. Inf. Sci. 177, 2726-2735 (2007)Ali, MI, Feng, F, Liu, X, Min, WK, Shabir, M: On some new operations in soft set theory. Comput. Math. Appl. 57, 1547-1553 (2009)Feng, F, Liu, X, Leoreanu-Fotea, V, Jun, YB: Soft sets and soft rough sets. Inf. Sci. 181, 1125-1137 (2011)Jiang, Y, Tang, Y, Chen, Q, Wang, J, Tang, S: Extending soft sets with description logics. Comput. Math. Appl. 59, 2087-2096 (2009)Jun, YB: Soft BCK/BCI-algebras. Comput. Math. Appl. 56, 1408-1413 (2008)Jun, YB, Lee, KJ, Khan, A: Soft ordered semigroups. Math. Log. Q. 56, 42-50 (2010)Jun, YB, Lee, KJ, Park, CH: Soft set theory applied to ideals in d-algebras. Comput. Math. Appl. 57, 367-378 (2009)Jun, YB, Park, CH: Applications of soft sets in ideal theory of BCK/BCI-algebras. Inf. Sci. 178, 2466-2475 (2008)Kong, Z, Gao, L, Wang, L, Li, S: The normal parameter reduction of soft sets and its algorithm. Comput. Math. Appl. 56, 3029-3037 (2008)Majumdar, P, Samanta, SK: Generalized fuzzy soft sets. Comput. Math. Appl. 59, 1425-1432 (2010)Li, F: Notes on the soft operations. ARPN J. Syst. Softw. 1, 205-208 (2011)Maji, PK, Roy, AR, Biswas, R: An application of soft sets in a decision making problem. Comput. Math. Appl. 44, 1077-1083 (2002)Qin, K, Hong, Z: On soft equality. J. Comput. Appl. Math. 234, 1347-1355 (2010)Xiao, Z, Gong, K, Xia, S, Zou, Y: Exclusive disjunctive soft sets. Comput. Math. Appl. 59, 2128-2137 (2009)Xiao, Z, Gong, K, Zou, Y: A combined forecasting approach based on fuzzy soft sets. J. Comput. Appl. Math. 228, 326-333 (2009)Xu, W, Ma, J, Wang, S, Hao, G: Vague soft sets and their properties. Comput. Math. Appl. 59, 787-794 (2010)Yang, CF: A note on soft set theory. Comput. Math. Appl. 56, 1899-1900 (2008)Yang, X, Lin, TY, Yang, J, Li, Y, Yu, D: Combination of interval-valued fuzzy set and soft set. Comput. Math. Appl. 58, 521-527 (2009)Zhu, P, Wen, Q: Operations on soft sets revisited (2012). arXiv:1205.2857v1Feng, F, Jun, YB, Liu, XY, Li, LF: An adjustable approach to fuzzy soft set based decision making. J. Comput. Appl. Math. 234, 10-20 (2009)Feng, F, Jun, YB, Zhao, X: Soft semirings. Comput. Math. Appl. 56, 2621-2628 (2008)Feng, F, Liu, X: Soft rough sets with applications to demand analysis. In: Int. Workshop Intell. Syst. Appl. (ISA 2009), pp. 1-4. (2009)Herawan, T, Deris, MM: On multi-soft sets construction in information systems. In: Emerging Intelligent Computing Technology and Applications with Aspects of Artificial Intelligence, pp. 101-110. Springer, Berlin (2009)Herawan, T, Rose, ANM, Deris, MM: Soft set theoretic approach for dimensionality reduction. In: Database Theory and Application, pp. 171-178. Springer, Berlin (2009)Kim, YK, Min, WK: Full soft sets and full soft decision systems. J. Intell. Fuzzy Syst. 26, 925-933 (2014). doi: 10.3233/IFS-130783Mushrif, MM, Sengupta, S, Ray, AK: Texture classification using a novel, soft-set theory based classification algorithm. Lect. Notes Comput. Sci. 3851, 246-254 (2006)Roy, AR, Maji, PK: A fuzzy soft set theoretic approach to decision making problems. J. Comput. Appl. Math. 203, 412-418 (2007)Zhu, P, Wen, Q: Probabilistic soft sets. In: IEEE Conference on Granular Computing (GrC 2010), pp. 635-638 (2010)Zou, Y, Xiao, Z: Data analysis approaches of soft sets under incomplete information. Knowl.-Based Syst. 21, 941-945 (2008)Cagman, N, Karatas, S, Enginoglu, S: Soft topology. Comput. Math. Appl. 62, 351-358 (2011)Das, S, Samanta, SK: Soft real sets, soft real numbers and their properties. J. Fuzzy Math. 20, 551-576 (2012)Das, S, Samanta, SK: Soft metric. Ann. Fuzzy Math. Inform. 6, 77-94 (2013)Abbas, M, Murtaza, G, Romaguera, S: Soft contraction theorem. J. Nonlinear Convex Anal. 16, 423-435 (2015)Chen, CM, Lin, IJ: Fixed point theory of the soft Meir-Keeler type contractive mappings on a complete soft metric space. Fixed Point Theory Appl. 2015, 184 (2015)Feng, F, Li, CX, Davvaz, B, Ali, MI: Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput. 14, 8999-9911 (2010)Maji, PK, Biswas, R, Roy, AR: Soft set theory. Comput. Math. Appl. 45, 555-562 (2003)Wardowski, D: On a soft mapping and its fixed points. Fixed Point Theory Appl. 2013, 182 (2013)Kannan, R: Some results on fixed points II. Am. Math. Mon. 76, 405-408 (1969)Meir, A, Keeler, E: A theorem on contraction mappings. J. Math. Anal. Appl. 28, 326-329 (1969)Caristi, J: Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 215, 241-251 (1976)Kirk, WA: Caristi’s fixed-point theorem and metric convexity. Colloq. Math. 36, 81-86 (1976

Symmetry in Applied Mathematics

Applied mathematics and symmetry work together as a powerful tool for problem reduction and solving. We are communicating applications in probability theory and statistics (A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested, The Asymmetric Alpha-Power Skew-t Distribution), fractals - geometry and alike (Khovanov Homology of Three-Strand Braid Links, Volume Preserving Maps Between p-Balls, Generation of Julia and Mandelbrot Sets via Fixed Points), supersymmetry - physics, nanostructures -chemistry, taxonomy - biology and alike (A Continuous Coordinate System for the Plane by Triangular Symmetry, One-Dimensional Optimal System for 2D Rotating Ideal Gas, Minimal Energy Configurations of Finite Molecular Arrays, Noether-Like Operators and First Integrals for Generalized Systems of Lane-Emden Equations), algorithms, programs and software analysis (Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory, On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems, On a Class of Optimal Fourth Order Multiple Root Solvers without Using Derivatives) to specific subjects (Facility Location Problem Approach for Distributed Drones, Parametric Jensen-Shannon Statistical Complexity and Its Applications on Full-Scale Compartment Fire Data). Diverse topics are thus combined to map out the mathematical core of practical problems

An intelligent system for risk classification of stock investment projects

The proposed paper demonstrates that a hybrid fuzzy neural network can serve as a risk classifier of stock investment projects. The training algorithm for the regular part of the network is based on bidirectional incremental evolution proving more efficient than direct evolution. The approach is compared with other crisp and soft investment appraisal and trading techniques, while building a multimodel domain representation for an intelligent decision support system. Thus the advantages of each model are utilised while looking at the investment problem from different perspectives. The empirical results are based on UK companies traded on the London Stock Exchange

Investigating the impact of combining handwritten signature and keyboard keystroke dynamics for gender prediction

© 2019 IEEE. The use of soft-biometric data as an auxiliary tool on user identification is already well known. Gender, handorientation and emotional state are some examples which can be called soft-biometrics. These soft-biometric data can be predicted directly from the biometric templates. It is very common to find researches using physiological modalities for soft-biometric prediction, but behavioural biometric is often not well explored for this context. Among the behavioural biometric modalities, keystroke dynamics and handwriting signature have been widely explored for user identification, including some soft-biometric predictions. However, in these modalities, the soft-biometric prediction is usually done in an individual way. In order to fill this space, this study aims to investigate whether the combination of those two biometric modalities can impact the performance of a soft-biometric data, gender prediction. The main aim is to assess the impact of combining data from two different biometric sources in gender prediction. Our findings indicated gains in terms of performance for gender prediction when combining these two biometric modalities, when compared to the individual ones

Soft-Decision-Driven Channel Estimation for Pipelined Turbo Receivers

We consider channel estimation specific to turbo equalization for multiple-input multiple-output (MIMO) wireless communication. We develop a soft-decision-driven sequential algorithm geared to the pipelined turbo equalizer architecture operating on orthogonal frequency division multiplexing (OFDM) symbols. One interesting feature of the pipelined turbo equalizer is that multiple soft-decisions become available at various processing stages. A tricky issue is that these multiple decisions from different pipeline stages have varying levels of reliability. This paper establishes an effective strategy for the channel estimator to track the target channel, while dealing with observation sets with different qualities. The resulting algorithm is basically a linear sequential estimation algorithm and, as such, is Kalman-based in nature. The main difference here, however, is that the proposed algorithm employs puncturing on observation samples to effectively deal with the inherent correlation among the multiple demapper/decoder module outputs that cannot easily be removed by the traditional innovations approach. The proposed algorithm continuously monitors the quality of the feedback decisions and incorporates it in the channel estimation process. The proposed channel estimation scheme shows clear performance advantages relative to existing channel estimation techniques.Comment: 11 pages; IEEE Transactions on Communications 201

Adaptive and Iterative Multi-Branch MMSE Decision Feedback Detection Algorithms for MIMO Systems

In this work, decision feedback (DF) detection algorithms based on multiple processing branches for multi-input multi-output (MIMO) spatial multiplexing systems are proposed. The proposed detector employs multiple cancellation branches with receive filters that are obtained from a common matrix inverse and achieves a performance close to the maximum likelihood detector (MLD). Constrained minimum mean-squared error (MMSE) receive filters designed with constraints on the shape and magnitude of the feedback filters for the multi-branch MMSE DF (MB-MMSE-DF) receivers are presented. An adaptive implementation of the proposed MB-MMSE-DF detector is developed along with a recursive least squares-type algorithm for estimating the parameters of the receive filters when the channel is time-varying. A soft-output version of the MB-MMSE-DF detector is also proposed as a component of an iterative detection and decoding receiver structure. A computational complexity analysis shows that the MB-MMSE-DF detector does not require a significant additional complexity over the conventional MMSE-DF detector, whereas a diversity analysis discusses the diversity order achieved by the MB-MMSE-DF detector. Simulation results show that the MB-MMSE-DF detector achieves a performance superior to existing suboptimal detectors and close to the MLD, while requiring significantly lower complexity.Comment: 10 figures, 3 tables; IEEE Transactions on Wireless Communications, 201