Research on fuzzy sets

[EN] This paper explores the advancements in soft sets and their extensions, contributing to the evolving field of soft computing. Soft sets, introduced by Molodtsov, provide a flexible framework for handling uncertainty and imprecision in decision-making processes. The research delves into various extensions of soft sets, including hybrid models with other mathematical structures, enhancing their applicability in diverse domains. Novel methodologies for parameterization and optimization within soft sets are investigated, aiming to improve their efficiency and effectiveness in real-world applications. The study emphasizes the integration of soft sets with machine learning techniques, fostering the development of intelligent systems capable of handling complex and uncertain information. The findings showcase the versatility and potential of soft sets and their extensions, opening new avenues for future research in this dynamic field

SOME PROPERTIES OF SOFT b-I-COMPACT AND SOFT GENERALIZED b-I-COMPACT TOPOLOGICAL SPACE

The main object of this paper is to study the relation between some types of weak soft compactness and soft ideals. We initiate new types of soft compactness modulo an soft ideal that generalize the concepts soft b-I-compact, we study some of their properties and characterizations. This paper, not only can form the theoretical basis for further applications of topology on soft sets, but also lead to the development of information systems. Keyword: Soft set, Soft topological space, Soft interior, Soft closure, Soft b-I-Compact space, Soft b-closed, Soft b#-closed, Soft generalized b-I-Compact spac

A capacity sharing and stealing strategy for open real-time systems

This paper focuses on the scheduling of tasks with hard and soft real-time constraints in open and dynamic real-time systems. It starts by presenting a capacity sharing and stealing (CSS) strategy that supports the coexistence of guaranteed and non-guaranteed bandwidth servers to efficiently handle soft-tasks’ overloads by making additional capacity available from two sources: (i) reclaiming unused reserved capacity when jobs complete in less than their budgeted execution time and (ii) stealing reserved capacity from inactive non-isolated servers used to schedule best-effort jobs. CSS is then combined with the concept of bandwidth inheritance to efficiently exchange reserved bandwidth among sets of inter-dependent tasks which share resources and exhibit precedence constraints, assuming no previous information on critical sections and computation times is available. The proposed Capacity Exchange Protocol (CXP) has a better performance and a lower overhead when compared against other available solutions and introduces a novel approach to integrate precedence constraints among tasks of open real-time systems

Soft set theory and topology

[EN] In this paper we study and discuss the soft set theory giving new definitions, examples, new classes of soft sets, and properties for mappings between different classes of soft sets. Furthermore, we investigate the theory of soft topological spaces and we present new definitions, characterizations, and properties concerning the soft closure, the soft interior, the soft boundary, the soft continuity, the soft open and closed maps, and the soft homeomorphism.Georgiou, DN.; Megaritis, AC. (2014). Soft set theory and topology. Applied General Topology. 15(1):93-109. doi:http://dx.doi.org/10.4995/agt.2014.2268.93109151Aktaş, H., & Çağman, N. (2007). Soft sets and soft groups. Information Sciences, 177(13), 2726-2735. doi:10.1016/j.ins.2006.12.008Ali, M. I., Feng, F., Liu, X., Min, W. K., & Shabir, M. (2009). On some new operations in soft set theory. Computers & Mathematics with Applications, 57(9), 1547-1553. doi:10.1016/j.camwa.2008.11.009Aygünoğlu, A., & Aygün, H. (2011). Some notes on soft topological spaces. Neural Computing and Applications, 21(S1), 113-119. doi:10.1007/s00521-011-0722-3Çağman, N., & Enginoğlu, S. (2010). Soft set theory and uni–int decision making. European Journal of Operational Research, 207(2), 848-855. doi:10.1016/j.ejor.2010.05.004Çağman, N., & Enginoğlu, S. (2010). Soft matrix theory and its decision making. Computers & Mathematics with Applications, 59(10), 3308-3314. doi:10.1016/j.camwa.2010.03.015Çağman, N., Karataş, S., & Enginoglu, S. (2011). Soft topology. Computers & Mathematics with Applications, 62(1), 351-358. doi:10.1016/j.camwa.2011.05.016Chen, D., Tsang, E. C. C., Yeung, D. S., & Wang, X. (2005). The parameterization reduction of soft sets and its applications. Computers & Mathematics with Applications, 49(5-6), 757-763. doi:10.1016/j.camwa.2004.10.036Feng, F., Jun, Y. B., & Zhao, X. (2008). Soft semirings. Computers & Mathematics with Applications, 56(10), 2621-2628. doi:10.1016/j.camwa.2008.05.011Hussain, S., & Ahmad, B. (2011). Some properties of soft topological spaces. Computers & Mathematics with Applications, 62(11), 4058-4067. doi:10.1016/j.camwa.2011.09.051O. Kazanci, S. Yilmaz and S. Yamak, Soft Sets and Soft BCH-Algebras, Hacettepe Journal of Mathematics and Statistics 39, no. 2 (2010), 205-217.KHARAL, A., & AHMAD, B. (2011). MAPPINGS ON SOFT CLASSES. New Mathematics and Natural Computation, 07(03), 471-481. doi:10.1142/s1793005711002025Maji, P. K., Roy, A. R., & Biswas, R. (2002). An application of soft sets in a decision making problem. Computers & Mathematics with Applications, 44(8-9), 1077-1083. doi:10.1016/s0898-1221(02)00216-xMaji, P. K., Biswas, R., & Roy, A. R. (2003). Soft set theory. Computers & Mathematics with Applications, 45(4-5), 555-562. doi:10.1016/s0898-1221(03)00016-6P. K. Maji, R. Biswas and A. R. Roy, Fuzzy soft sets, J. Fuzzy Math. 9, no. 3 (2001), 589-602.MAJUMDAR, P., & SAMANTA, S. K. (2008). SIMILARITY MEASURE OF SOFT SETS. New Mathematics and Natural Computation, 04(01), 1-12. doi:10.1142/s1793005708000908Min, W. K. (2011). A note on soft topological spaces. Computers & Mathematics with Applications, 62(9), 3524-3528. doi:10.1016/j.camwa.2011.08.068Molodtsov, D. (1999). Soft set theory—First results. Computers & Mathematics with Applications, 37(4-5), 19-31. doi:10.1016/s0898-1221(99)00056-5D. A. Molodtsov, The description of a dependence with the help of soft sets, J. Comput. Sys. Sc. Int. 40, no. 6 (2001), 977-984.D. A. Molodtsov, The theory of soft sets (in Russian), URSS Publishers, Moscow, 2004.D. A. Molodtsov, V. Y. Leonov and D. V. Kovkov, Soft sets technique and its application, Nechetkie Sistemy i Myagkie Vychisleniya 1, no. 1 (2006), 8-39.D. Pei and D. Miao, From soft sets to information systems, In: X. Hu, Q. Liu, A. Skowron, T. Y. Lin, R. R. Yager, B. Zhang, eds., Proceedings of Granular Computing, IEEE, 2 (2005), 617-621.Shabir, M., & Naz, M. (2011). On soft topological spaces. Computers & Mathematics with Applications, 61(7), 1786-1799. doi:10.1016/j.camwa.2011.02.006Shao, Y., & Qin, K. (2011). The lattice structure of the soft groups. Procedia Engineering, 15, 3621-3625. doi:10.1016/j.proeng.2011.08.678I. Zorlutuna, M. Akdag, W. K. Min and S. Atmaca, Remarks on soft topological spaces, Annals of Fuzzy Mathematics and Informatics 3, no. 2 (2012), 171-185.Zou, Y., & Xiao, Z. (2008). Data analysis approaches of soft sets under incomplete information. Knowledge-Based Systems, 21(8), 941-945. doi:10.1016/j.knosys.2008.04.00

Cybernetics, Fuzziness and Scientific Revolutions

Settimo Termini ​pioneered along with Aldo de Luca the concept of fuzziness measures in the sixties. Today he is a Full Professor of Theoretical Computer Science at the University of Palermo and an affiliated researcher at the European Center for Soft Computing, Mieres (Asturias), Spain. He has directed from 2002 to 2009 the Istituto di Cibernetica "Eduardo Caianiello" of CNR (National Research Council) in Italy. Among his scientific interests, the introduction and formal development of the theory of (entropy) measures of fuzziness; an analysis in innovative terms of the notion of vague predicate as it appears and is used in Information Sciences, Cybernetics and AI. Recently he has been interested also in the connections between scientific research and economic development and the conceptual foundations of Fuzzy Sets and Soft Computing. He is Fellow of the International Fuzzy Systems Association and of the Accademia Nazionale di Scienze, Lettere ed Arti of Palermo. In 2015 he will be 70, and we want to celebrate his birthday with the Soft Computing community with this interview where he discusses history of Cybernetics. The interview was conducted in Italian and translated by the authors

New Trends in Neutrosophic Theory and Applications Volume II

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, by many authors around the world. Also, an international journal - Neutrosophic Sets and Systems started its journey in 2013. Single valued neutrosophic sets have found their way into several hybrid systems, such as neutrosophic soft set, rough neutrosophic set, neutrosophic bipolar set, neutrosophic expert set, rough bipolar neutrosophic set, neutrosophic hesitant fuzzy set, etc. Successful applications of single valued neutrosophic sets have been developed in multiple criteria and multiple attribute decision making. This second volume collects original research and application papers from different perspectives covering different areas of neutrosophic studies, such as decision making, graph theory, image processing, probability theory, topology, and some theoretical papers. This volume contains four sections: DECISION MAKING, NEUTROSOPHIC GRAPH THEORY, IMAGE PROCESSING, ALGEBRA AND OTHER PAPERS. First paper (Pu Ji, Peng-fei Cheng, Hongyu Zhang, Jianqiang Wang. Interval valued neutrosophic Bonferroni mean operators and the application in the selection of renewable energy) aims to construct selection approaches for renewable energy considering the interrelationships among criteria. To do that, Bonferroni mean (BM) and geometric BM (GBM) are employed

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. 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Using machine learning techniques to evaluate multicore soft error reliability

Virtual platform frameworks have been extended to allow earlier soft error analysis of more realistic multicore systems (i.e., real software stacks, state-of-the-art ISAs). The high observability and simulation performance of underlying frameworks enable to generate and collect more error/failurerelated data, considering complex software stack configurations, in a reasonable time. When dealing with sizeable failure-related data sets obtained from multiple fault campaigns, it is essential to filter out parameters (i.e., features) without a direct relationship with the system soft error analysis. In this regard, this paper proposes the use of supervised and unsupervised machine learning techniques, aiming to eliminate non-relevant information as well as identify the correlation between fault injection results and application and platform characteristics. This novel approach provides engineers with appropriate means that able are able to investigate new and more efficient fault mitigation techniques. The underlying approach is validated with an extensive data set gathered from more than 1.2 million fault injections, comprising several benchmarks, a Linux OS and parallelization libraries (e.g., MPI, OpenMP), as well as through a realistic automotive case study