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If general relativity is correct, then the origin of the universe is a simple mathematical problem. The Friedmann equation in cosmology is a well-structured ordinary differential equation, and the global properties of its solutions can be qualitatively analyzed by the phase-trajectory method. In this paper we show that the total energy density of matter in the universe is positive, and the total pressure near the Big Bang is negative. By analyzing the global properties of the solutions to the Friedmann equation according to these two conditions of state functions, we find that the Big Bang is impossible, and the space must be a closed 3-dimensional sphere, the cosmological constant is likely to be zero, and the evolution of the universe should be cyclic. The analysis and the proof are simple and straight forward, therefore these conclusions should be reliable.
Fermat’s last theorem appears not as a unique property of natural numbers but as the bottom line of extended possible issues involving larger dimensions and powers when observed from a natural vector space viewpoint. The fabric of this general Fermat’s theorem structure consists of a well-defined set of vectors associated with dimensional vector spaces and the Minkowski norms one can define there. Here, a special vector set is studied and named a Fermat surface. Besides, a connection between Fermat surfaces and hypercubes is unveiled.
A new product for soft sets with its decision-making: Soft lambda-product
Article ID: 3139
Vol 3, Issue 1, 2025
DOI: https://doi.org/10.54517/mss3139
Vol 3, Issue 1, 2025
Received: 28 December 2024; Accepted: 3 February 2025; Available online: 17 February 2025; Issue release: 31 March 2025
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Abstract
Soft sets provide a strong mathematical foundation for managing uncertainty and inventing solutions to parametric data problems. Soft set operations are fundamental elements within soft set theory. In this paper, we introduce a new product operation for soft sets, called the “soft lambda-product,” and thoroughly examine its algebraic properties in relation to various types of soft equalities and subsets. By studying the distribution of the soft lambda-product over different soft set operations, we further investigate its relationship with other soft set operations. We conclude with an example demonstrating the method’s effectiveness across various applications, employing the int-uni operator and int-uni decision function within the soft lambda-product for the int-uni decision-making method, which identifies an optimal set of elements from available options. This work significantly contributes to the soft set literature, as the theoretical foundations of soft computing methods rely on solid mathematical principles.
Keywords
soft set; soft lambda-product; soft subset; soft equal relations
References
Zadeh LA. Fuzzy sets. Inform. Control. 1965; 8: 338–353.
Molodtsov D. Soft set theory-First results. Comput. Math. Appl. 1999; 37: 19–31.
Maji PK, Roy AR, Biswas R. An application of soft sets in a decision making problem, Comput. Math. Appl. 2002; 44: 1077–1083.
Chen D, Tsang ECC, Yeung DS. Some notes on the parameterization reduction of soft sets. Int Conf Mach Learn Cyber. 2003; 3: 1442–1445.
Chen D, Tsang ECC, Yeung DS, et al. The parameterization reduction of soft sets and its applications. Computers & Mathematics with Applications. 2005; 49(5–6): 757–763. doi: 10.1016/j.camwa.2004.10.036
Xiao Z, Chen, L, Zhong B, Ye S. Recognition for soft information based on the theory of soft sets. In: Proceedings of the IEEE proceedings of ICSSSM-05; 2005. pp 1104–1106.
Mushrif MM, Sengupta S, Ray AK. (2006). Texture Classification Using a Novel, Soft-Set Theory Based Classification Algorithm. In: Narayanan PJ, Nayar SK, Shum HY. (editors). Computer Vision—ACCV 2006. Springer, Berlin, Heidelberg; 2006.
Herawan T, Deris MM. A Direct Proof of Every Rough Set is a Soft Set. In: Proceedings of the 2009 Third Asia International Conference on Modelling & Simulation; 2009. pp. 119–124.
Herawan T, Deris MM. Soft Decision Making for Patients Suspected Influenza. In: Proceedings of the Computational Science and Its Applications—ICCSA 2010. Springer, Berlin, Heidelberg; 2010.
Herawan T. Soft set-based decision making for patients suspected influenza-like illness. Int J Mod Phys Conf Ser. 2010; 1: 1–5.
Çağman N, Enginoğlu S. Soft set theory and uni–int decision making. European Journal of Operational Research. 2010; 207(2): 848–855. doi: 10.1016/j.ejor.2010.05.004
Çağman N, Enginoğlu S. Soft matrix theory and its decision making. Computers & Mathematics with Applications. 2010; 59(10): 3308–3314. doi: 10.1016/j.camwa.2010.03.015
Gong K, Xiao Z, Zhang X. The bijective soft set with its operations. Computers & Mathematics with Applications. 2010; 60(8): 2270–2278. doi: 10.1016/j.camwa.2010.08.017
Xiao Z, Gong K, Xia S, et al. Exclusive disjunctive soft sets. Computers & Mathematics with Applications. 2010; 59(6): 2128–2137. doi: 10.1016/j.camwa.2009.12.018
Feng F, Li Y, Çağman N. Generalized uni-int decision making schemes based on choice value soft sets. European Journal of Operational Research. 2012; 220(1): 162–170. doi: 10.1016/j.ejor.2012.01.015
Feng Q, Zhou Y. Soft discernibility matrix and its applications in decision making. Applied Soft Computing. 2014; 24: 749–756. doi: 10.1016/j.asoc.2014.08.042
Kharal A. Soft Approximations and Uni-Int Decision Making. The Scientific World Journal. 2014; 2014: 1–7. doi: 10.1155/2014/327408
Dauda MK, Mamat M, Waziri MY. An Application of Soft Set in Decision Making. Jurnal Teknologi. 2015; 77(13): 119–122. doi: 10.11113/jt.v77.6367
Inthumathi V, Chitra V, Jayasree S. The role of operators on soft set in decision making problems. International Journal of Computational and Applied Mathematics. 2017; 12(3): 899–910.
Atagün AO, Kamacı H, Oktay O. Reduced soft matrices and generalized products with applications in decision making. Neural Computing and Applications. 2018; 29(9): 445–456. doi: 10.1007/s00521-016-2542-y
Kamacı H, Saltık K, Fulya Akız H, et al. Cardinality inverse soft matrix theory and its applications in multicriteria group decision making. Journal of Intelligent & Fuzzy Systems. 2018; 34(3): 2031–2049. doi: 10.3233/jifs-17876
Yang J, Yao Y. Semantics of soft sets and three-way decision with soft sets. Knowledge-Based Systems. 2020; 194: 105538. doi: 10.1016/j.knosys.2020.105538
Petchimuthu S, Garg H, Kamacı H, et al. The mean operators and generalized products of fuzzy soft matrices and their applications in MCGDM. Computational and Applied Mathematics. 2020; 39(2): 1–32. doi: 10.1007/s40314-020-1083-2
Zorlutuna İ. Soft set-valued mappings and their application in decision making problems. Filomat. 2021; 35(5): 1725–1733. doi: 10.2298/fil2105725z
Maji PK, Biswas R, Roy AR. Soft set theory. Comput. Math. Appl. 2003; 45: 555–562.
Pei D, Miao D. From soft sets to information systems. In: Proceedings of the 2005 IEEE International Conference on Granular Computing; 2005. pp. 617–621.
Ali MI, Feng F, Liu X, et al. On some new operations in soft set theory. Computers & Mathematics with Applications. 2009; 57(9): 1547–1553. doi: 10.1016/j.camwa.2008.11.009
Yang CF. A note on: “Soft set theory” [Computers & Mathematics with Applications. 45(4–5) (2003) 555–562]. Computers & Mathematics with Applications. 2008; 56(7): 1899–1900.
Feng F, Li C, Davvaz B, et al. Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Computing. 2010; 14(9): 899–911. doi: 10.1007/s00500-009-0465-6
Jiang Y, Tang Y, Chen Q, et al. Extending soft sets with description logics. Computers & Mathematics with Applications. 2010; 59(6): 2087–2096. doi: 10.1016/j.camwa.2009.12.014
Ali MI, Shabir M, Naz M. Algebraic structures of soft sets associated with new operations. Computers & Mathematics with Applications. 2011; 61(9): 2647–2654. doi: 10.1016/j.camwa.2011.03.011
Yang CF. A note on “Soft Set Theory” [Comput. Math. Appl. 45 (4–5) (2003) 555–562]. Computers & Mathematics with Applications. 2008; 56(7): 1899–1900. doi: 10.1016/j.camwa.2008.03.019
Neog TJ, Sut DK. A new approach to the theory of soft sets. International journal of computer applications. 2011; 32(2): 1–6.
Li F. Notes on the soft operations. ARPN journal of systems and software. 2011; 1(6): 205–208.
Ge X, Yang S. Investigations on some operations of soft sets. World academy of science engineering and technology. 2011; 75: 1113–1116.
Singh D, Onyeozili IA. Notes on soft matrices operations. ARPN journal of science and technology. 2012; 2(9): 861–869.
Singh D, A. Onyeozili I. On Some New Properties of Soft Set Operations. International Journal of Computer Applications. 2012; 59(4): 39–44. doi: 10.5120/9538-3975
Singh D, Onyeozili IA. Some results on distributive and absorption properties on soft operations. IOSR journal of mathematics. 2012; 4(2): 18–30.
Singh D, Onyeozili IA. Some conceptual misunderstandings of the fundamentals of soft set theory. ARPN journal of systems and software. 2012; 2(9): 251–254.
Zhu P, Wen Q. Operations on Soft Sets Revisited. Journal of Applied Mathematics. 2013; 2013: 1–7. doi: 10.1155/2013/105752
Sen J. On algebraic structure of soft sets. Annals of fuzzy mathematics and informatics. 2014; 7(6): 1013–1020.
Eren ÖF, Çalışıcı H. On some operations of soft sets. In: Proceedings of the fourth international conference on computational mathematics and engineering sciences (CMES-2019); 2019.
Stojanović N. A new operation on soft sets: 791 extended symmetric difference of soft sets. Vojnotehnicki glasnik. 2021; 69(4): 779–791. doi: 10.5937/vojtehg69-33655
Sezgin A, Yavuz E. A new soft set operation: Soft binary piecewise symmetric difference operation. Necmettin erbakan university journal of science and engineering. 2023; 5(2): 189–208.
Sezgin A, Sarıalioğlu M. A new soft set operation: Complementary soft binary piecewise theta operation. Journal of kadirli faculty of applied sciences. 2024; 4(2): 325–357.
Sezgin A, Çağman N. A new soft set operation: Complementary soft binary piecewise difference operation. Osmaniye korkut ata university journal of the institute of science and technology. 2024; 7(1): 58–94. doi: 10.47495/okufbed.1308379
Sezgin A, Nur Aybek F, Bilgili Güngör N. A new soft set operation: Complementary soft binary piecewise union operation. Acta Informatica Malaysia. 2023; 7(1): 38–53. doi: 10.26480/aim.01.2023.38.53
Sezgin A, Dagtoros K. Complementary soft binary piecewise symmetric difference operation: A novel soft set operation. Scientific Journal of Mehmet Akif Ersoy University. 2023; 6(2): 31–45.
Sezgin A, Çalışıcı H. A comprehensive study on soft binary piecewise difference operation. Eskişehir Technical University Journal of Science and Technology B- Theoretical Sciences. 2024; 12(1): 32–54. doi: 10.20290/estubtdb.1356881
Qin K, Hong Z. On soft equality. Journal of Computational and Applied Mathematics. 2010; 234(5): 1347–1355. doi: 10.1016/j.cam.2010.02.028
Jun YB, Yang X. A note on the paper “Combination of interval-valued fuzzy set and soft set” [Comput. Math. Appl. 58 (2009) 521–527]. Computers & Mathematics with Applications. 2011; 61(5): 1468–1470. doi: 10.1016/j.camwa.2010.12.077
Liu X, Feng F, Jun YB. A note on generalized soft equal relations. Computers & Mathematics with Applications. 2012; 64(4): 572–578. doi: 10.1016/j.camwa.2011.12.052
Feng F, Li Y. Soft subsets and soft product operations. Information Sciences. 2013; 232: 44–57. doi: 10.1016/j.ins.2013.01.001
Abbas M, Ali B, Romaguera S. On generalized soft equality and soft Lattice structure. Filomat. 2014; 28(6): 1191–1203. doi: 10.2298/fil1406191a
Abbas M, Ali M, Romaguera S. Generalized operations in soft set theory via relaxed conditions on parameters. Filomat. 2017; 31(19): 5955–5964. doi: 10.2298/fil1719955a
Al-Shami T. Investigation and corrigendum to some results related to g-soft equality and gf -soft equality relations. Filomat. 2019; 33(11): 3375–3383. doi: 10.2298/fil1911375a
Al-Shami TM, El-Shafei ME. T-soft equality relation. TURKISH JOURNAL OF MATHEMATICS. 2020; 44(4): 1427–1441. doi: 10.3906/mat-2005-117
Ali B, Saleem N, Sundus N, et al. A Contribution to the Theory of Soft Sets via Generalized Relaxed Operations. Mathematics. 2022; 10(15): 2636. doi: 10.3390/math10152636
Sezgin A, Atagün A, Çağman N. A complete study on and-product of soft sets. Sigma Journal of Engineering and Natural Sciences. 2024; 42(6).
Çağman N. Conditional complements of sets and their application to group theory. Journal of New Results in Science. 2021; 10(3): 67–74. doi: 10.54187/jnrs.1003890
Sezgin A, Çağman N, Atagün AO, et al. Complemental Binary Operations of Sets and Their Application to Group Theory. Matrix Science Mathematic. 2023; 7(2): 114–121. doi: 10.26480/msmk.02.2023.114.121
Sezgin A, Aybek FN, Stojanovic N. An in-depth analysis of restricted and extended lambda operations for soft sets. Optimality. 2024; 1(2): 232-261. https://doi.org/10.22105/opt.v1i2.55
Sezgin A, Yavuz E. A New Soft Set Operation: Complementary Soft Binary Piecewise Lambda Operation. Sinop Üniversitesi Fen Bilimleri Dergisi. 2024; 8(2): 101–133.
Sezgin A, Yavuz E, Özlü Ş. Insight into soft binary piecewise lambda operation: a new operation for soft sets. Journal of Umm Al-Qura University for Applied Sciences. 2024; 10 (4). doi: 10.1007/s43994-024-00187-1
Sezer AS, Atagün AO, Çağman N. A new view to N-group theory: soft N-groups. Fasciculi mathematici. 2013; 51: 123–140.
Sezer AS. Certain characterizations of LA-semigroups by soft sets. Journal of Intelligent & Fuzzy Systems. 2014; 27(2): 1035–1046. doi: 10.3233/ifs-131064
Sezer AS. A new approach to LA-semigroup theory via the soft sets. Journal of Intelligent & Fuzzy Systems. 2014; 26(5): 2483–2495. doi: 10.3233/ifs-130918
Sezer AS, Çağman N, Atagün AO. Soft intersection interior ideals, quasi-ideals and generalized bi-ideals: a new approach to semigroup theory II. journal of multiple-valued logic and soft computing. 2014; 23(1–2), 161–207.
Sezer AS, Atagün AO, Çağman N. N-group SI-action and its applications to N-Group Theory. Fasciculi mathematici. 2014; 52: 139–153.
Sezer AS, Çağman N, Atagün AO. Uni-soft substructures of groups. Annals of fuzzy mathematics and informatics. 2015; 9(2): 235–246.
Atagün AO, Sezer AS. Soft sets, soft semimodules and soft substructures of semimodules. Mathematical sciences letters. 2015; 4(3): 235–242.
Gulistan M, Shahzad M. On soft KU-algebras. Journal of Algebra, Number Theory: Advances and Applications. 2014; 11(1): 1–20.
Gulistan M, Khan M, Yaqoob N, et al. Structural Properties of Cubic Sets in Regular LA-semihypergroups. Fuzzy Information and Engineering. 2017; 9(1): 93–116. doi: 10.1016/j.fiae.2017.03.005
Sezer AS, Atagün AO. A new kind of vector space: soft vector space. South east asian bulletin of mathematics. 2016; 40: 753–770.
Gulistan M, Beg I, Yaqoob N. A new approach in decision making problems under the environment of neutrosophic cubic soft matrices. Journal of Intelligent & Fuzzy Systems. 2019; 36(1): 295–307. doi: 10.3233/jifs-181296
Khan M, Davvaz B, Yaqoob N, Gulistan M, Khalaf MM. On (e,evqk) -intuitionistic (fuzzy ideals, fuzzy soft ideals) of subtraction algebras. Songklanakarin J. Sci. Technol. 2015; 37 (4): 465–475.
Rehman I, Gulistan M, Asif GM, Nawaz S. Structures of generalized fuzzy sets in non-associative rings. International Journal of Pure and Applied Mathematics.2017; 113(2): 299–325.
Yaqoob N, Gulistan M, Tang J, et al. On generalized fuzzy hyperideals in ordered LA-semihypergroups. Computational and Applied Mathematics. 2019; 38(3): 124. doi: 10.1007/s40314-019-0876-7
Jana C, Pal M, Karaaslan F, Sezgi̇n A. (α, β)-soft intersectional rings and ideals with their applications. New Mathematics and Natural Computation. 2019; 15(2): 333–350. doi: 10.1142/S1793005719500182
Sezgin A, Orbay M. Analysis of semigroups with soft intersection ideals. Acta Universitatis Sapientiae, Mathematica. 2022; 14(1): 166–210. doi: 10.2478/ausm-2022-0012
Atagün AO, Kamacı H, Taştekin İ, Sezgin A. P-properties in Near-rings. Journal of Mathematical and Fundamental Sciences. 2019; 51(2): 152–167.
Khan SK, Gulistan M, Wahab HA. Development of the structure of q-Rung Orthopair Fuzzy Hypersoft Set with basic Operations. Punjab University Journal of Mathematics. 2022: 881–892. doi: 10.52280/pujm.2021.531204
Khan A, Izhar M, Sezgin A. Characterizations of Abel Grassmann's Groupoids by the properties of their double-framed soft ideals. International Journal of Analysis and Applications. 2017; 15(1): 62–74.
Khan S, Gulistan M, Kausar N, et al. Analysis of Cryptocurrency Market by Using q‐Rung Orthopair Fuzzy Hypersoft Set Algorithm Based on Aggregation Operators. Complexity. 2022; 2022(1). doi: 10.1155/2022/7257449
Naeem K, Memiş S. Picture fuzzy soft $$sigma$$-algebra and picture fuzzy soft measure and their applications to multi-criteria decision-making. Granular Computing. 2022; 8(2): 397–410. doi: 10.1007/s41066-022-00333-2
Gulistan M, Hassan N. A Generalized Approach towards Soft Expert Sets via Neutrosophic Cubic Sets with Applications in Games. Symmetry. 2019; 11(2): 289. doi: 10.3390/sym11020289
MEMİŞ S. Another View on Picture Fuzzy Soft Sets and Their Product Operations with Soft Decision-Making. Journal of New Theory. 2022; (38): 1–13. doi: 10.53570/jnt.1037280
Khan M, Ilyas F, Gulistan M, Anis S. A study of soft AG-groupoids. Annals of Fuzzy Mathematics and Informatics. 2015; 9(4): 621–638.
Khan S, Gulistan M, Kausar N, et al. Aggregation Operators for Decision Making Based on q-Rung Orthopair Fuzzy Hypersoft Sets: An Application in Real Estate Project. Computer Modeling in Engineering & Sciences. 2023; 136(3): 3141–3156. doi: 10.32604/cmes.2023.026169
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