A Benchmark Generalization of Fuzzy Soft Ideals in Ordered Semigroups

Khan, Faiz Muhammad; Leoreanu-Fotea, Violeta; Saifullah; Amanullah

doi:10.2478/auom-2021-0023

Abstract

In real life, variability and inaccuracy are always presentand must be calculated by either possibilistic, probabilistic, polymorphic or other uncertainty approach. This benchmark study is about to construct new types of fuzzy soft ideals i.e., (∈, ∈ ∨q_k)-FSR(L)Is of ordered semigroup(OSG). Based on this inception, fuzzy soft level subsets are defined which link ordinary ideals with (∈, ∈ ∨q_k)-fuzzy soft left(right) ideals. Some binary operations like ◦_λ, intersection ∩_λ and union of fuzzy soft sets ∪_λ are given and various fundamental results of ideal theory are developed through these types of fuzzy soft ideals.

References

[1] J. Slingo and T. Palmer, Uncertainty in weather and climate prediction. Philosophical Transactions of the Royal Society A Mathematical, Physical and Engineering Sciences, 369:4751 - 4767, 2011.10.1098/rsta.2011.0161
Search in Google Scholar Back to article
[2] S. J. Fletcher, Data Assimilation for the Geosciences From Theory to Application. Elsevier, 2017.10.1016/B978-0-12-804444-5.00023-4
Search in Google Scholar Back to article
[3] F. Bostelmann and G. Strydom. Nuclear data uncertainty and sensitivity analysis of the vhtrc benchmark using scale. Annals of Nuclear Energy, 110, 317 - 329, 2017.10.1016/j.anucene.2017.06.052
Search in Google Scholar Back to article
[4] A. Csebfalvi, Structural optimization under uncertainty in loading directions: Benchmark results. Advances in Engineering Software, 120:68-78, 2018.
Search in Google Scholar Back to article
[5] T. Gernay, R. V. Coile, N. E. Khorasani and D. Hopkin, Efficient uncertainty quantification method applied to structural fire engineering computations. Engineering Structures, 183:1 - 17, 2019.10.1016/j.engstruct.2019.01.002
Search in Google Scholar Back to article
[6] H. Zhai and J. Zhang, Equilibrium reliability measure for structural design under twofold uncertainty. Information Sciences, 477:466 - 489, 2019.10.1016/j.ins.2018.10.059
Search in Google Scholar Back to article
[7] Y. Zhang, Y. Lu, Y. Zhou and Q. Zhang, Resistance uncertainty and structural reliability of hypar tensioned membrane structures with pvc coated polyesters. Thin-Walled Structures, 124:392 - 401, 2018.10.1016/j.tws.2017.12.026
Search in Google Scholar Back to article
[8] M. Guedri, S. Cogan and N. Bouhaddi, Robustness of structural reliability analyses to epistemic uncertainties. Mechanical Systems and Signal Processing, 28:458 - 469, 2012.10.1016/j.ymssp.2011.11.024
Search in Google Scholar Back to article
[9] G.Schueller and H.Pradlwarter, Benchmark study on reliability estimation in higher dimensions of structural systems an overview. Structural Safety, 29(3):167-182, 2007.10.1016/j.strusafe.2006.07.010
Search in Google Scholar Back to article
[10] M. Huber, Reducing forecast uncertainty by using observations in geotechnical engineering. Probabilistic Engineering Mechanics, 45:212-219, 201610.1016/j.probengmech.2016.02.002
Search in Google Scholar Back to article
[11] D.Molodtsov, Soft set theory-first results, Comput. Math. Applic. 37(4), 19-31 (1999).10.1016/S0898-1221(99)00056-5
Search in Google Scholar Back to article
[12] F.Feng, Soft rough sets applied to multicriteria group decision making, Ann. Fuzzy Math. Inform., 2, 69-80,(2011)
Search in Google Scholar Back to article
[13] P.K.Maji, A.R.Roy and R.Biswas, An application of soft sets in a decision making problem, Comput. Math. Applic., 44, 1077-1083,(2002).10.1016/S0898-1221(02)00216-X
Search in Google Scholar Back to article
[14] A.R.Roy and P.K.Maji, A soft set theoretic approach to decision making problems, Journal of Computational and Applied Mathematics 203,412-418.(2007).10.1016/j.cam.2006.04.008
Search in Google Scholar Back to article
[15] N.cagman and S.Enginoglu, Soft matrix theory and its decision making, Comput. Math. Appl. 59, 3308-3314.(2010).
Search in Google Scholar Back to article
[16] N.cagman and S.Enginoglu, Soft set theory and uni-int decision making, Eur. J. Oper. Res. 207, 848-855.(2010).
Search in Google Scholar Back to article
[17] F.Feng, Y.B.Jun, X.Liu and L.Li, An adjustable approach to fuzzy soft set based decision making, J. Comput. Appl. Math. 234, 10-20.(2010).
Search in Google Scholar Back to article
[18] P.K.Maji, A.R.Roy and R.Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl. 44, 1077-1083.(2002).
Search in Google Scholar Back to article
[19] D.Molodtsov, V.Yu.Leonov and D.V.Kovkov, Soft set technique and its applications, Nechetkie Sistemy i Myagkie Vychisleniya, 1(1), 8-39.(2006).
Search in Google Scholar Back to article
[20] U.Acar, F.Koyuncu and B.Tanay, Soft sets and soft rings, Comput. Math. Appl., 59, 3458-3463.(2010).10.1016/j.camwa.2010.03.034
Search in Google Scholar Back to article
[21] A.Sezgin and A.O.Atagun, On operations of soft sets, Comput. Math. Appl., 61, 1457-1467.(2011).10.1016/j.camwa.2011.01.018
Search in Google Scholar Back to article
[22] N.Cagman and S.Enginoglu, FP-soft set theory and its applications, Ann. Fuzzy Math. Inform., 2, 219-226.(2011).
Search in Google Scholar Back to article
[23] F.Feng, X.Y.Liu, V.Leoreanu-Fotea and Y.B.Jun, Soft sets and soft rough sets, Inform. Sci., 181, 1125-1137.(2011).10.1016/j.ins.2010.11.004
Search in Google Scholar Back to article
[24] Z.Xiao, K.Gong, S.Xia and Y.Zou, Exclusive disjunctive soft sets, Comput. Math. Appl., 59, 2128-2137.(2010).10.1016/j.camwa.2009.12.018
Search in Google Scholar Back to article
[25] Y.Zou and Z.Xiao, Data analysis approaches of soft sets under incomplete information, Knowledge Based Systems, 21, 941-945.(2008).10.1016/j.knosys.2008.04.004
Search in Google Scholar Back to article
[26] A.O.Atagun and A.Sezgin, Soft substructures of rings, fields and modules, Comput. Math. Appl., 61, 592-601.(2011).10.1016/j.camwa.2010.12.005
Search in Google Scholar Back to article
[27] F.Feng, Y.B.Jun and X.Zhao, Soft semirings, Comput. Math. Appl. 56, 2621-2628.(2008).
Search in Google Scholar Back to article
[28] P.Majumdar and S.K.Samanta, Similarity measure of soft sets, New Mathematics and Natural Computation, 4(1), 1-12.(2008).10.1142/S1793005708000908
Search in Google Scholar Back to article
[29] Y. B.Jun, Soft BCK/BCI-algebras. Comput. Math. Applic., 56, 1408-1413.(2008).10.1016/j.camwa.2008.02.035
Search in Google Scholar Back to article
[30] Y. B.Jun, K.J.Lee and A.Khan, Soft OSGs. Math.Logic Q., 56, 42-50.(2010).10.1002/malq.200810030
Search in Google Scholar Back to article
[31] Y. B.Jun, K.J.Lee and C.H.Park, Soft set theory applied to ideals in d-algebras. Comput. Math. Applic., 57, 367-378.(2009).10.1016/j.camwa.2008.11.002
Search in Google Scholar Back to article
[32] Y. B.Jun, K.J.Lee and J.Zhan, Soft p-ideals of soft BCI-algebras, Comput. Math. Applic., 58, 2060-2068.(2009).10.1016/j.camwa.2009.07.072
Search in Google Scholar Back to article
[33] Y. B.Jun and C.H.Park, Applications of soft sets in ideal theory.,Inform. Sci., 178, 2466-2475.(2008).10.1016/j.ins.2008.01.017
Search in Google Scholar Back to article
[34] J.Zhan and Y. B.Jun, Soft BL-algebras based on fuzzy sets., Comput. Math. Applic., 59, 2037-2046.(2010).10.1016/j.camwa.2009.12.008
Search in Google Scholar Back to article
[35] L. A. Zadeh, Fuzzy sets., Inform. Control. 8, 338-353 (1965).10.1016/S0019-9958(65)90241-X
Search in Google Scholar Back to article
[36] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning., Inform. Sci. 8, 199-249 (1975).10.1016/0020-0255(75)90036-5
Search in Google Scholar Back to article
[37] A.Rosenfeld, Fuzzy groups., J. Math. Anal. Appl. 35, 512-517 (1971).10.1016/0022-247X(71)90199-5
Search in Google Scholar Back to article
[38] R.Biswas Rosenfelds, fuzzy subgroups with interval-valued membership functions., Fuzzy Sets and Systems volume. 63, 87-90 (1994).10.1016/0165-0114(94)90148-1
Search in Google Scholar Back to article
[39] P. K. Maji, R. Biswas, A. R. Roy, Fuzzy soft sets, J. Fuzzy. Math. 9(3), 589-602 (2001).
Search in Google Scholar Back to article
[40] A. Aygunoglu, H. Aygun Introduction to fuzzy soft group Coumpt. Math. Appl. 58, 1279-1286 (2009)
Search in Google Scholar Back to article
[41] Feng Feng, Young Bae Jun, Xianzhong Zhao Soft semirings, Computers and Mathematics with Applications. 56, 2621-2628 (2008)10.1016/j.camwa.2008.05.011
Search in Google Scholar Back to article
[42] Sana. H, F. M. Khan, N. Yufeng, A new concept of possibility fuzzy soft OSGs via its applications, J. Int. Fuzzy Sys. 36, 3685-3696 (2019).
Search in Google Scholar Back to article
[43] S. K. Bhakat, P. Das (∈, ∈ Vq)-fuzzy subgroups, Fuzzy Sets and Systems. 80, 359-368 (1996).
Search in Google Scholar Back to article
[44] Y. B. Jun, Generalizations of (∈, ∈ Vq) -fuzzy subalgebras in BCK/BCI- algebras, Comput. Math. Applic. 58(7), 1383-1390 (2009).10.1016/j.camwa.2009.07.043
Search in Google Scholar Back to article
[45] M. Shabir, Y. B. Jun, H. Nawaz, Semigroups characterized by (∈,∈ Vqk) -fuzzy ideals, Comput. Math. Applic. 60, 1473-1493 (2010).
Search in Google Scholar Back to article
[46] F. M. Khan, N. H. Sarmin, A. Khan, Some study of (α, β)-fuzzy ideals in OSGs, Anal. Fuzzy. Math. Inform. 3(2), 213-227 (2012).
Search in Google Scholar Back to article
[47] Cheng-Fu Yang,Fuzzy soft semigroups and fuzzy soft ideals, Computers and Mathematics with Applications 61 (2011) 255-26110.1016/j.camwa.2010.10.047
Search in Google Scholar Back to article

A Benchmark Generalization of Fuzzy Soft Ideals in Ordered Semigroups

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