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## REFINED SOFT SETS AND ITS APPLICATIONS

#### Anjan MUKHERJEE [1] , Mithun DATTA [2] , Abhijit SAHA [3]

Many disciplines, including engineering, economics, medical science and social science are highly dependent on the task of modeling and computing uncertain data. When the uncertainty is highly complicated and difficult to characterize, classical mathematical approaches are often insufficient to derive effective or useful models. Testifying to the importance of uncertainties that cannot be defined by classical mathematics, researchers are introducing alternative theories every day. In addition to classical probability theory, some of the most important results on this topic are fuzzy sets, intuitionistic fuzzy sets, vague sets, interval-valued fuzzy set and rough sets. But each of these theories has its inherent limitations as pointed out by Molodtsov. For example, in probability theory, we require a large number of experiments in order to check the stability of the system. To define a membership function in case of fuzzy set theory is not always an easy task. Theory of rough sets requires an equivalence relation defined on the universal set under consideration. But in many real life situations such an equivalence relation is very difficult to find due to imprecise human knowledge. Perhaps the above mentioned difficulties associated with these theories are due to their incompatibility with the parameterization tools. Molodtsov introduced soft set theory as a completely new approach for modeling vagueness and uncertainty. This so-called soft set theory is free from the above mentioned difficulties as it has enough parameters. In soft set theory, the problem of setting membership function simply doesn’t arise. This makes the theory convenient and easy to apply in practice. Soft set theory has potential applications in various fields including smoothness of functions, game theory, operations research, Riemann integration, probability theory and measurement theory. Most of these applications have already been demonstrated by MolodtsovMany disciplines, including engineering, economics, medical science and social science are highly dependent on the task of modeling and computing uncertain data. When the uncertainty is highly complicated and difficult to characterize, classical mathematical approaches are often insufficient to derive effective or useful models. Testifying to the importance of uncertainties that cannot be defined by classical mathematics, researchers are introducing alternative theories every day. In addition to classical probability theory, some of the most important results on this topic are fuzzy sets, intuitionistic fuzzy sets, vague sets, interval-valued fuzzy set and rough sets. But each of these theories has its inherent limitations as pointed out by Molodtsov. For example, in probability theory, we require a large number of experiments in order to check the stability of the system. To define a membership function in case of fuzzy set theory is not always an easy task. Theory of rough sets requires an equivalence relation defined on the universal set under consideration. But in many real life situations such an equivalence relation is very difficult to find due to imprecise human knowledge. Perhaps the above mentioned difficulties associated with these theories are due to their incompatibility with the parameterization tools. Molodtsov introduced soft set theory as a completely new approach for modeling vagueness and uncertainty. This so-called soft set theory is free from the above mentioned difficulties as it has enough parameters. In soft set theory, the problem of setting membership function simply doesn’t arise. This makes the theory convenient and easy to apply in practice. Soft set theory has potential applications in various fields including smoothness of functions, game theory, operations research, Riemann integration, probability theory and measurement theory. Most of these applications have already been demonstrated by Molodtsov.
Other ID JA44BT93UM Research Article Author: Anjan MUKHERJEE Author: Mithun DATTA Author: Abhijit SAHA Publication Date : November 1, 2016
 Bibtex @ { jnt381360, journal = {Journal of New Theory}, issn = {2149-1402}, eissn = {2149-1402}, address = {Mathematics Department, Gaziosmanpasa University 60250 Tokat-TURKEY.}, publisher = {Gaziosmanpasa University}, year = {2016}, volume = {}, pages = {10 - 25}, doi = {}, title = {REFINED SOFT SETS AND ITS APPLICATIONS}, key = {cite}, author = {MUKHERJEE, Anjan and DATTA, Mithun and SAHA, Abhijit} } APA MUKHERJEE, A , DATTA, M , SAHA, A . (2016). REFINED SOFT SETS AND ITS APPLICATIONS. Journal of New Theory , (14) , 10-25 . Retrieved from https://dergipark.org.tr/en/pub/jnt/issue/34513/381360 MLA MUKHERJEE, A , DATTA, M , SAHA, A . "REFINED SOFT SETS AND ITS APPLICATIONS". Journal of New Theory (2016 ): 10-25 Chicago MUKHERJEE, A , DATTA, M , SAHA, A . "REFINED SOFT SETS AND ITS APPLICATIONS". Journal of New Theory (2016 ): 10-25 RIS TY - JOUR T1 - REFINED SOFT SETS AND ITS APPLICATIONS AU - Anjan MUKHERJEE , Mithun DATTA , Abhijit SAHA Y1 - 2016 PY - 2016 N1 - DO - T2 - Journal of New Theory JF - Journal JO - JOR SP - 10 EP - 25 VL - IS - 14 SN - 2149-1402-2149-1402 M3 - UR - Y2 - 2020 ER - EndNote %0 Journal of New Theory REFINED SOFT SETS AND ITS APPLICATIONS %A Anjan MUKHERJEE , Mithun DATTA , Abhijit SAHA %T REFINED SOFT SETS AND ITS APPLICATIONS %D 2016 %J Journal of New Theory %P 2149-1402-2149-1402 %V %N 14 %R %U ISNAD MUKHERJEE, Anjan , DATTA, Mithun , SAHA, Abhijit . "REFINED SOFT SETS AND ITS APPLICATIONS". Journal of New Theory / 14 (November 2016): 10-25 . AMA MUKHERJEE A , DATTA M , SAHA A . REFINED SOFT SETS AND ITS APPLICATIONS. JNT. 2016; (14): 10-25. Vancouver MUKHERJEE A , DATTA M , SAHA A . REFINED SOFT SETS AND ITS APPLICATIONS. Journal of New Theory. 2016; (14): 25-10.

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