Applications of Extended Plithogenic Sets in Plithogenic Sociogram
S.Sudha1, Nivetha Martin2, Florentin Smarandache3
1 School of Mathematics, Madurai Kamaraj University, Madurai, Tamil Nadu, India
2 Department of Mathematics, Arul Anandar College(Autonomous),Karumathur, Tamil Nadu, India
3 University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA
Emails: sudhasikkanan@gmail.com; nivetha.martin710@gmail.com; fsmarandache@gmail.com
Abstract
The theory of plithogeny developed by Smarandache is described as a more generalized form of representing sets of different nature such as crisp, fuzzy, intuitionistic and neutrosophic. Plithogenic set comprises degree of appurtenance and contradiction degree with respect only to the dominant attribute. This paper introduces extended plithogenic sets comprising degrees of appurtenance and contradiction with respect to both dominant and recessive attributes. The extension of the 5-tuple Plithogenic sets to a 7- tuple plithogenic sets helps in developing a more comprehensive kind of Plithogenic sociogram. The newly developed plithogenic sets and its implications in Plithogenic sociogram is validated by the decision making problem on food processing industries. The obtained results using extended plithogenic sets are more promising in comparison to the conventional plithogenic sets. The proposed kind of plithogenic sets will benefit the decision makers to make optimal decisions based on both optimistic and pessimistic approaches.
Keywords: Plithogenic Sociogram; Extended Plithogenic Sets; Food Packaging materials; Decision making