Asian Journal of Current Research

Relations on Fs-sets and Some Results

Asian Journal of Current Research, Volume 8, Issue 1, Page 7-21
DOI: 10.56557/ajocr/2023/v8i18114

Abstract


In this paper, we define an Fs-binary relation on a pair of Fs-sets and also define a partial order on the collection of all Fs-binary relations between the given pair of Fs-sets and prove that the collection with this given partial order is an infinitely distributive lattice. An Fs-set is a four triple in which first two components are crips sets such that the second component is sub set of first component. The fourth component is a complete Boolean algebra which is also the co-domain of two sub component functions while the third component is a function with combinations of two sub components given in which the first sub component is a complete Boolean valued function with first component as its domain and second sub component is another complete Boolean valued function with the second component as its domain and both sub component functions have fourth component as theirs co-domain and also the first sub component function is more valued than the second sub component function value.The third component which is the combination of two sub components is called the membership function of the given Fs-set. Here, the so called sub components are given within simple brackets after the third component.

Keywords:
  • Fs-set
  • Fs-subset
  • Fs-objects
  • Fs-binary relation

How to Cite

Yogeswara, V., & Rao, G. S. (2023). Relations on Fs-sets and Some Results. Asian Journal of Current Research, 8(1), 7–21. https://doi.org/10.56557/ajocr/2023/v8i18114

References

Zadeh L. Fuzzy sets, Information and control. ;8:338-353.

Vaddiparthi Yogeswara,G.Srinivas and Biswajit Rath, A Theory of Fs-sets, Fs-Complements and
Fs-De Morgan Laws. IJARCS. 2013;4(10).

Goguen JA. L-fuzzy sets. Journal of Mathematical Analysis and Applications. 1967;18:145–174.

Steven Givant, Paul Halmos, Introduction to Boolean algebras, Springer.

Hemanta K. Baruah, towards forming a field of fuzzy sets. IJEIC. 2011;2(1).

Hemanta K. Baruah, the theory of fuzzy sets: Beliefs and realities. IJEIC. 2011;2(2).

Vaddiparthi Yogeswara, Biswajit Rath A Study of Fs-function and study of Images of Fs-Subsets In The Light of Refined Definition of Images Under Various Fs-Functions. IJATCSE. 2014;3:06- Special Issue of ICIITEM 2014.

Vaddiparthi Yogeswara, Biswajit Rath, Reddy SVG. A Study of Fs-Functions and Properties of Images of Fs-Subsets under Various Fs- Functions.MS-IRJ. 2014;3(1).

Yogeswara V, Rath B, Rao CR, Umakameswari KV. Generalized Definition of Image of An FS-Subset Under An FS-Function-Resultant Properties of Images. Mathematical Sciences International Research Journal ISSN. 2015:2278-8697.

Nistala VES. Murthy and Peruru G. Prasad, Representation of L-Fuzzy Binary Relations via A Galois Connection. Tamkang Journal of Mathematics. 2009;40(3):287-305, Autumn.

Nistala VES. Murthy, Is the Axiom of Choice True for Fuzzy Sets?. JFM. 1997;5(3):P495-523. U.S.A.

Szasz G. An Introduction to Lattice Academic press, New York.
  • 0 times
    PDF Download: 0 times

Download Statistics

Downloads

Download data is not yet available.

Current Issue

Subscription

Login to access subscriber-only resources.

Information