Abstract
In this paper, union, and intersection of generalised fuzzy soft sets are introduced and some of their basic properties are studied. The objective of this paper is to introduce the generalised fuzzy soft topology over a soft universe with a fixed set of parameters. Generalised fuzzy soft points, generalised fuzzy soft closure, generalised fuzzy soft neighbourhood, generalised fuzzy soft interior, generalised fuzzy soft base are introduced and their basic properties are investigated. Finally, generalised fuzzy soft compact spaces are introduced and a few basic properties are taken up for consideration. Key words: Fuzzy soft set, generalised fuzzy soft set, generalised fuzzy soft topology, generalised fuzzy soft open sets, generalised fuzzy soft closed sets, generalised fuzzy soft topological spaces, generalised fuzzy soft compact spaces.
Highlights
Most of our real life problems in engineering, social and medical science, economics, environment etc. involve imprecise data and their solutions involve the use of mathematical principles based on uncertainty and imprecision
The analytical part of fuzzy set theory was practically started with the paper of Chang (1968) who introduced the concept of fuzzy topological spaces; this theory is associated with an inherent limitation, which is the inadequacy of the parametrization tool associated with this theory as it was mentioned by Molodtsov (1999)
In 2001, Maji et al introduced the fuzzy soft set which is a combination of fuzzy set and soft set
Summary
Most of our real life problems in engineering, social and medical science, economics, environment etc. involve imprecise data and their solutions involve the use of mathematical principles based on uncertainty and imprecision. We discussed some basic properties of generalised fuzzy soft topological spaces with an example and define generalised fuzzy soft open and closed sets. Let F be the mapping F : E I X I be a function defined as follows: F~ e F e , e , where F e ~ I X and e ~ I E F~ is called a generalised fuzzy soft set (GFSS in short) over X , E .
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