a b s t r a c tIn this paper, the concept of fuzzy soft topology is introduced and some of its structural properties such as neighborhood of a fuzzy soft set, interior fuzzy soft set, fuzzy soft basis, fuzzy soft subspace topology are studied.

In this study, we define the fuzzy cone metric space, the topology induced by this space and some related results of them. Also we state and prove the fuzzy cone Banach contraction theorem. c ⃝2015 All rights reserved.

A lmost every branch of science has its own uncertainties and ambiguities. These uncertainties depend on the existence of many parameters. So it is not always easy to model a daily life problem mathematically using classical mathematical methods. In this sense, mankind has gone to find new mathematical models. In 1999, Molodtsov [1] established the soft set theory to model uncertainties in any phenomenon. He defined the concept of soft set as follows; Definition 1.1. Set-theoretic operations for soft sets given by Maji et al. and Ali et al. in [2, 3]. The operations between two soft sets such as soft union, soft intersection, soft complement etc. defined in [2, 3] as follows.

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