Properties of Fuzzy Inner Product Spaces

has been introduced by several authors like Ahmed and Hamouly [1], Kohli and Kumar [5], Biswas [4], etc. Also the notion of fuzzy norm on a linear space was introduced by Katsaras [9]. Later on many other mathematicians like Felbin [3], Cheng and Mordeso [10], Bag and Samanta [6], etc, have given different definitions of fuzzy normed spaces. In recent past lots of work have been done in the topic of fuzzy functional analysis, but only a few works have been done on fuzzy inner product spaces. Biswas [4] tried to give a meaningful definition of fuzzy inner product space and associated fuzzy norm functions. Later on, a modification of the definition given by Biswas [4] was done by Kohli and Kumar [5] and they also introduced the notion of fuzzy co-inner product space. But still there is no useful definition of fuzzy inner product available to work with in the sense that not much development has yet been found in fuzzy inner product (or fuzzy Hilbert) space with these definitions.