if we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. in this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.

Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...

In the last decades, many efforts have been made to solve multimodal optimization problems using Particle Swarm Optimization (PSO). To produce good results, these PSO algorithms need to specify some niching parameters to define the local neighborhood. In this paper, our motivation is to propose the novel neighborhood structures that remove undesirable niching parameters without sacrificing perf...

Bin Chen 2013 Soft Semi-Open Sets and Related Properties in Soft Topological Spaces. Applied Mathematics and Information Sciences, No. 1, (2013), 287-294. Gnanambal Ilango, Arun, B. , and Saravana Kumar, K. 2014. Some Properties of Soft ?-Open Sets in Soft Topological Space. IOSR Journal of Mathematics, Vol. 9, Issue 6 (Jan 2014), 20-24. Kannan, K. 2012. Soft Generalized-Closed Sets in Soft Top...

The main purpose of this paper is to introduce the compatibility of $M$-fuzzifying topologies and $M$-fuzzifying convexities, define an $M$-fuzzifying topological convex space, and give a method to generate an $M$-fuzzifying topological convex space. Some characterizations of $M$-fuzzifying topological convex spaces are presented. Finally, the notion of $M$-fuzzifying weak topologies is obtaine...

in this paper, we establish the theory of fuzzy ideal convergence on completely distributive lattices and give characterizations of some topological notions. we also study fuzzy limit structures and discuss the relationship between fuzzy co-topologies and fuzzy limit structures.

        In this paper, we study and discussion new type of fuzzy soft operator which is projection perpendicular ,and given some properties with characterization tis also theorems related on have been given. addition introduce the relation between other types.