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In the present work, firstly uniform boundedness principle (UBP) theorem is established in a generalized fuzzy normed space from which Banach–Steinhaus theorem in fuzzy settings is derived. An example of an incomplete fuzzy normed linear space is constructed by applying the UBP theorem. Finally relation between our result and the existing UBP theorem of Bag and Samanta is studied.

In the present paper, a notion of M-basis and multi dimension of a multi vector space is introduced and some of its properties are studied.

In this paper an attempt has been made to study the effects of the process parameters of wire cut electrical discharge machining (WEDM) on Magnesium-Silicon Carbide MMC with 5% SiC in particulate form. For the analysis, six factors, namely pulse on time, pulse off time, spark gap voltage, peak current, dielectric flushing pressure and servo feed have been taken and a Taguchi L16 orthogonal array for two levels was used. Response surface methodology was also used to develop second-order models for material removal rate (MRR) and surface roughness (SR). From the analysis of variances, it has been observed that pulse on time and pulse off time were the most significant parameters among all those observed in predicting the MRR and SR, respectively.

The widespread applications of similarity measures in varied avenues such as multi-criteria decision making, medical diagnosis, clustering methods etc. elucidates the immense potential of the measures of similarity in neutrosophic setting. The contributions of the works of various authors have enriched the neutrosophic theory pertaining to the study of similarity measures as is evident from the recurrent existence of several measures of similarity (distance based similarity measure, tangent similarity measure, vector similarity measure etc. to name a few) in the literature. The chapter aims to consider the various similarity measures for neutrosophic sets. The deliberation is an endeavour to throw light on most of the existing measures thereby providing a concise yet comprehensive portrayal of the vast spectrum of similarity measures existent in the neutrosophic literature.

In the present paper, self-adjoint operator and completely continuous operator on soft inner product spaces have been introduced and some basic properties of such operators are studied.

In this paper, the notions of topology on soft subsets and soft topology have been introduced. Some basic properties of these topologies are studied. Also the definition of continuity of soft mappings in both the topologies is given with their properties studied.

Soft set, as a parametrized family of subsets of a crisp universal set, has more ability to handle uncertain information. In this paper, we propose two types of similarity measure between soft sets and made a comparative study of these two techniques. Also we have shown an application of this similarity measure of soft sets.

A new definition of fuzzy proximity is given and some of its properties are studied. We also give a definition of fuzzy uniformity whose underlying fuzzy proximity is a fuzzy proximity in our sense.

In this paper definitions of fuzzy closure operator, fuzzy compactness and fuzzy connectedness are given in a redefined fuzzy topological space and then some characteristic properties of fuzzy closure operator, product theorems of fuzzy compactness, invariance of fuzzy compactness and fuzzy connectedness under gradation preserving maps and invariance of fuzzy connectedness under the fuzzy closure operator are studied.

In an earlier paper, we have given a new definition of fuzzy topology by introducing a concept of gradation of openness of fuzzy subsets. In order to make the concept more appropriate, in this paper we modify the definition of gradation function and then study subspace of fuzzy topological spaces, gradation preserving maps and category of fuzzy topological spaces and gradation preserving maps.

In this paper we give a new definition of fuzzy topology by introducing a concept of gradation of openness of fuzzy subsets, and then study fuzzy continuity.

In this paper the notion of fuzzy nearness structure is introduced and some investigations are made towards the unification of several structures: namely, fuzzy topological structure, fuzzy proximity structure, fuzzy contiguity structure and fuzzy uniform structure.

In this paper, a concept of operator’s fuzzy norm is introduced for the first time in general t -norm setting. Ideas of fuzzy continuous operators, fuzzy bounded linear operators are given with some properties of such operators studied in this general setting.

Notions of Lowen type fuzzy soft topological space are introduced and some of their properties are established in the present paper. Besides this, a combined structure of a fuzzy soft topological space and a fuzzy soft group, which is termed here as fuzzy soft topological group is introduced. Homomorphic images and preimages are also examined. Finally, some definitions and results on fuzzy soft set are studied.

Purpose The purpose of this paper is to introduce several notions, such as soft topological soft groups, soft topological soft normal subgroups, and soft topological soft factor groups, and to study their properties.