The concept of soft sets was proposed as an effective tool to deal with uncertainty and vagueness. Topologists employed this concept to define and study soft topological spaces. In this paper, we introduce the concepts of soft SD-continuous, soft SD-open, soft SD-closed and soft SD-homeomorphism maps by using soft somewhere dense and soft cs-dense sets. We characterize them and discuss their main properties with the help of examples. In particular, we investigate under what conditions the restriction of soft SD-continuous, soft SD-open and soft SD-closed maps are respectively soft SD-continuous, soft SD-open and soft SD-closed maps. We logically explain the reasons of adding the null and absolute soft sets to the definitions of soft SD-continuous and soft SD-closed maps, respectively, and removing the null soft set from the definition of a soft SD-open map.

Data sets were compiled from the MHIDAS data bank for incidents where there had been five or more fatalities, ten or more injuries, 50 evacuations, or US$1 million damage. The data were converted to magnitudes on the Bradford Disaster Scale and analysed using maximum likelihood. Parameters determined from the estimation procedures were compared for compatibility between themselves and the results of analyses using other data.

A space (X, τ) is called epi-mildly normal if there exists a coarser topology τ′ on X such that (X, τ′) is Hausdorff (T2) mildly normal. We investigate this property and present some examples to illustrate the relationships between epi-mild normality and other weaker kinds of normality.

Our aim of writing this manuscript is to found novel rough-approximation operators inspired by an abstract structure called “supra-topology”. This approach is more relaxed than topological ones and extends the scope of applications because an intersection condition of topology is dispensed. Firstly, we generate eight types of supra-topologies using -neighborhood systems induced from any arbitrary relation. We elucidate the relationships between them and investigate the conditions under which some of them are identical. Then, we create new rough sets models from these supra-topologies and present the main characterizations of their lower and upper approximations. We apply these approximations to classify the regions of the subset and compute its accuracy measures. The master merits of the current approach are to produce the highest accuracy values compared with all approaches given in the published literature under a reflexive relation as well as preserve the monotonicity property of accuracy and roughness measures. Moreover, we demonstrate the good performance of the followed technique through analysis of some data of dengue fever disease. Ultimately, we debate the advantages and disadvantages of the followed approach and make a plan for some upcoming work.

In 1982, Pawlak proposed the concept of rough sets as a novel mathematical tool to address the issues of vagueness and uncertain knowledge. Topological concepts and results are close to the concepts and results in rough set theory; therefore, some researchers have investigated topological aspects and their applications in rough set theory. In this discussion, we study further properties of Nj-neighborhoods; especially, those are related to a topological space. Then, we define new kinds of approximation spaces and establish main properties. Finally, we make some comparisons of the approximations and accuracy measures introduced herein and their counterparts induced from interior and closure topological operators and E-neighborhoods.

A q-rung orthopair fuzzy set is one of the effective generalizations of fuzzy set for dealing with uncertainties in information. Under this environment, in this study, we define a new type of extensions of fuzzy sets called n,m-rung orthopair fuzzy sets and investigate their relationship with Fermatean fuzzy sets, Pythagorean fuzzy sets and intuitionistic fuzzy sets. The n,m-rung orthopair fuzzy sets can supply with more doubtful circumstances than Fermatean fuzzy sets, Pythagorean fuzzy sets and intuitionistic fuzzy sets because of their larger range of depicting the membership grades. There is a symmetry between the values of this membership function and non-membership function. Here, any power function scales are utilized to widen the scope of the decision-making problems. In addition, the novel notion of an n,m-rung orthopair fuzzy set through double universes is more flexible when debating the symmetry between two or more objects that are better than the diffusing concept of an n-rung orthopair fuzzy set, as well as mrung orthopair fuzzy set. The main advantage of n,m-rung orthopair fuzzy sets is that it can describe more uncertainties than Fermatean fuzzy sets, which can be applie in many decision-making problems. Then, we discover the essential set of operations for the n,m-rung orthopair fuzzy sets along with their several properties. Finally, we introduce a new operator, namely, n,m-rung orthopair fuzzy weighted power average (n,m-ROFWPA) over n,m-rung orthopair fuzzy sets and apply this operator to the MADM problems for evaluation of alternatives with n,m-rung orthopair fuzzy information.INDEX TERMS n,m-rung orthopair fuzzy sets, operations, score function, aggregation operator.

Picture fuzzy nano topological spaces is an extension of intuitionistic fuzzy nano topological spaces. Every decision in life ends with an answer such as yes or no, or true or false, but we have an another component called abstain, which we have not yet considered. This work is a gateway to study such a problem. This paper motivates an enquiry of the third component—abstain—in practical problems. The aim of this paper is to investigate the contemporary notion of picture fuzzy nano topological spaces and explore some of its properties. The stated properties are quantified with numerical data. Furthermore, an algorithm for Multiple Attribute Decision-Making (MADM) with an application regarding the file selection of building material under uncertainty by using picture fuzzy nano topological spaces is developed. As a practical problem, a comparison table is presented to show the difference between the novel concept and the existing methods.

Based on the concepts of pseudocomplement of L -subsets and the implication operator where L is a completely distributive lattice with order-reversing involution, the definition of countable RL -fuzzy compactness degree and the Lindelöf property degree of an L -subset in RL -fuzzy topology are introduced and characterized. Since L -fuzzy topology in the sense of Kubiak and Šostak is a special case of RL -fuzzy topology, the degrees of RL -fuzzy compactness and the Lindelöf property are generalizations of the corresponding degrees in L -fuzzy topology.