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When diverse decision makers are involved in the decision-making process, taking average of decision values might not reflect an accurate point of view. To overcome such a scenario, the circular Fermatean fuzzy (CFF) set, an advancement of the Fermatean fuzzy (FF) set, and the interval-valued Fermatean fuzzy set (IVFFS) are introduced in this current study. The proposed CFF set is a circle with a centre as association value (AV) and nonassociation value (NAV) with a radius at most equal to 2. It is built in such a way that it covers all the decision makers’ opinion value through a circle. Due to its geometric structure, the CFF set resolves ambiguity and risk more accurately and effectively than FF and IVFF. FF t-norm and t-conorm are used to investigate the properties of CFF sets, subsequent to which the algebraic operations between them are defined. A couple of CFF distance measures between CFF numbers are introduced and used in the selection of an electric autorickshaw along with the CFF weighted averaging and geometric aggregation operators. The overview and comparison analysis of the generated reports exemplifies the viability and compatibility of the CFF set strategy for selecting the best choices.

The concepts of cubic spherical neutrosophic sets (CSNSs), introduced and investigated by Gomathi et al. [5], offer a geometric representation of collection of neutrosophic sets (NSs), enhancing their ability to capture uncertainty. The formulation characterizes information using points on a sphere with a defined center and radius, providing a more precise depiction of fuzziness inherent in uncertain data. The cubic spherical neutrosophic Archimedean triangular norms(ATN) and conorms (ATCN), expanding the model's capabilities to handle uncertainty. These algebraic operators enable the aggregation and combination of uncertain information, offering a more comprehensive approach to decision-making. The research further presents a method for solving multiple-criteria decision-making problems within the cubic spherical neutrosophic context, leveraging the newly integrated norms and conorms. The algorithm utilizes the cosine similarity measure of cubic spherical neutrosophic sets, exemplified through an application involving the selection of the most effective electric truck. This extended framework provides decision-makers with enhanced tools to navigate complex decision landscapes amidst uncertainty, facilitating more informed and robust choices across diverse domains. [ABSTRACT FROM AUTHOR]

This study introduces cubic spherical neutrosophic sets as a novel approach to represent uncertainty within mathematical frameworks. By employing a spherical representation, these sets offer a comprehensive depiction of varying degrees of truth, indeterminacy and falsity associated with elements. The concept of cubic spherical neutrosophic topological space is introduced as a generalization of neutrosophic topology. Using illustrative examples, we explore fundamental theorems and characteristics of these spaces. Cubic spherical neutrosophic sets provide a flexible framework for integrating multiple perspectives and sources of uncertainty, making them suitable for modeling real-world phenomena. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study the notions of local closure functions and also we introduce the operator ΨΓ in hereditary generalized topological spaces. [ABSTRACT FROM AUTHOR]

The notion of γ b -open sets in generalized topological spaces was introduced and studied by Sivagami [5] in 2008: By using the notion of μ - b -open sets, we introduce and study (b, μY ) - continuous functions, μ - b -kernel and (μX, μY) - b -open functions in generalized topological spaces. Also some characterizations of (b, μY) - continuous functions are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study the notion of μ-b-separateness. Using this notion, the concept of μ-b-connectedness and μ-b-compactness are studied. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of expansions of open sets, A-expansion continuous mappings, closed-B-continuous mappings and relative-I-continuous mappings in ideal topological spaces. Using these notions we obtain decompositions of continuity in ideal topological spaces. [ABSTRACT FROM AUTHOR]