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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]

In this paper, we introduce Spherical Fermatean Neutrosophic Topological Spaces (SFNTS), expanding on neutrosophic sets characterized by Degrees of Membership (DoM), Degrees of Indeterminacy (DoI) and Degrees of Non-Membership (DoN). Fermatean neutrosophic sets in a universe satisfy the conditions where the sum of the cubes of the DoM and DoN is between zero and one and the cube of the DoI is between zero and one. The DoM, DoI and DoN are represented accordingly. We define a Spherical Fermatean Neutrosophic Set (SFNS) as a set where each element consists of an element in the universe, along with its DoM, DoN, DoI and a radius. The DoM, DoN, DoI and the radius are functions mapping the universe to the interval from zero to one. We extend this to a topological framework by defining an SFNTS on a set. We also studied the properties of the SFN closure and SFN interior operators, provided numerical examples and presented a geometric representation of SFNTS. Additionally, we explored the separation of two SFNSs, the intersection of two SFNSs and the overlapping of two SFNSs. [ABSTRACT FROM AUTHOR]

In the context of aggregation operators and multiple criteria decision-making, this article presents the idea of cubic spherical neutrosophic sets. The notion of neutrosophic informations are transform into a geometric sphere by determining its center and radius. This advanced geometrical representation extends traditional neutrosophic informations. This study defines and discusses weighted additive and weighted geometric aggregation operators tailored to cubic spherical neutrosophic sets that are vital for handling complex and uncertain information. Practical example, such as evaluating fertilizer brands for coconut farming, illustrate their application in decision-making contexts. By integrating cubic spherical neutrosophic sets into multiple criteria decision-making frameworks, decision makers can effectively manage uncertainty and make informed decisions. When multiple stakeholders are involved in the decision-making process, averaging their decision values may not accurately reflect a true perspective. This multiple criteria decision-making approach overcomes the limitations of traditional averaging method. Theoretical discussions and practical examples contribute to advancing the understanding and application of multiple criteria decision-making, enhancing the reliability of decision support systems. [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]