The modern world uses an increasing number of robots, notably service robots. Robots will be able to easily manipulate everyday objects in the future, but only if they are paired with planning and decision-making procedures that allow them to comprehend how to complete a task. This research presents new techniques to handling multi-attribute problem solving with trigonometric Pythagorean normal fuzzy numbers. The sine trigonometric Pythagorean fuzzy sets combine the concept of Pythagorean fuzzy sets with sine trigonometric functions to represent uncertainty in decision-making. It is feasible to combine trigonometric Pythagorean fuzzy numbers and normal fuzzy numbers to get trigonometric Pythagorean fuzzy normal numbers. In addition to the fundamental interaction aggregation operators, we define the trigonometric Pythagorean fuzzy normal numbers. The trigonometric Pythagorean fuzzy normal numbers satisfy the following properties: associative, distributive, idempotent, bounded, commutative and monotonicity. Four novel approaches are introduced such as weighted averaging, weighted geometric, generalized weighted averaging and generalized weighted geometric. These operators can be used in the development of a multi-attribute decision-making algorithm. We demonstrate how improved Euclidean and Hamming distances are used in practical situations. For industrial robots, the two most crucial elements are computer science and machine tool technology. The four criteria of weights, orientations, speeds and accuracy may be used to assess robotic systems. They are also more practical, easier to understand, and more adept at identifying the best answer more quickly. The effectiveness and accuracy of the models we are looking at are demonstrated by comparing many existing models with those that have been developed.

The cosine trigonometric single valued neutrosophic number (CT-SVNN) is a suitable expansion of the standard neutrosophic number. Single-valued neutrosophic sets (SVNSs) may effectively overcome three components: degree of truth, indeterminacy, and falsity. In recent years, the aggregation operator (AO) and its applications have undergone development. This study introduces a few new AOs for multi-attribute decision-making (MADM). We introduce a novel approach for cosine trigonometric SVNS (CT-SVNS) and CT-SVNS with normal (CT-SVNNS), which are SVNS extensions. It is also required to discuss the CT-SVNNS method fundamental features in this communication, such as idempotency, boundedness, commutativity and monotonicity. There are numerous CT-SVNNS operators that have been proposed, including CT-SVN normal weighted averaging (CT-SVNNWA), CT-SVN normal weighted geometric (CT-SVNNWG), generalized CT-SVNNWA (GCT-SVNNWA) and generalized CT-SVNNWG. A powerful strategy for solving the MADM problem is provided that makes use of new developed generalized operators. Through a case study, the value of the suggested MADM approach is demonstrated. The new strategy is shown using a market share problem, and the outcomes are contrasted and examined against an existing method. This combination of generalized AO was rated successful based on expert preferences. As a result, a varied collection of experts may be accepted.

The goal of a quadri partitioned Pythagorean neutrosophic normal interval-valued fuzzy set (QPPNNIVFS) is to provide the neutrosophic sets a more comprehensive mathematical foundation. QPPNNIVFS divides the indeterminacy component into unknown and contradiction classes. The several aggregating operations that have been understood thus far are discussed here. The fuzzy weighted QPPNNIVFW averaging (QPPNNIVFWA), QPPNNIVFW geometric (QPPNNIVFWG), generalized QPPNNIVFW averaging (GQPPNNIVFWA) and generalized QPPNNIVFW geometric (GQPPNNIVFWG) are considered as a novel concept. We show that algebraic structures like associative, distributive, idempotent, bounded, commutative, and monotonic characteristics are satisfied by QPPNNIVFSs. We illustrate the practical applications of increased Euclidean distance, Hamming distance, score, and accuracy values. Unless there is a mathematical justification for selecting one cluster technique over another, the clustering strategy must be selected empirically. An algorithm that performs well on one set of data will not perform well on another. There are several approaches of conducting cluster analysis. These include social network analysis, distribution-based, density-based, centroid-based and hierarchical. Therefore, it is clear that the natural number θ has a big impact on the models. To illustrate the comparison analysis, sensitivity analysis and the validity of our suggested methodologies are also conducted. The outcomes will be very helpful to decision makers in handling uncertain and conflicting data effectively.