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To express the opinions of decision-makers, q-rung orthopair hesitant fuzzy sets (q-ROHFSs) have been employed extensively. Therefore, it is necessary to construct q-rung orthopair hesitant fuzzy preference relations (q-ROHFPRs) as a crucial decision-making tool for decision-makers. The goal of this paper aims to define a new consistency and consensus approach for solving q-ROHFPR group decision-making (GDM) problems. To do this, we first state the definitions of q-ROHFPRs and additive consistent q-ROHFPRs based on q-ROHFSs, an additive consistency index and acceptable additive consistent q-ROHFPRs. Second, based on minimizing the deviation, we establish an acceptable goal programming model for unacceptable additive consistent q-ROHFPRs. Third, an iterative algorithm is created for achieving acceptable consistency and reaching a rational consensus. The degree of rational consensus among individual q-ROHFPRs is quantified by a distance-based consensus index. Afterward, a non-linear programming model is formulated to derive the priority vector of alternatives, which are q-rung orthopair hesitant fuzzy numbers (q-ROHFNs). Based on this model, a GDM model for q-ROHFPRs is then developed. To demonstrate the validity and utility of the proposed GDM model, a case study on the risk assessment of hypertension is provided. The finding of sensitivity and comparison analyses supports the feasibility and efficacy of the suggested approach.

The K-Means algorithm is a powerful tool for data analysis, but it faces several challenges when dealing with large multi-feature data. Centroid initialization and centroid determination are two significant hurdles that can reduce the performance of the K-Means algorithm. To address these challenges, based on partial-order relations, an enhanced K-Means algorithm, the multi-feature induced order K-Means algorithm (OWAK-Means) is developed which combines with a novel centroid initialization based on partial-order relations and a multi-feature induced ordered weighted average (MFIOWA) operator. By using a weighted iteration method based on partial-order relations, the OWAK-Means algorithm initializes centroids with greater precision. The MFIOWA operator is designed based on database indexing theory and the Sigmoid weight function that improves its information filtering ability. These techniques, combined with an ordered weighted distance metric and the MFIOWA operator, make the OWAK-Means algorithm an effective tool for multi-feature data analysis. In comparative analysis with the variants of the K-Means algorithm, the OWAK-Means algorithm has significant improvement in the adjusted rand score, normalized mutual information, and purity. Statistical tests, comprehensive evaluation methods, and sensitivity analysis prove that the OWAK-Means algorithm is effective and reliable.

A new approach is presented for easily testable two-dimensional iterative arrays. It is an improvement on GI-testability (Group Identical testability) and is referred to as GID-testability (Group Identical and Different testability). In a GID-testable two-dimensional array, the primaryxandyoutputs are organized into groups and every group has more than one output. This is similar to the GI-testable arrays. However, GID-testability not only ensures that identical test responses can be obtained from every output in the same group when an array is fault free, but also ensures that at least one output has different test responses (from the other outputs in a group) when a cell in the array is faulty. Therefore, all faults can be detected under the assumption of a single faulty cell model. It is proved that an arbitrary two-dimensional iterative array is GID-testable if sevenx-states and seveny-states are added to the original flow table of the basic cell of the array.

A new approach to repair memory chips with redundancy is proposed. This approach is based on the minimization of the repair cost. Algorithms for cost driven repair are presented. The algorithms can be executed either on-line (concurrently with the testing of the memory), or off-line (at completion of testing).