Department of Mathematics, School of Science, University of Management and Technology, Sialkot Campus, Lahore, Pakistan.
Department of Mathematics, School of Science, University of Management and Technology, Lahore 54770, Pakistan.
Comput Intell Neurosci. 2021 Nov 10;2021:7211399. doi: 10.1155/2021/7211399. eCollection 2021.
Similarity measures (SM) and correlation coefficients (CC) are used to solve many problems. These problems include vague and imprecise information, excluding the inability to deal with general vagueness and numerous information problems. The main purpose of this research is to propose an m-polar interval-valued neutrosophic soft set (mPIVNSS) by merging the m-polar fuzzy set and interval-valued neutrosophic soft set and then study various operations based on the proposed notion, such as AND operator, OR operator, truth-favorite, and false-favorite operators with their properties. This research also puts forward the concept of the necessity and possibility operations of mPIVNSS and also the m-polar interval-valued neutrosophic soft weighted average operator (mPIVNSWA) with its desirable properties. Cosine and set-theoretic similarity measures have been proposed for mPIVNSS using Bhattacharya distance and discussed their fundamental properties. Furthermore, we extend the concept of CC and weighted correlation coefficient (WCC) for mPIVNSS and presented their necessary characteristics. Moreover, utilizing the mPIVNSWA operator, CC, and SM developed three novel algorithms for mPIVNSS to solve the multicriteria decision-making problem. Finally, the advantages, effectiveness, flexibility, and comparative analysis of the developed algorithms are given with the prevailing techniques.
相似性度量 (SM) 和相关系数 (CC) 可用于解决许多问题。这些问题包括模糊和不精确的信息，不包括无法处理一般模糊和大量信息问题。本研究的主要目的是通过合并 m-极模糊集和区间值 Neutrosophic 软集来提出 m-极区间值 Neutrosophic 软集 (mPIVNSS)，然后基于所提出的概念研究各种运算，如 AND 运算、OR 运算、真值偏好和假值偏好运算符及其属性。本研究还提出了 mPIVNSS 的必要性和可能性运算的概念，以及具有理想属性的 m-极区间值 Neutrosophic 软加权平均运算符 (mPIVNSWA)。利用 Bhattacharya 距离为 mPIVNSS 提出了余弦和集合相似性度量，并讨论了它们的基本性质。此外，我们为 mPIVNSS 扩展了 CC 和加权相关系数 (WCC) 的概念，并提出了它们的必要特征。此外，利用 mPIVNSWA 运算符、CC 和 SM，为 mPIVNSS 开发了三个新的算法来解决多准则决策问题。最后，给出了所开发算法的优势、有效性、灵活性和与现有技术的比较分析。
