This paper formalizes a novel model that is able to use both interval representations, parameterizations, partial memberships and multi-polarity. These are differing modalities of uncertain knowledge that are supported by many models in the literature. The new structure that embraces all these features simultaneously is called interval-valued multi-polar fuzzy soft set (IVmFSS, for short). An enhanced combination of interval-valued m-polar fuzzy (IVmF) sets and soft sets produces this model. As such, the theory of IVmFSSs constitutes both an interval-valued multipolar-fuzzy generalization of soft set theory; a multipolar generalization of interval-valued fuzzy soft set theory; and an interval-valued generalization of multi-polar fuzzy set theory. Some fundamental operations for IVmFSSs, including intersection, union, complement, “OR”, “AND”, are explored and investigated through examples. An algorithm is developed to solve decision-making problems having data in interval-valued m-polar fuzzy soft form. It is applied to two numerical examples. In addition, three parameter reduction approaches and their algorithmic formulation are proposed for IVmFSSs. They are respectively called parameter reduction based on optimal choice, rank based parameter reduction, and normal parameter reduction. Moreover, these outcomes are compared with existing interval-valued fuzzy methods; relatedly, a comparative analysis among reduction approaches is investigated. Two real case studies for the selection of best site for an airport construction and best rotavator are studied.

本文形式化了一种新模型，该模型能够同时使用区间表示、参数化、部分隶属度和多极性。这些是不确定知识的不同模式，文献中的许多模型都支持这些模式。同时包含所有这些特征的新结构称为区间值多极模糊软集（IV m FSS，简称为）。区间值m极模糊 (IV m F) 集和软集的增强组合产生了该模型。因此，IV m的理论FSS 既构成了软集理论的区间值多极模糊推广；区间值模糊软集理论的多极推广；以及多极模糊集理论的区间值推广。通过实例探索和研究了 IV m FSS 的一些基本运算，包括交、并、补、“或”、“与”。开发了一种算法来解决具有区间值m极模糊软形式数据的决策问题。它适用于两个数值例子。此外，还针对IV m提出了三种参数约简方法及其算法公式。FSS。它们分别称为基于最优选择的参数约简、基于等级的参数约简和正常的参数约简。此外，这些结果与现有的区间值模糊方法进行了比较；相关地，研究了减少方法之间的比较分析。研究了选择机场建设最佳场地和最佳旋转器的两个真实案例研究。