Abstract
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.
Highlights
Interval representations, parameterizations, partial memberships and multi-polarity are various modalities of uncertain knowledge
We give a comparison of the developed model with certain existing hybrid models and provide a comparative analysis of the proposed reduction approaches with some existing reduction methods
The theory of interval-valued fuzzy soft sets (IVFSSs) is arising as a helpful expansion of soft sets which is upheld by genuine data-sets
Summary
Parameterizations, partial memberships and multi-polarity are various modalities of uncertain knowledge. They have been combined in a myriad of forms in the literature (Akram et al 2018; Alcantud et al 2020b; Atanassov 1986; Chen et al.2014; Jiang et al 2010; Maji et al 2001; Molodtsov 1999; Roy and Maji 2007; Yang et al.2009; Zadeh 1965). We prove its versality with several theoretical and applied developments, inclusive of fundamental operations, parameter reductions, and applications to decision-making.
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