Some Algorithms for Decision-Making Problems Based on the Extensions of Intuitionistic Fuzzy Sets

Abstract

Decision making (DM) is a cognitive process in which actions are taken to frame rational decisions subjected to problems. These problems may be a constituted part of any discipline such as engineering, economics, psychology, management etc. However, under a decisive situation, multi-criteria decision making (MCDM) problems are a valuable format of analyzing different alternatives classified under relevant criteria information. The persistent situations of modernization and rapid advancements have made data handling and processing highly vulnerable to uncertainties. To address the influence of uncertain information, theories such as fuzzy set (FS), intuitionistic fuzzy set (IFS), interval-valued fuzzy/intuitionistic fuzzy set (IVFS/IVIFS), hesitant fuzzy set (HFS) etc, have done a remarkable job. Apparently, amid the breakneck growth in uncertainty possessing situations, there felt need of advanced genres of the existing theories so that sure decisions can be framed out of the unsure data values. For it, progressive minds involved in research developed advanced tools such as aggregation operators and information measures. Deploying these tools in the DM approaches helps to choose a suitable alternative(s) out of the available ones. Driven by the present state-of-art, this research work focuses on building a novel environment called cubic intuitionistic fuzzy set (CIFS) and its related aggregation operators and information measures. In addition to it, this work also addresses the uncertainty quantification under probabilistic environments where non-membership hesitant information plays a dominant role. For that, DM approaches as well as algorithms have been developed under probabilistic dual hesitant fuzzy set (PDHFS) environment. Under these, various statistical tools such as correlation measure, distance measure, entropy etc, have been proposed and several aggregation operators such as generalized operators, Einstein, Bonferroni, Maclaurin Symmteric Mean operators etc, have been formulated. For strengthening the desirability and applicability of the proposed research, all related mathematical aspects in form of theorems, properties as well as results have been investigated in detail. In order to facilitate the practical DM scenarios, the presented work has also been applied to various application domains such as CPU job scheduling, personnel recruitment/selection problems, signal processing, inventory management, analysis of consumer's buying behavior, gesture quantification in brain hemorrhage patients etc. Afterwards, each proposed aspect is checked for its superiority or alignment in comparison to the existing work.