Real-world decision support in hospitality using pessimistic multi-granulation roughness of cubic intuitionistic fuzzy soft sets

Traditional fuzzy and rough set models usually have a hard time in providing sufficient ambiguity, hesitancy, and partiality to information that is common in actual hospitality decision-making. In order to overcome these problems, this paper suggests a new decision-support model that is built upon pessimistic multi-granulation rough sets combined with cubic intuitionistic fuzzy soft relation. The model proposed is a unification of interval-valued membership, intuitionistic non-membership and soft binary relations in a structure of pessimistic rough approximations. The framework characterizes multi-dimensional uncertainty of complex hospitality appraisals by modelling membership, non-membership, hesitation and boundary regions together in a variety of granulations. Soft binary relations defined in terms of foresets and aftersets are used to form lower and upper pessimistic multi-granulation approximations of internal cubic intuitionistic fuzzy sets. Approximation operators are formally defined in two pairs and the algebraic property of the operators is explored. In addition, measures of similarity among internal cubic intuitionistic fuzzy sets on soft relational structures are created to facilitate the robust alternative comparison. On the grounds of these theoretical bases, a systematic decision-making scheme that is composed of two structured algorithms is set up. The relevance of the suggested framework can be proved by a practical hotel selection case study with the usage of several factors and professional evaluations. Comparative and sensitivity analysis demonstrates that the model proposed gives consistent rankings and minimizes the effects of boundary ambiguity in different levels of uncertainty, which can be used as a trusted and risk-conscious decision support device in hospitality management.