Knowledge reasoning approach with linguistic-valued intuitionistic fuzzy credibility

Linguistic term evaluations are always collected from two opposite sides at the same time in an assessment system. To process the linguistic knowledge, we propose an approximate reasoning approach with linguistic-valued intuitionistic fuzzy credibility based on linguistic-valued intuitionistic fuzzy lattice implication algebra and apply it to the assessment system. Firstly, we give a knowledge representation model with linguistic-valued intuitionistic fuzzy credibility. Based on the representation model, the forms and patterns of linguistic intuitionistic fuzzy modus ponens (LI-FMP) and linguistic intuitionistic fuzzy modus tollens (LI-FMT) are defined. Then there are three main phases of the knowledge reasoning with linguistic-valued intuitionistic fuzzy credibility. For a single rule, the similarity-based algorithms for LI-FMP and LI-FMT are given to get the sub-conclusion and the properties of similarity-based algorithms are discussed. For the multi-rule, we propose a rule aggregation operator to get the final conclusion by combining all the sub-conclusions. Some incomparable results are further processed if it is necessary. An intuitionistic linguistic-real valuation function is defined implying a linguistic intuitionistic fuzzy distance which is proved to be a positive valuation function. The ranking method of the incomparable results utilizes the linguistic intuitionistic distance. Lastly, the example about individual credit risk assessment shows how the proposed approach work and the contrast example illustrates that the proposed approach is rational and applied.