(α, β)-Generalized Lock Resolution Method Based On Intuitionistic Fuzzy Propositional Logic

The expansion of intuitionistic fuzzy sets is fuzzy sets, it can reflect the credible degree of things at the same time and not believable degree of collection. So, intuitionistic fuzzy logic is a broader interpretation of things or phenomena in daily life the uncertainty of fuzzy phenomena than fuzzy logic. Resolution method is an important tool of theorem automated proving. The concise and beautiful of resolution principle, attracting many scholars attribute into the research work of principle. Due to the traditional resolution principle of intuitionistic fuzzy logic exists the phenomenon that the process is relatively complex and the workload of computer larger, therefore, in this paper, intuitionistic fuzzy propositional logic(α, β)-generalized lock resolution method based on lock resolution methods in classical resolution method is proposed. The method is more simple than the resolution method of traditional Intuitionistic fuzzy logic. In addition, in this paper, on the basis of the(α, β)-generalized lock resolution method of intuitionistic fuzzy propositional logic, proposing the(α, β)-quasi lock semantic resolution method of intuitionistic fuzzy propositional logic. Further constrain the redundant clauses, reducing the workload of the computer.The main research results are as follows:To reduce the resolution process of intuitionistic fuzzy logic, the concepts of(α, β)-satisfiable and(α, β)-resolvent are proposed based on the general form of resolution principle of intuitionistic fuzzy logic in this paper, the satisfiability problem of generalized clauses and its resolvent is proved. The indexed of generalized clauses are given in intuitionistic fuzzy logic system. Resolution is then permitted only on literals of the lowest index in each clause, therefore,(α, β)-generalized lock resolution method is introduced in intuitionistic fuzzy logic system, and its soundness and completeness are proved. Then the step of resolution algorithm is presented and an example illustrates the effectiveness of the proposed method.To improve the(α, β)-resolution efficiency of intuitionistic fuzzy propositional logic, we applied quasi lock semantic resolution to(α, β)-resolution. The(α, β)-quasi lock semantic resolution method is introduced in intuitionistic fuzzy logic system, and its soundness and completeness are proved. The concepts of(α, β)- quasi lock semantic resolution and(α, β)- quasi lock semantic resolution reasoning of intuitionistic fuzzy propositional logic are proposed. The formula of(α, β)- quasi lock semantic resolution and the merger rule of generalized lock clauses are discussed. The(α, β)-quasi lock semantic resolution algorithm is presented and an example is given to illustrate the effectiveness of the proposed method.