A Multi-valued Fuzzy Logic for Qualitative Reasoning in Healthcare

摘要

In this paper, we propose a 2n-valued fuzzy logic (2nvFL), which is especially suitable for representing linguistic terms, fuzzy concepts and qualitative reasoning and meanwhile avoids the difficulties of constructing fuzzy membership functions. More specifically, we present its syntax, semantics and minimal axiomatic system FLo, and prove some logical properties and soundness of it. In addition, we also compare the 2nvFL method with another fuzzy reasoning method in solving a healthcare problem. The results show that in the same data environment, our 2nvFL method can also complete fuzzy reasoning based on fuzzy numbers. Moreover, our 2nvFL's method has several advantages: (1) Our 2nvFL method does not involve membership functions of fuzzy sets and avoids the difficulty of setting membership functions of fuzzy linguistic terms. (2) Our 2nvFL can be established on an axiomatic system, and its theorem derivation is sound. (3) Our 2nvFL method can be used for qualitative reasoning with heterogeneous data, so it has a great potential in a wide range of applications. (4) It is easy to flexibly determine the truth value set of our 2n-valued logic according to specific application environments and specific problems.