Fuzzy Decision Making in Medical Diagnosis Using Vague Sets
Z. Shao, S. Kosari, Hossein Rashmanlou and F. Mofidnakhaei
Fuzzy sets theory (cf. Zadeh [71]) and its related fuzzy logic has been proposed for dealing with and solving various problems in which variables, parameters, relations, etc. are only imprecisely known and hence approximate reasoning schemes should be used. Such a situation is common in the case of virtually all non-trivial, in particular human centered, phenomena, processes and systems that prevail in reality and it is difficult to use conventional mathematics, based on binary logic, for their adequate characterization. The classic fuzzy set with the degrees of membership and non-membership of elements summing up to 1, has then been extended to many other concepts, and in our context these can be notably the intuitionistic (ordinary and interval) fuzzy sets (cf. Atanassov [1–5], hesitant fuzzy sets (cf. Torra [65] and Torra and Narukawa [66]) or vague sets (cf. Gau and Buehrer [22], Xu, Ma,Wang and Hao [70] (2010). Here we use the concept and tools and technique of vague sets in which basically for each element of a universe of discourse a true membership degree and a false membership degree, both from [0, 1], are assigned, and their sum is up to 1. We are concerned with a general decision making problem in medical diagnosis under imprecise information in which imprecision is represented by vague sets, In particular, a new definition of the basic concept of a distance between the vague sets is proposed as a crucial element of the approach. A graph theoretic perspective is assumed. An example is shown.
Keywords: fuzzy set, vague set, vague graph, intuitionistic fuzzy set, intuitionistic graph, distance between intuitionistic fuzzy sets, distance between vague sets, symptoms, disease