delta-equality of intuitionistic fuzzy sets: a new proximity measure and applications in medical diagnosis

作者：Roan Thi Ngan; Ali, Mumtaz; Le Hoang Son^*

来源：Applied Intelligence, 2018, 48(2): 499-525.

DOI：10.1007/s10489-017-0986-0

• delta-equalities
• Algebraic operations
• Intuitionistic fuzzy set
• Intuitionistic fuzzy relations
• Medical diagnosis

Intuitionistic fuzzy set is capable of handling uncertainty with counterpart falsities which exist in nature. Proximity measure is a convenient way to demonstrate impractical significance of values of memberships in the intuitionistic fuzzy set. However, the related works of Pappis (Fuzzy Sets Syst 39(1):111-115, 1991), Hong and Hwang (Fuzzy Sets Syst 66(3):383-386, 1994), Virant (2000) and Cai (IEEE Trans Fuzzy Syst 9(5):738-750, 2001) did not model the measure in the context of the intuitionistic fuzzy set but in the Zadeh's fuzzy set instead. In this paper, we examine this problem and propose new notions of delta-equalities for the intuitionistic fuzzy set and delta-equalities for intuitionistic fuzzy relations. Two fuzzy sets are said to be delta-equal if they are equal to an extent of delta. The applications of delta-equalities are important to fuzzy statistics and fuzzy reasoning. Several characteristics of delta-equalities that were not discussed in the previous works are also investigated. We apply the delta-equalities to the application of medical diagnosis to investigate a patient's diseases from symptoms. The idea is using delta-equalities for intuitionistic fuzzy relations to find groups of intuitionistic fuzzified set with certain equality or similar degrees then combining them. Numerical examples are given to illustrate validity of the proposed algorithm. Further, we conduct experiments on real medical datasets to check the efficiency and applicability on real-world problems. The results obtained are also better in comparison with 10 existing diagnosis methods namely De et al. (Fuzzy Sets Syst 117:209-213, 2001), Samuel and Balamurugan (Appl Math Sci 6(35):1741-1746, 2012), Szmidt and Kacprzyk (2004), Zhang et al. (Procedia Eng 29:4336-4342, 2012), Hung and Yang (Pattern Recogn Lett 25:1603-1611, 2004), Wang and Xin (Pattern Recogn Lett 26:2063-2069, 2005), Vlachos and Sergiadis (Pattern Recogn Lett 28(2):197206, 2007), Zhang and Jiang (Inf Sci 178(6):4184-4191, 2008), Maheshwari and Srivastava (J Appl Anal Comput 6(3):772-789, 2016) and Support Vector Machine (SVM).

• 出版日期2018-2