δ-equality of intuitionistic fuzzy sets: a new proximity measure and applications in 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 δ-equalities for the intuitionistic fuzzy set and δ-equalities for intuitionistic fuzzy relations. Two fuzzy sets are said to be δ-equal if they are equal to an extent of δ. The applications of δ-equalities are important to fuzzy statistics and fuzzy reasoning. Several characteristics of δ-equalities that were not discussed in the previous works are also investigated. We apply the δ-equalities to the application of medical diagnosis to investigate a patient’s diseases from symptoms. The idea is using δ-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):197– 206, 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)

Some New De Morgan Picture Operator Triples in Picture Fuzzy Logic

A new concept of picture fuzzy sets (PFS) were introduced in 2013, which are directextensions of the fuzzy sets and the intuitonistic fuzzy sets. Then some operations on PFS withsome properties are considered in [ 9,10 ]. Some basic operators of fuzzy logic as negation, tnorms, t-conorms for picture fuzzy sets firstly are defined and studied in [13,14]. This paper isdevoted to some classes of representable picture fuzzy t-norms and representable picture fuzzyt-conorms on PFS and a basic algebra structure of Picture Fuzzy Logic – De Morgan triples ofpicture operators

A classification of representable t-norm operators for picture fuzzy sets

T-norms and t-conorms are basic operators of fuzzy logics. The classifications of these operators are significant problems. Some results of the classifications of fuzzy logics operators for fuzzy sets are known. In 2013, we defined the picture fuzzy sets, and in 2015 some representable t-norms operators and t-conorms operators were defined. In this paper, we investigate the classification of representable picture t-norms and picture t-conorms operators for picture fuzzy sets

H-max distance measure of intuitionistic fuzzy sets in decision making

Intuitionistic fuzzy sets (IFSs) are successful to handle the uncertain situations of data. Distance measures of IFSs are important in the evaluation of IFSs relationships. In this paper, we analyzed the disadvantagesof existing distance measures of IFSs and proposed a new distance measure called H-max of IFSs. We con-tinued to point out some new results on intuitionistic t-norms and intuitionistic t-conorms and evaluateddistance measure between two IFSs which are basically structured from these operations. Further, wecombined the classification of t-representable intuitionistic fuzzy t-norms and t-conorms with the pro-posed distance measure to study some interesting properties. Moreover, we studied De Morgan tripletsof IFSs based on the proposed distance measure. Finally, we applied the proposed distance measure tomedical diagnosis problem examples and experimental validation on real-world datasets to check theapplicability and effectiveness

The Picture Fuzzy Distance Measure in Controlling Network Power Consumption

[EN] In order to solve the complex decision-making problems, there are many approaches and systems based on the fuzzy theory were proposed. In 1998, Smarandache introduced the concept of single-valued neutrosophic set as a complete development of fuzzy theory. In this paper, we research on the distance measure between single-valued neutrosophic sets based on the H-max measure of Ngan et al. [8]. The proposed measure is also a distance measure between picture fuzzy sets which was introduced by Cuong in 2013 [15]. Based on the proposed measure, an Adaptive Neuro Picture Fuzzy Inference System (ANPFIS) is built and applied to the decision making for the link states in interconnection networks. In experimental evaluation on the real datasets taken from the UPV (Universitat Politècnica de València) university, the performance of the proposed model is better than that of the related fuzzy methods.This work has been supported by MINECO and the European ERDF under grants PID2019-105903RB-I00 and RTI2018-098156-B-C51. The autor (R.T. Ngan) also would like to thank the Erasmus+ Mobility Program (2016-1-ES01-KA107-023453) for supporting her work.Roan, NT.; Coll, S.; Alonso Díaz, M.; Martínez-Rubio, J.; López Rodríguez, PJ.; Andújar, F.; Le, SH.... (2020). The Picture Fuzzy Distance Measure in Controlling Network Power Consumption. Journal of Fuzzy Extension & Applications. 1(3):148-168. https://doi.org/10.22105/JFEA.2020.249183.1009S1481681