A new generalized intuitionistic fuzzy set

Abstract

A generalized intuitionistic fuzzy set (GIF SB) is proposed. It is shown that Atanassov's intuitionistic fuzzy set, intuitionistic fuzzy sets of root type and intuitionistic fuzzy sets of second type are special cases of this new one. Some important notions, basic algebraic properties of GIF SB, three operators and their relationship are discussed. The algebraic properties include being closed under union, being closed under intersection, being closed under a necessity measure, being closed under a possibility measure and de Morgan type identities.Keywords: Generalized intuitionistic fuzzy set, Intuitionistic fuzzy set, Intuitionistic fuzzy sets of root type, Intuitionistic fuzzy sets of second type. AMS Classification:47S40.

Interpolative Boolean Algebra for Generalizations of Intuitionistic Fuzzy Sets

“…Definition 4 [10]. A generalized intuitionistic fuzzy set A JN in a universe X in the sense of [10] is defined as an object:…”

“…Graphical interpretation of one of the generalization (GAIFS6) given in[7] is not correct. The correct graphical interpretation may be found in[10].…”

On the Modal Operators Over the Generalized Interval Valued Intuitionistic Fuzzy Sets

“…Yilmaz and Cuvalcioglu [13] introduced N B (A) and N B * (A) operators on temporal IFSs and examined their properties. Baloui Jamkhaneh and Nadarajah [14] introduced a new generalized IFS (GIFS B ) and some operators over GIFS B . Baloui Jamkhnaeh [15] and Baloui Jamkhaneh and Nadi Ghara [16] defined level operators over the GIFS B s. In 2017 Baloui Jamkhaneh and Garg [17] considered some new operations over the generalized intuitionistic fuzzy sets and their application to decision making process.…”

“…This study shows the exibility of GIFS B s in terms of different operators. The study is expected to encourage applicability of GIFS B to the many areas of application of IFSs like sustainable energy planning, image fusion, agricultural production planning, medical diagnosis, pattern recognition, reservoir flood control operation, reliability optimization of complex systems, fault diagnosis and prediction of the best quality of two-wheelers, see Baloui Jamkhaneh and Nadarajah [14] for references and other areas of application of IFSs. The contents of this note are organized as follows: Section 2 states some definitions including the definition of GIFS B given in Baloui Jamkhaneh and Nadarajah [14]; Section 3 summarizes some results on GIFS B given in Baloui Jamkhaneh and Nadarajah [14]; Section 4 defines operators acting on GIFS B and derives their properties; some conclusions and future work are noted in Section 5.…”

Investment decision-making based on an intuitionistic fuzzy soft set

“…Recently, Zhan [22] investigated a new soft union set to hemirings. Since the idea of fuzzy set was started by Zadeh [21], many new methodologies and theories treating imprecision and uncertainty have been proposed, such as the intuitionistic fuzzy sets was published by Atanassov [2], A new generalized intuitionistic fuzzy set introduced by Jamkhaneh and Nadarajah [6] and so on [ [3], [38], [40], [44]]. Combining soft sets [15] with fuzzy sets [21] and intuitionistic fuzzy sets [2], Maji et al [9][10][11][12] defined fuzzy soft sets and intuitionistic fuzzy soft sets, which are rich potential for solving decision making problems.…”