Introduction to Intuitionistic Fuzzy Multisets and Its Applications

Abstract

In this chapter a new concept named Intuitionistic Fuzzy Multiset is introduced, which is an attempt to combine the two concepts: Intuitionistic Fuzzy sets and Fuzzy Multisets. The basic operations and their various properties are discussed. The authors discussed two significant applications of Intuitionistic Fuzzy Multisets. Most of human reasoning involves the use of variables whose values are fuzzy sets. This is the basis for the concept of a linguistic variable. But in some situations like decision making problems, the description by a linguistic variable in terms of membership function only is not adequate. There is chance of existing a non-null complement. There are situations that each element has different membership values. In such situations Intuitionistic Fuzzy Multisets is more adequate. Here the authors present Intuitionistic Fuzzy Multisets as a tool for reasoning such a situation through a medical diagnosis problem. As the second application, accuracy of Collaborative Robots using the concept of Intuitionistic Fuzzy Multiset is discussed.

An Improved Weighted Correlation Coefficient Based on Integrated Weight for Interval Neutrosophic Sets and its Application in Multi-criteria Decision-making Problems

“…Hesitant fuzzy sets (HFSs) were introduced by Torra and Narukawa 8 to deal with situations where people are hesitant in expressing their preference regarding objects in a decision-making process. Moreover, all these extensions of FSs have been developed by authors working in various fields [9][10][11] with further extensions still being proposed [12][13][14][15][16][17] . In particular, Florentin Smarandache 18,19 introduced neutrosophic logic and neutrosophic sets (NSs) in 1995, with the latter being characterized by the functions of truth, indeterminacy and falsity.…”

Intuitionistic Fuzzy Planar Graphs

“…Let be a nonempty set. An intuitionistic fuzzy multiset (IFMS) [29] drawn from is characterized by two functions: "count membership" of (CM ) and "count nonmembership" of (CN ) given by CM : → and CN : → where is the set of all crisp multisets drawn from the unit interval [0, 1] such that, for each ∈ , the membership sequence is defined as a decreasingly ordered sequence of elements in CM ( ) which is denoted by…”

Neutrosophic Multigroups and Applications

“…The fuzzy set theory [1] has been an age old and effective tool to tackle uncertainty information by introduced Zadeh but it can be applied only on random process. Therefore, on the basis of fuzzy set theory, Sebastian and Ramakrishnan [2] introduced Multi-Fuzzy Sets, Atanassov [3] proposed intuitionistic fuzzy set theory, Shinoj and John [4] initiated intuitionistic fuzzy multisets. Recently, the above theories have developed in many directions and found its applications in a wide variety of fields including algebraic structures.…”