On generalized intuitionistic fuzzy soft set

In this section we recall some definitions and properties regarding intuitionistic fuzzy soft set, possibility intuitionistic fuzzy soft set, and mappings on intuitionistic fuzzy soft classes.

arXiv (Cornell University), 2012

In this paper, we present the concept of relations in intuitionistic fuzzy soft set and study some of their properties and also discuss symmetric, transitive and reflexive intuitionistic fuzzy soft relations.

arXiv (Cornell University), 2013

In this work, we present definition of intuitionistic fuzzy parameterized (IF P) intuitionistic fuzzy soft set and its operations. Then we define IF P-aggregation operator to form IF P-intuitionistic fuzzy soft-decision-making method which allows constructing more efficient decision processes.

International Conferences on Science and Technology Natural Science and Technology, 2019

The concept of intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets (ifpifs-sets) is a new and useful mathematical tool propounded to model uncertainties. In this study, to improve this concept, we first present the difference and the symmetric difference between two intuitionistic fuzzy sets (if-sets) and investigate some properties. Secondly, on ifpifs-sets, we propose some new operations such as the relative union/intersection/difference and study some properties. We then suggest a new soft decision-making method and apply this method to a decision-making problem. Finally, we discuss ifpifs-sets and the method mentioned above for further research.

Journal of Korean Institute of Intelligent Systems, 2014

Park et al. introduced the concept of generalized intuitionistic fuzzy soft sets, which can be seen as an effective mathematical tool to deal with uncertainties. In this paper, we introduce new operations such as restricted union and restricted intersection and study their basic properties, and deal with the algebraic structure of generalized intuitionistic fuzzy soft sets. The lattice structures of generalized intuitionistic fuzzy soft sets are constructed.

Computers & Mathematics with Applications, 2010

Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. However, it has been pointed out that classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. In this paper, the notion of the interval-valued intuitionistic fuzzy soft set theory is proposed. Our interval-valued intuitionistic fuzzy soft set theory is a combination of an interval-valued intuitionistic fuzzy set theory and a soft set theory. In other words, our interval-valued intuitionistic fuzzy soft set theory is an interval-valued fuzzy extension of the intuitionistic fuzzy soft set theory or an intuitionistic fuzzy extension of the interval-valued fuzzy soft set theory. The complement, ''and'', ''or'', union, intersection, necessity and possibility operations are defined on the interval-valued intuitionistic fuzzy soft sets. The basic properties of the interval-valued intuitionistic fuzzy soft sets are also presented and discussed.

Lecture Notes in Computer Science, 2013

Soft set theory initiated by Molodtsov in 1999 has been emerging as a generic mathematical tool for dealing with uncertainty. A noticeable progress is found concerning the practical use of soft set in decision making problems. This paper introduces the concept of intuitionistic multi fuzzy soft set (IMFSS) by combining the intuitionistic multi fuzzy set (IMFS) and soft set models. Then an algorithmic approach is presented by using induced fuzzy soft set and level soft set for dealing with decision making problem based on IMFSS. Finally the proposed algorithm has also been illustrated through a numerical example.

Journal of Fuzzy Set Valued Analysis, 2016

In this paper, we have defined the notion of the fuzzy number intuitionistic fuzzy soft sets. For it, different operations such as union, intersection, complement, max, min, AND and OR have been introduced on fuzzy number intuitionistic fuzzy soft sets environment. Some examples of these operations are given and a few properties are also studied.

In this paper , we have defined First Zadeh’s implication , First Zadeh’s intuitionistic fuzzy conjunction and intuitionistic fuzzy disjunction of two intuitionistic fuzzy soft sets and some their basic properties are studied with proofs and examples.

In this paper, three new operations have been introduced on intuitionistic fuzzy soft sets. They are based on Second Zadeh‟s implication, conjunction and disjunction operations on intuitionistic fuzzy sets. Some examples of these operations were given and a few important properties were also studied.