Fuzzy number Intuitionistic fuzzy soft sets and its properties

2013

In this paper, the definition of intuitionistic fuzzy parameterised fuzzy soft set (ifpfs-sets) is introduced with their properties. Two operations on ifpfs-set, namely union and intersection are introduced. Also, some examples for these operations are given. The definition of ifpfsaggregation operator which forms ifpfs-decision making method is introduced.

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.

DergiPark (Istanbul University), 2016

In this paper, we review some operations in intuitionistic fuzzy soft multi set theory in different approach and show that the De Morgan's types of results hold in intuitionistic fuzzy soft multi set theory for these operations in our way. Basic supporting tools in information system are also defined. Application of intuitionistic fuzzy soft multi sets in information system are presented and discussed. Also we show that every intuitionistic fuzzy soft multi set is an intuitionistic fuzzy multi valued information system.

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.

Advances in Decision Sciences, 2012

Possibility intuitionistic fuzzy soft set and its operations are introduced, and a few of their properties are studied. An application of possibility intuitionistic fuzzy soft sets in decision making is investigated. A similarity measure of two possibility intuitionistic fuzzy soft sets has been discussed. An application of this similarity measure in medical diagnosis has been shown.

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.

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.

Soft sets are fantastic mathematical tools to handle imprecise and uncertain information in complicated situations. In this paper, we defined the hybrid structure which is the combination of soft set and complex number representation of intuitionistic fuzzy set. We defined basic set theoretic operations such as complement, union, intersection, restricted union, restricted intersection etc. for this hybrid structure. Moreover, we developed this theory to establish some more set theoretic operations like Disjunctive sum, difference, product, conjugate etc.

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.