Ordered Intuitionistic Fuzzy Soft Sets and Its Application in Decision Making Problem

2018 ◽  
Vol 7 (3) ◽  
pp. 76-98
Author(s):  
Pachaiyappan Muthukumar ◽  
Sai Sundara Krishnan Gangadharan
Keyword(s):  
Decision Making ◽  
Soft Sets ◽  
Numerical Example ◽  
Intuitionistic Fuzzy ◽  
Decision Making Problem ◽  
Algebraic Properties ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Soft Sets

In this article, some new basic operations and results of Ordered Intuitionistic Fuzzy Soft (OIFS) sets, such as equality, complement, subset, union, intersection, OR, and AND operators along with several examples are investigated. Further, based on the analysis of several operations on OIFS sets, numerous algebraic properties and famous De Morgans inclusions and De Morgans laws are established. Finally, using the notions of OIFS sets, an algorithm is developed and implemented in a numerical example.

On lattice ordered intuitionistic fuzzy soft sets

2018 ◽  
Vol 7 (1-2) ◽  
pp. 46-61 ◽  
Author(s):  
Tahir Mahmood ◽  
Muhammad Irfan Ali ◽  
Muhammad Aamir Malik ◽  
Waseem Ahmed
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Soft Sets

Lattices, soft sets, fuzzy sets and their generalizations have always been important for Mathematicians and the researchers working on uncertaities. In this paper our aim is to introduce the concept of lattice ordered intuitionistic fuzzy soft sets. After introducing extended union, extended intersection,  AND-product, OR-product, basic union, basic intersection of intuitionistic fuzzy soft sets, in this paper the affects of lattice ordered intuitionistic fuzzy soft sets and anti-lattice ordered intuitionistic fuzzy soft sets on restricted union, restricted intersection, extended union, extended intersection,AND-product, OR-product, basic union, basic intersection of intuitionistic fuzzy sets are discussed. Further a decision making problem is solved by using these concepts.

scholarly journals Intuitionistic Fuzzy Soft Hyper BCK Algebras

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 399
Author(s):  
Xiaolong Xin ◽  
Rajab Borzooei ◽  
Mahmood Bakhshi ◽  
Young Jun
Keyword(s):  
Decision Making ◽  
Soft Set ◽  
Fuzzy Mathematics ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Soft Sets

Maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets, and presented an application of fuzzy soft sets in a decision-making problem. Maji et al. also introduced the notion of intuitionistic fuzzy soft sets in the paper [P.K. Maji, R. Biswas and A.R. Roy, Intuitionistic fuzzy soft sets, The Journal of Fuzzy Mathematics, 9 (2001), no. 3, 677–692]. The aim of this manuscript is to apply the notion of intuitionistic fuzzy soft set to hyper BCK algebras. The notions of intuitionistic fuzzy soft hyper BCK ideal, intuitionistic fuzzy soft weak hyper BCK ideal, intuitionistic fuzzy soft s-weak hyper BCK-ideal and intuitionistic fuzzy soft strong hyper BCK-ideal are introduced, and related properties and relations are investigated. Characterizations of intuitionistic fuzzy soft (weak) hyper BCK ideal are considered. Conditions for an intuitionistic fuzzy soft weak hyper BCK ideal to be an intuitionistic fuzzy soft s-weak hyper BCK ideal are provided. Conditions for an intuitionistic fuzzy soft set to be an intuitionistic fuzzy soft strong hyper BCK ideal are given.

Application of Bipolar Intuitionistic Fuzzy Soft Sets in Decision Making Problem

2018 ◽  
Vol 7 (3) ◽  
pp. 32-55 ◽  
Author(s):  
Chiranjibe Jana ◽  
Madhumangal Pal
Keyword(s):  
Decision Making ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Graphs ◽  
Intuitionistic Fuzzy Soft Sets

This article describes how recently, a paper by D. Ezhilmaran and K. Sankar called Morphism of bipolar intuitionistic fuzzy graphs, has introduced bipolar intuitionistic fuzzy sets and morphism of bipolar intuitionistic fuzzy graphs. By using this concept, the authors of this article have combined a bipolar intuitionistic fuzzy set and a soft set. They introduce the notion of bipolar intuitionistic fuzzy soft set and study their basic properties. Also, presented in this article are the basic operations on bipolar intuitionistic fuzzy soft sets, extended unions, and the intersection of two bipolar intuitionistic fuzzy soft sets. An application of bipolar intuitionistic fuzzy soft set provides into a decision-making problem and a general algorithm to solve this decision making problem.

scholarly journals Minkowski Weighted Score Functions of Intuitionistic Fuzzy Values

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1143
Author(s):  
Feng Feng ◽  
Yujuan Zheng ◽  
José Carlos R. Alcantud ◽  
Qian Wang
Keyword(s):  
Decision Making ◽  
Score Function ◽  
Soft Sets ◽  
Score Functions ◽  
Intuitionistic Fuzzy ◽  
Geometric Point ◽  
Weighted Score ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Value ◽  
Intuitionistic Fuzzy Soft Sets

In multiple attribute decision-making in an intuitionistic fuzzy environment, the decision information is sometimes given by intuitionistic fuzzy soft sets. In order to address intuitionistic fuzzy decision-making problems in a more efficient way, many scholars have produced increasingly better procedures for ranking intuitionistic fuzzy values. In this study, we further investigate the problem of ranking intuitionistic fuzzy values from a geometric point of view, and we produce related applications to decision-making. We present Minkowski score functions of intuitionistic fuzzy values, which are natural generalizations of the expectation score function and other useful score functions in the literature. The rationale for Minkowski score functions lies in the geometric intuition that a better score should be assigned to an intuitionistic fuzzy value farther from the negative ideal intuitionistic fuzzy value. To capture the subjective attitude of decision makers, we further propose the Minkowski weighted score function that incorporates an attitudinal parameter. The Minkowski score function is a special case corresponding to a neutral attitude. Some fundamental properties of Minkowski (weighted) score functions are examined in detail. With the aid of the Minkowski weighted score function and the maximizing deviation method, we design a new algorithm for solving decision-making problems based on intuitionistic fuzzy soft sets. Moreover, two numerical examples regarding risk investment and supplier selection are employed to conduct comparative analyses and to demonstrate the feasibility of the approach proposed in this article.

An Adjustable Reduction Approach of Interval-valued Intuitionistic Fuzzy Soft Sets for Decision Making

2017 ◽  
Vol 11 (4) ◽  
pp. 999-1009 ◽  
Author(s):  
Hongwu Qin ◽  
Ahmad ShukriMohd Noor ◽  
Xiuqin Ma ◽  
Haruna Chiroma ◽  
Tutut Herawan
Keyword(s):  
Decision Making ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Soft Sets ◽  
Interval Valued ◽  
Intuitionistic Fuzzy Soft Sets ◽  
Reduction Approach
Sign in / Sign up

Export Citation Format

Share Document