scholarly journals Correlation measure for interval valued pythagorean fuzzy sets

10.26524/cm91 ◽  
2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Saji Antonia ◽  
Mohana K
Keyword(s):  
Fuzzy Sets ◽  
Correlation Measure ◽  
Pythagorean Fuzzy Sets ◽  
Special Cases ◽  
Set Membership ◽  
Interval Valued

In this paper, We study the concep of interval valued pythagorean sets is the set we have two special cases we take one of the special cases. That is membership and non membership degrees are dependent and Interval valued pythagorean fuzzy sets .In IVPS set membership , non membership degrees are satisfying the condition 0 = (uA(x))2 + (νA(x))2 ≤ 1 Instead ofuA(x) + νA(x) > 1. .There basic operations on IVPS setAlso the correlation measure of IVPFS set is the extension of correlation measure of interval valued  Pythagorean fuzzy sets

scholarly journals On Some Nonclassical Algebraic Properties of Interval-Valued Fuzzy Soft Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaoyan Liu ◽  
Feng Feng ◽  
Hui Zhang
Keyword(s):  
Fuzzy Sets ◽  
Soft Computing ◽  
General Framework ◽  
Soft Sets ◽  
Computing Model ◽  
Special Cases ◽  
Algebraic Properties ◽  
Different Types ◽  
Fuzzy Soft Sets ◽  
Interval Valued

Interval-valued fuzzy soft sets realize a hybrid soft computing model in a general framework. Both Molodtsov’s soft sets and interval-valued fuzzy sets can be seen as special cases of interval-valued fuzzy soft sets. In this study, we first compare four different types of interval-valued fuzzy soft subsets and reveal the relations among them. Then we concentrate on investigating some nonclassical algebraic properties of interval-valued fuzzy soft sets under the soft product operations. We show that some fundamental algebraic properties including the commutative and associative laws do not hold in the conventional sense, but hold in weaker forms characterized in terms of the relation=L. We obtain a number of algebraic inequalities of interval-valued fuzzy soft sets characterized by interval-valued fuzzy soft inclusions. We also establish the weak idempotent law and the weak absorptive law of interval-valued fuzzy soft sets using interval-valued fuzzy softJ-equal relations. It is revealed that the soft product operations∧and∨of interval-valued fuzzy soft sets do not always have similar algebraic properties. Moreover, we find that only distributive inequalities described by the interval-valued fuzzy softL-inclusions hold for interval-valued fuzzy soft sets.

scholarly journals A new divergence measure of interval-valued pythagorean fuzzy sets and its application

2021 ◽  
Vol 5 (2) ◽  
pp. 9-24
Author(s):  
Arthi N ◽  
Mohana K
Keyword(s):  
Fuzzy Sets ◽  
Distance Measure ◽  
Evidence Theory ◽  
Belief Function ◽  
Divergence Measure ◽  
Pythagorean Fuzzy Sets ◽  
Practical Applications ◽  
Basic Probability ◽  
Jensen Shannon Divergence ◽  
Interval Valued

As the extension of the Fuzzy sets (FSs) theory, the Interval-valued Pythagorean Fuzzy Sets (IVPFS) was introduced which play an important role in handling the uncertainty. The Pythagorean fuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Interval-valued Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Interval-valued Pythagorean fuzzy sets,which is based on the belief function in Dempster–Shafer evidence theory, and is called IVPFSDM distance. It describes the Interval-Valued Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of IVPFSs, which is the step in establishing a link between the IVPFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods.

scholarly journals A FAMILY OF FINITE DE MORGAN AND KLEENE ALGEBRAS

2012 ◽  
Vol 20 (05) ◽  
pp. 631-653 ◽  
Author(s):  
CAROL L. WALKER ◽  
ELBERT A. WALKER
Keyword(s):  
Fuzzy Sets ◽  
Unit Interval ◽  
Point Of View ◽  
Truth Values ◽  
Special Cases ◽  
Per Se ◽  
Special Circumstances ◽  
Interval Valued

The algebra of truth values for fuzzy sets of type-2 consists of all mappings from the unit interval into itself, with operations certain convolutions of these mappings with respect to pointwise max and min. This algebra generalizes the truth-value algebras of both type-1 and of interval-valued fuzzy sets, and has been studied rather extensively both from a theoretical and applied point of view. This paper addresses the situation when the unit interval is replaced by two finite chains. Most of the basic theory goes through, but there are several special circumstances of interest. These algebras are of interest on two counts, both as special cases of bases for fuzzy theories, and as mathematical entities per se.

A chance-constraint programming model with interval-valued pythagorean fuzzy constraints

2021 ◽  
pp. 1-17
Author(s):  
Muhammad Touqeer ◽  
Rimsha Umer ◽  
Muhammad Irfan Ali
Keyword(s):  
Fuzzy Sets ◽  
Constraint Programming ◽  
Fuzzy Numbers ◽  
Chance Constraint ◽  
Pythagorean Fuzzy Sets ◽  
Fuzzy Constraints ◽  
Network Problems ◽  
Chance Constraint Programming ◽  
Pythagorean Fuzzy Numbers ◽  
Interval Valued

Pythagorean fuzzy sets and interval-valued Pythagorean fuzzy sets are more proficient in handling uncertain and imprecise information than intuitionistic fuzzy sets and fuzzy sets. In this article, we put forward a chance-constraint programming method to solve linear programming network problems with interval-valued Pythagorean fuzzy constraints. This practice is developed using score function and upper and lower membership functions of interval-valued Pythagorean fuzzy numbers. The feasibility of the anticipated approach is illustrated by solving an airway network application and shown to be used to solve different types of network problems with objective function having interval-valued Pythagorean fuzzy numbers by employing it on shortest path problem and minimum spanning tree problem. Furthermore, a comparative examination was performed to validate the effectiveness and usefulness of the projected methodology.

A Class of New Interval-Valued Intuitionistic Fuzzy Distance Measures and their Applications in Discriminant Analysis

2012 ◽  
Vol 182-183 ◽  
pp. 1743-1745 ◽  
Author(s):  
Hua Zhao ◽  
Ming Fang Ni ◽  
Hai Feng Liu
Keyword(s):  
Discriminant Analysis ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Fuzzy Information ◽  
Fuzzy Distance ◽  
Intuitionistic Fuzzy ◽  
Special Cases ◽  
Interval Valued

In this paper we develop a class of new distance measures for interval-valued intuitionistic fuzzy sets. Then we discuss some of the special cases of it by taking different parameters. Finally we apply them for discriminant analysis with interval-valued intuitionistic fuzzy information.

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