scholarly journals KARAKTERISTIK MATRIKS SOFT

2021 ◽  
Vol 21 (2) ◽  
pp. 73-88
Author(s):  
Saman Abdurrahman ◽  
Thresye Thresye
Keyword(s):  
Fuzzy Set ◽  
Essential Role ◽  
Soft Set ◽  
Soft Matrix ◽  
Matrix Operations ◽  
Algebraic Properties ◽  
Membership Value

A soft set is a concept of the set that plays an essential role in overcoming vagueness. The soft set is an extension of the fuzzy set concept. One of the products of the soft set is a soft matrix. A soft matrix is a matrix formed into a soft set's membership value whose entries are elements at {0,1}. This paper aims to introduce operations on soft matrices, i.e., intersection, union, and complements. Further, algebraic properties of soft matrix operations were investigated, commutative, associative, distributive laws, De Morgan’s laws, and absorption. Himpunan soft merupakan suatu konsep himpunan yang berperan penting dalam mengatasi ketidakpastian. Himpunan soft merupakan perluasan dari konsep himpunan fuzzy. Salah satu produk dari himpunan soft adalah matriks soft. Matriks soft adalah matriks yang dibentuk dari nilai keanggotaan himpunan soft yang entri-entrinya elemen di {0,1}. Paper ini, bertujuan memperkenalkan operasi-operasi pada matriks soft, yaitu irisan, gabungan, dan komplemen. Lebih lanjut, diselidiki sifat-sifat aljabar operasi matriks soft, yaitu komutatif, asosiatif, hukum distributive, hukum De Morgan’s, dan absorpsi.

A Trust Evaluation of Networks Utilizing Matrix Operations Based on t-norms and t-conorms

2012 ◽  
Vol 16 (1) ◽  
pp. 154-161
Author(s):  
Masaya Nohmi ◽  
◽  
Aoi Honda ◽  
Yoshiaki Okazaki
Keyword(s):  
Trust Evaluation ◽  
Matrix Operations ◽  
Fuzzy Graphs ◽  
Algebraic Properties ◽  
The Matrix ◽  
Membership Value

A new scheme for numerical trust evaluation of networks is proposed. Matrix operations based on t-norms and t-conorms are used for the evaluation. The algebraic properties of the matrix operations are studied. Fuzzy graphs, in which nodes are linked with some membership value, are proposed, using the matrices as adjacent matrices. Furthermore, the fuzzinesses of the trustability distribution are calculated.

scholarly journals Similarity measures of Pythagorean fuzzy soft sets and clustering analysis

2021 ◽  
Author(s):  
Athira T M ◽  
Sunil Jacob John ◽  
Harish Garg
Keyword(s):  
Similarity Measure ◽  
Fuzzy Set ◽  
Clustering Algorithm ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
Soft Set ◽  
Soft Sets ◽  
Pythagorean Fuzzy Set ◽  
Fuzzy Soft Sets ◽  
Membership Value

Abstract Pythagorean fuzzy set (PFS) is a broadening of intuitionistic fuzzy set that can represent the situations where the sum of membership and the non-membership values exceeds one. Adding parameterization to PFS we obtain a structure named as Pythagorean fuzzy soft set (PFSS). It has a higher capacity to deal with vagueness as it captures both the structures of a PFS and a soft set. Several practical situations demand the measure of similarity between two structures, whose sum of membership value and non-membership value exceeds one. There are no existing tools to measure the similarity between PFSS and this paper put forward similarity measures for PFSS. An axiomatic definition for similarity measure is proposed for PFSS and certain expressions for similarity measure are introduced. Further, some theorems which express the properties of similarity measures are proved. A comparative study between proposed expressions for similarity measure is carried out. Also, a clustering algorithm based on PFSS is introduced by utilizing the proposed similarity measure.

scholarly journals Application of Repeated Average Method on Generalized Fuzzy Soft Matrix for Decision Making

2019 ◽  
Vol 45 (2) ◽  
pp. 249-259
Author(s):  
MK Hasan ◽  
MM Rahman ◽  
Abeda Sultana
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Average Method ◽  
Soft Set ◽  
Mathematical Approach ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Soft Matrix

Molodtsov introduced the theory of soft sets, which can be seen as a new mathematical approach to vagueness. Maji and his associates have further initiated several basic notions of soft set theory. They have also introduced the concept of fuzzy soft set, a more generalized concept, which is a combination of fuzzy set and soft set. In this paper, Repeated Average Method has been used in Generalized Fuzzy Soft Matrix for prompt decision making. Asiat. Soc. Bangladesh, Sci. 45(2): 249-259, December 2019

scholarly journals Hybrid structures applied to ideals in near-rings

2021 ◽  
Author(s):  
B. Elavarasan ◽  
G. Muhiuddin ◽  
K. Porselvi ◽  
Y. B. Jun
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Real World ◽  
Rough Set Theory ◽  
Wide Spectrum ◽  
Hybrid Structure ◽  
Soft Set ◽  
Hybrid Structures ◽  
Classical Mathematics ◽  
Classical Means

AbstractHuman endeavours span a wide spectrum of activities which includes solving fascinating problems in the realms of engineering, arts, sciences, medical sciences, social sciences, economics and environment. To solve these problems, classical mathematics methods are insufficient. The real-world problems involve many uncertainties making them difficult to solve by classical means. The researchers world over have established new mathematical theories such as fuzzy set theory and rough set theory in order to model the uncertainties that appear in various fields mentioned above. In the recent days, soft set theory has been developed which offers a novel way of solving real world issues as the issue of setting the membership function does not arise. This comes handy in solving numerous problems and many advancements are being made now-a-days. Jun introduced hybrid structure utilizing the ideas of a fuzzy set and a soft set. It is to be noted that hybrid structures are a speculation of soft set and fuzzy set. In the present work, the notion of hybrid ideals of a near-ring is introduced. Significant work has been carried out to investigate a portion of their significant properties. These notions are characterized and their relations are established furthermore. For a hybrid left (resp., right) ideal, different left (resp., right) ideal structures of near-rings are constructed. Efforts have been undertaken to display the relations between the hybrid product and hybrid intersection. Finally, results based on homomorphic hybrid preimage of a hybrid left (resp., right) ideals are proved.

scholarly journals Generalised Interval-Valued Fuzzy Soft Set

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Abdul Razak Salleh
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Interval Valued

We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in a medical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised fuzzy soft set; generalised interval-valued fuzzy soft set; interval-valued fuzzy set; interval-valued fuzzy soft set.

Intuitionistic Fuzzy X-Subalgebra of Near-Subtraction Semigroups

2021 ◽  
Vol 7 (3) ◽  
Author(s):  
J. Siva Ranjini ◽  
V. Mahalakshmi
Keyword(s):  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Algebraic Properties

The theory of Intuitionistic fuzzy set is the extension of the fuzzy set that deals with truth and false membership data. We will discuss along with some fundamentals and their algebraic Properties. The results obtained are entirely more beneficial to the researchers. We also expand the Complement of the Set and Homomorphism. The motivation of the present manuscript is to extend the concept of Intuitionistic fuzzy X-subalgebra in near-subtraction semigroups.

scholarly journals Fuzzy Soft Multiset Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Abdul Razak Salleh
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Soft Set ◽  
Mathematical Tool ◽  
Basic Properties ◽  
Definition Of

In 1999 Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. Alkhazaleh et al. in 2011 introduced the definition of a soft multiset as a generalization of Molodtsov's soft set. In this paper we give the definition of fuzzy soft multiset as a combination of soft multiset and fuzzy set and study its properties and operations. We give examples for these concepts. Basic properties of the operations are also given. An application of this theory in decision-making problems is shown.

New expected impact functions and algorithms for modeling games under soft sets

2020 ◽  
Vol 39 (3) ◽  
pp. 4463-4472
Author(s):  
Irfan Deli ◽  
Hoang Viet Long ◽  
Le Hoang Son ◽  
Raghvendra Kumar ◽  
Arindam Dey
Keyword(s):  
Decision Making ◽  
Nash Equilibrium ◽  
Model Theory ◽  
Saddle Points ◽  
Soft Set ◽  
Soft Sets ◽  
Matrix Games ◽  
Soft Matrix ◽  
Dominated Strategies

Soft set is the power tool to deal with uncertainty in a parametric manner. In applications of soft set, one of the most important steps is to define mappings on soft sets. In this study, we model theory of game under theory of soft set which is an effective tool for handling uncertainties events and problems that may exist in a game. To this end, we first define some expected impact functions of players in soft games. Then, we propose three new decision making algorithms to solve the 2.2 × p, 2 . n × p and m . 2 × p soft matrix games, which cannot be settled by the relevant soft methods such as saddle points, lover and upper values, dominated strategies and Nash equilibrium. The proposed soft game algorithms are illustrated by examples.

scholarly journals Combination of the Single-Valued Neutrosophic Fuzzy Set and the Soft Set with Applications in Decision-Making

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1361 ◽  
Author(s):  
Ahmed Mostafa Khalil ◽  
Dunqian Cao ◽  
Abdelfatah Azzam ◽  
Florentin Smarandache ◽  
Wedad R. Alharbi
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Soft Set ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Numerical Example ◽  
Fuzzy Soft Sets ◽  
Novel Concept

In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic fuzzy soft sets are presented. Then, several theoretical operations of single-valued neutrosophic fuzzy soft sets are given. In addition, the first type for the fuzzy decision-making based on single-valued neutrosophic fuzzy soft set matrix is constructed. Finally, we present the second type by using the AND operation of the single-valued neutrosophic fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example.

scholarly journals Revised Max-Min Average Composition Method for Decision Making Using Intuitionistic Fuzzy Soft Matrix Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
P. Shanmugasundaram ◽  
C. V. Seshaiah ◽  
K. Rathi
Keyword(s):  
Decision Making ◽  
Matrix Theory ◽  
Fuzzy Soft Set ◽  
Average Composition ◽  
Soft Matrix ◽  
Professional Students ◽  
Intuitionistic Fuzzy ◽  
Composition Method ◽  
Matrix Operations ◽  
Selection Of

In this paper a revised Intuitionistic Fuzzy Max-Min Average Composition Method is proposed to construct the decision method for the selection of the professional students based on their skills by the recruiters using the operations of Intuitionistic Fuzzy Soft Matrices. In Shanmugasundaram et al. (2014), Intuitionistic Fuzzy Max-Min Average Composition Method was introduced and applied in Medical diagnosis problem. Sanchez’s approach (Sanchez (1979)) for decision making is studied and the concept is modified for the application of Intuitionistic fuzzy soft set theory. Through a survey, the opportunities and selection of the students with the help of Intuitionistic fuzzy soft matrix operations along with Intuitionistic fuzzy max-min average composition method is discussed.

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