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 Interval-Valued Fuzzy Soft Graphs

2017 ◽  
Vol 5 (1) ◽  
pp. 19-27 ◽  
Author(s):  
Onur Zihni ◽  
Yıldıray Çelik ◽  
Güven Kara
Keyword(s):  
Graph Theory ◽  
Cartesian Product ◽  
Soft Sets ◽  
Strong Product ◽  
Different Types ◽  
Fuzzy Soft Sets ◽  
Interval Valued

Abstract In this paper, we combine concepts of interval-valued fuzzy soft sets and graph theory. Then we introduce notations of interval-valued fuzzy soft graphs and complete interval-valued fuzzy soft graphs. We also present several different types operations including cartesian product, strong product and composition on interval-valued fuzzy soft graphs and investigate some properties of them.

scholarly journals Lattice ordered interval-valued hesitant fuzzy soft sets in decision making problem

2017 ◽  
Vol 7 (1.3) ◽  
pp. 52 ◽  
Author(s):  
Ar. Pandipriya ◽  
J. Vimala ◽  
S. Sabeena Begam
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Hesitant Fuzzy Sets ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Interval Valued

In 2015, Haidong Zhang enhanced the idea of Hesitant Fuzzy Sets and Soft Sets into Interval-Valued Hesitant Fuzzy Soft Sets along with its properties. In this present work, we establish the Lattice Ordered Interval-Valued Hesitant Fuzzy Soft Sets and examined its vital properties with examples. Eventually the application of Lattice Ordered Interval-Valued Hesitant Fuzzy Soft Set to decision making problem is established by means of elegant algorithm.

Generalized interval-valued hesitant intuitionistic fuzzy soft sets

2021 ◽  
pp. 1-12
Author(s):  
Admi Nazra ◽  
Yudiantri Asdi ◽  
Sisri Wahyuni ◽  
Hafizah Ramadhani ◽  
Zulvera
Keyword(s):  
Hesitant Fuzzy Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Binary Operations ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Soft Sets ◽  
Comparison Table ◽  
Definition Of ◽  
Interval Valued ◽  
Intuitionistic Fuzzy Soft Sets

This paper aims to extend the Interval-valued Intuitionistic Hesitant Fuzzy Set to a Generalized Interval-valued Hesitant Intuitionistic Fuzzy Soft Set (GIVHIFSS). Definition of a GIVHIFSS and some of their operations are defined, and some of their properties are studied. In these GIVHIFSSs, the authors have defined complement, null, and absolute. Soft binary operations like operations union, intersection, a subset are also defined. Here is also verified De Morgan’s laws and the algebraic structure of GIVHIFSSs. Finally, by using the comparison table, a different approach to GIVHIFSS based decision-making is presented.

An algebraic approach to N-soft sets with application in decision-making using TOPSIS

2021 ◽  
pp. 1-21
Author(s):  
Muhammad Shabir ◽  
Rimsha Mushtaq ◽  
Munazza Naz
Keyword(s):  
Decision Making ◽  
Mathematical Models ◽  
Real World ◽  
Algebraic Approach ◽  
Multi Criteria Decision Making ◽  
Commutative Monoids ◽  
Soft Sets ◽  
Algebraic Properties ◽  
Different Types ◽  
Selection Of

In this paper, we focus on two main objectives. Firstly, we define some binary and unary operations on N-soft sets and study their algebraic properties. In unary operations, three different types of complements are studied. We prove De Morgan’s laws concerning top complements and for bottom complements for N-soft sets where N is fixed and provide a counterexample to show that De Morgan’s laws do not hold if we take different N. Then, we study different collections of N-soft sets which become idempotent commutative monoids and consequently show, that, these monoids give rise to hemirings of N-soft sets. Some of these hemirings are turned out as lattices. Finally, we show that the collection of all N-soft sets with full parameter set E and collection of all N-soft sets with parameter subset A are Stone Algebras. The second objective is to integrate the well-known technique of TOPSIS and N-soft set-based mathematical models from the real world. We discuss a hybrid model of multi-criteria decision-making combining the TOPSIS and N-soft sets and present an algorithm with implementation on the selection of the best model of laptop.

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.

scholarly journals Generalized Picture Fuzzy Soft Sets and Their Application in Decision Support Systems

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 415 ◽  
Author(s):  
Muhammad Khan ◽  
Poom Kumam ◽  
Shahzaib Ashraf ◽  
Wiyada Kumam
Keyword(s):  
Decision Support ◽  
Decision Support Systems ◽  
Fuzzy Sets ◽  
Support Systems ◽  
Soft Information ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Existing Structures ◽  
Fuzzy Soft Sets ◽  
Picture Fuzzy Sets

In this paper, a generalized picture fuzzy soft set is proposed, which is an extension of the picture fuzzy soft sets. We investigate the basic properties of picture fuzzy soft sets and define an F-subset, M-subset, extended union, extended intersection, restricted union, restricted intersection and also prove the De Morgan’s laws for picture fuzzy soft information. We investigate upper and lower substitution for both picture fuzzy sets and generalized picture fuzzy soft sets. Meanwhile, the related proofs are given in detail. Finally, we propose an algorithm to deal with generalized picture fuzzy soft information. To show the supremacy and effectiveness of the proposed technique, we illustrate a descriptive example using generalized picture fuzzy soft information. Results indicate that the proposed technique is more generalized and effective over all the existing structures of fuzzy soft sets.

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.

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