scholarly journals Fuzzy soft set approach to ideal theory of regular AG-groupoids

2016 ◽  
Vol 24 (1) ◽  
pp. 263-288 ◽  
Author(s):  
Feng Feng ◽  
Madad Khan ◽  
Violeta Leoreanu-Fotea ◽  
Saima Anis ◽  
Nadeem Ajaib
Keyword(s):  
Fuzzy Sets ◽  
Ideal Theory ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Algebraic Properties

Abstract This paper aims to apply fuzzy sets and soft sets in combination to investigate algebraic properties of regular AG-groupoids. We initiate (∈γ; ∈γ qδ)-fuzzy soft left ideals (right ideals, bi-ideals and quasi-ideals) over AG-groupoids and explore some related properties. Moreover, we give a number of characterizations for regular AG-groupoids by virtue of various types of fuzzy soft ideals over them.

scholarly journals Hesitant Fuzzy Soft Subalgebras and Ideals inBCK/BCI-Algebras

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Young Bae Jun ◽  
Sun Shin Ahn ◽  
G. Muhiuddin
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Hesitant Fuzzy Sets ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets

As a link between classical soft sets and hesitant fuzzy sets, the notion of hesitant fuzzy soft sets is introduced and applied to a decision making problem in the papers by Babitha and John (2013) and Wang et al. (2014). The aim of this paper is to apply hesitant fuzzy soft set for dealing with several kinds of theories inBCK/BCI-algebras. The notions of hesitant fuzzy soft subalgebras and (closed) hesitant fuzzy soft ideals are introduced, and related properties are investigated. Relations between a hesitant fuzzy soft subalgebra and a (closed) hesitant fuzzy soft ideal are discussed. Conditions for a hesitant fuzzy soft set to be a hesitant fuzzy soft subalgebra are given, and conditions for a hesitant fuzzy soft subalgebra to be a hesitant fuzzy soft ideal are provided. Characterizations of a (closed) hesitant fuzzy soft ideal are considered.

scholarly journals Decision making algorithmic techniques based on aggregation operations and similarity measures of possibility intuitionistic fuzzy hypersoft sets

2021 ◽  
Vol 7 (3) ◽  
pp. 3866-3895
Author(s):  
Atiqe Ur Rahman ◽  
◽  
Muhammad Saeed ◽  
Hamiden Abd El-Wahed Khalifa ◽  
Walaa Abdullah Afifi ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Approximate Function

<abstract><p>Soft set has limitation for the consideration of disjoint attribute-valued sets corresponding to distinct attributes whereas hypersoft set, an extension of soft set, fully addresses this scarcity by replacing the approximate function of soft sets with multi-argument approximate function. Some structures (i.e., possibility fuzzy soft set, possibility intuitionistic fuzzy soft set) exist in literature in which a possibility of each element in the universe is attached with the parameterization of fuzzy sets and intuitionistic fuzzy sets while defining fuzzy soft set and intuitionistic fuzzy soft set respectively. This study aims to generalize the existing structure (i.e., possibility intuitionistic fuzzy soft set) and to make it adequate for multi-argument approximate function. Therefore, firstly, the elementary notion of possibility intuitionistic fuzzy hypersoft set is developed and some of its elementary properties i.e., subset, null set, absolute set and complement, are discussed with numerical examples. Secondly, its set-theoretic operations i.e., union, intersection, AND, OR and relevant laws are investigated with the help of numerical examples, matrix and graphical representations. Moreover, algorithms based on AND/OR operations are proposed and are elaborated with illustrative examples. Lastly, similarity measure between two possibility intuitionistic fuzzy hypersoft sets is characterized with the help of example. This concept of similarity measure is successfully applied in decision making to judge the eligibility of a candidate for an appropriate job. The proposed similarity formulation is compared with the relevant existing models and validity of the generalization of the proposed structure is discussed.</p></abstract>

scholarly journals Hesitant Bipolar-Valued Fuzzy Soft Sets and Their Application in Decision Making

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Jin-Ying Wang ◽  
Yan-Ping Wang ◽  
Lei Liu
Keyword(s):  
Mathematical Model ◽  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Score Function ◽  
Soft Set ◽  
Mathematical Tool ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Fuzzy Soft Sets

As an extension of fuzzy sets, hesitant bipolar-valued fuzzy set is a new mathematical tool for dealing with fuzzy problems, but it still has the problem with the inadequacy of the parametric tools. In order to further improve the accuracy of decision making, a new mixed mathematical model, named hesitant bipolar-valued fuzzy soft set, is constructed by combining hesitant bipolar-valued fuzzy sets with soft sets. Firstly, some related theories of hesitant bipolar-valued fuzzy sets are discussed. Secondly, the concept of hesitant bipolar-valued fuzzy soft set is given, and the algorithms of complement, union, intersection, “AND,” and “OR” are defined. Based on the above algorithms, the corresponding results of operation are analyzed and the relevant properties are discussed. Finally, a multiattribute decision-making method of hesitant bipolar-valued fuzzy soft sets is proposed by using the idea of score function and level soft sets. The effectiveness of the proposed method is illustrated by an example.

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.

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 An algorithm for fuzzy soft set based decision making approach

2020 ◽  
Vol 30 (1) ◽  
pp. 59-70
Author(s):  
Shehu Mohammed ◽  
Akbar Azam
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Group Decision Making ◽  
Group Decision ◽  
Soft Set ◽  
Mathematical Tool ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Fuzzy Soft Sets ◽  
Priority Table

The notion of soft set theory was initiated as a general mathematical tool for handling ambiguities. Decision making is viewed as a cognitive-based human activity for selecting the best alternative. In the present time, decision making techniques based on fuzzy soft sets have gained enormous attentions. On this development, this paper proposes a new algorithm for decision making in fuzzy soft set environment by hybridizing some existing techniques. The first novelty is the idea of absolute scores. The second concerns the concept of priority table in group decision making problems. The advantages of our approach herein are stronger power of objects discrimination and a well-determined inference.

scholarly journals On Fuzzy Soft Sets

2009 ◽  
Vol 2009 ◽  
pp. 1-6 ◽  
Author(s):  
B. Ahmad ◽  
Athar Kharal
Keyword(s):  
Set Theory ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Fuzzy Soft Sets

We further contribute to the properties of fuzzy soft sets as defined and studied in the work of Maji et al. ( 2001), Roy and Maji (2007), and Yang et al. (2007) and support them with examples and counterexamples. We improve Proposition 3.3 by Maji et al., (2001). Finally we define arbitrary fuzzy soft union and fuzzy soft intersection and prove DeMorgan Inclusions and DeMorgan Laws in Fuzzy Soft Set Theory.

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.

An Interval Valued Fuzzy Soft Set Based Optimization Algorithm for High Yielding Seed Selection

2018 ◽  
Vol 7 (2) ◽  
pp. 44-61 ◽  
Author(s):  
T. R. Sooraj ◽  
B. K. Tripathy
Keyword(s):  
Decision Making ◽  
Experimental Verification ◽  
Hybrid Models ◽  
Soft Set ◽  
Seed Selection ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
New Varieties ◽  
Interval Valued ◽  
Selection Of

As seed selection is a challenging task due to the presence of hundreds of varieties of seeds of each kind, some homework is necessary for selecting suitable seeds as new varieties and kinds of seeds are introduced in the market every year having their own strengths and weaknesses. The complexities involved in the characteristics in the form of parameters results in uncertainties and as a result some uncertainty based model or hybrid models of more than is required to model the scenario and come out with a decision. Soft sets have enough of parameterization tools to support and hence is the most suitable one for such a study. However, as hybrid models are more efficient, the authors select a model called the interval valued fuzzy soft set (IVFSS) and propose a decision-making algorithm for the selection of seeds. A real database of seeds is used for experimental verification of the efficiency of the algorithm. This is the first attempt for such a study. The use of signed priorities and intervals for the membership of values for entities makes the study more efficient and realistic.

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