scholarly journals Applying the Dijkstra Algorithm to Solve a Linear Diophantine Fuzzy Environment

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1616
Author(s):  
Mani Parimala ◽  
Saeid Jafari ◽  
Muhamad Riaz ◽  
Muhammad Aslam
Keyword(s):  
Shortest Path ◽  
Fuzzy Set ◽  
Telecommunication Network ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Solution Technique ◽  
Directed Network ◽  
Uncertain Information ◽  
Dijkstra Algorithm ◽  
Pythagorean Fuzzy Set

Linear Diophantine fuzzy set (LDFS) theory expands Intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PyFS) theories, widening the space of vague and uncertain information via reference parameters owing to its magnificent feature of a broad depiction area for permissible doublets. We codify the shortest path (SP) problem for linear Diophantine fuzzy graphs. Linear Diophantine fuzzy numbers (LDFNs) are used to represent the weights associated with arcs. The main goal of the presented work is to create a solution technique for directed network graphs by introducing linear Diophantine fuzzy (LDF) optimality constraints. The weights of distinct routes are calculated using an improved score function (SF) with the arc values represented by LDFNs. The conventional Dijkstra method is further modified to find the arc weights of the linear Diophantine fuzzy shortest path (LDFSP) and coterminal LDFSP based on these enhanced score functions and optimality requirements. A comparative analysis was carried out with the current approaches demonstrating the benefits of the new algorithm. Finally, to validate the possible use of the proposed technique, a small-sized telecommunication network is presented.

scholarly journals Extended Fuzzy Sets and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 770
Author(s):  
Bahram Farhadinia ◽  
Francisco Chiclana
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Algebraic Operations ◽  
Innovative Concept

This contribution deals with introducing the innovative concept of extended fuzzy set (E-FS), in which the S-norm function of membership and non-membership grades is less than or equal to one. The proposed concept not only encompasses the concept of the fuzzy set (FS), but it also includes the concepts of the intuitionistic fuzzy set (IFS), the Pythagorean fuzzy set (PFS) and the p-rung orthopair fuzzy set (p-ROFS). In order to explore the features of the E-FS concept, set and algebraic operations on E-FSs, average and geometric operations of E-FSs are studied and an E-FS score function is defined. The superiority of the E-FS concept is further confirmed with a score-based decision making technique in which the concepts of FS, IFS, PFS and p-ROFS do not make sense.

scholarly journals Application of Pythagorean Fuzzy Digraphs in Package Delivery Robots

2021 ◽  
Author(s):  
Kanagaraj Sangeetha ◽  
◽  
Mani X Mani Parimala ◽  
Mohammed A. Al Shumrani ◽  
Said Broumi ◽  
...  
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Driving Forces ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Fuzzy Graph ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Package Delivery ◽  
Vertex Set

The fuzzy set concept was developed to cope with uncertainty, whereas traditional sets are intended to deal with certainty. To address flaws in fuzzy set theory, extensions such as Intuitionistic Fuzzy Set (IFS), neutrosophic fuzzy sets, image fuzzy sets, and Pythagorean fuzzy set (PyFS) were developed. Pythagorean fuzzy set is useful tool for more clearly defining hazy concepts. In comparison to other fuzzy models, Pythagorean fuzzy set-based models allow more flexibility in handling human judgement information. The fuzzy graph structure is used to deal with the uncertainty in a network and to characterize its relationship with the non-empty vertex set. Pythagorean fuzzy graph (PyFG) was one of the Intuitionistic Fuzzy Graph (IFG) extensions. PyFG was created to cope with the uncertainty of an object and its relationship with other objects. PyFS and PyFG are the driving forces behind this innovative concept. This work defines Pythagorean Fuzzy Digraph (PyFDG), and PyFDG's score function. An algorithm is proposed for an issue to find the Pythagorean shortest path in package delivery robots.

scholarly journals Linear Diophantine Fuzzy Einstein Aggregation Operators for Multi-Criteria Decision-Making Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-31
Author(s):  
Aiyared Iampan ◽  
Gustavo Santos García ◽  
Muhammad Riaz ◽  
Hafiz Muhammad Athar Farid ◽  
Ronnason Chinram
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multicriteria Decision Making ◽  
Cerebrovascular Diseases ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Uncertain Information ◽  
Health Administration ◽  
Pythagorean Fuzzy Set

The linear Diophantine fuzzy set (LDFS) has been proved to be an efficient tool in expressing decision maker (DM) evaluation values in multicriteria decision-making (MCDM) procedure. To more effectively represent DMs’ evaluation information in complicated MCDM process, this paper proposes a MCDM method based on proposed novel aggregation operators (AOs) under linear Diophantine fuzzy set (LDFS). A q -Rung orthopair fuzzy set ( q -ROFS), Pythagorean fuzzy set (PFS), and intuitionistic fuzzy set (IFS) are rudimentary concepts in computational intelligence, which have diverse applications in modeling uncertainty and MCDM. Unfortunately, these theories have their own limitations related to the membership and nonmembership grades. The linear Diophantine fuzzy set (LDFS) is a new approach towards uncertainty which has the ability to relax the strict constraints of IFS, PFS, and q –ROFS by considering reference/control parameters. LDFS provides an appropriate way to the decision experts (DEs) in order to deal with vague and uncertain information in a comprehensive way. Under these environments, we introduce several AOs named as linear Diophantine fuzzy Einstein weighted averaging (LDFEWA) operator, linear Diophantine fuzzy Einstein ordered weighted averaging (LDFEOWA) operator, linear Diophantine fuzzy Einstein weighted geometric (LDFEWG) operator, and linear Diophantine fuzzy Einstein ordered weighted geometric (LDFEOWG) operator. We investigate certain characteristics and operational laws with some illustrations. Ultimately, an innovative approach for MCDM under the linear Diophantine fuzzy information is examined by implementing suggested aggregation operators. A useful example related to a country’s national health administration (NHA) to create a fully developed postacute care (PAC) model network for the health recovery of patients suffering from cerebrovascular diseases (CVDs) is exhibited to specify the practicability and efficacy of the intended approach.

scholarly journals Shortest path algorithm of a network via spherical fuzzy digraphs

2021 ◽  
Author(s):  
Parimala Mani ◽  
◽  
Ibtesam Alshammari ◽  
Halimah Alshehri ◽  
◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Shortest Path ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Fuzzy Graph ◽  
Shortest Path Algorithm ◽  
Picture Fuzzy Set ◽  
Choice Decision

Many extension and generalization of fuzzy sets have been introduced and studied in the literature. Picture fuzzy set acquired more concentration in the domain of decision making, as many real time circumstances might have choices of more than one and researchers are looking for optimum choice/decision. Spherical fuzzy digraph is a generalization of intuitionistic fuzzy set and fuzzy graph. In this paper, we redefine some preliminary operations of Spherical fuzzy graph and it is referred as spherical fuzzy digraph. We discuss some arithmetic operations and relations among spherical fuzzy digraph. We further proposed a method to solve a shortest path problem using score function.

scholarly journals Some results on χ-single valued neutrosophic subgroups

2021 ◽  
Vol 23 (3) ◽  
pp. 1583
Author(s):  
M. Shazib Hameed ◽  
Zaheer Ahmad ◽  
Salman Mukhtar ◽  
Asad Ullah
Keyword(s):  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Vital Role ◽  
Neutrosophic Set ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Novel Structure ◽  
Fuzzy Subgroups

<p>In this study, we develop a novel structure χ-single valued neutrosophic set, which is a generalization of the intuitionistic set, inconsistent intuitionistic fuzzy set, Pythagorean fuzzy set, spherical fuzzy set, paraconsistent set, etc. Fuzzy subgroups play a vital role in vagueness structure, it differ from regular subgroups in that it is impossible to determine which group elements belong and which do not. In this paper, we investigate the concept of a χ-single valued neutrosophic set and χ-single valued neutrosophic subgroups. We explore the idea of χ-single valued neutrosophic set on fuzzy subgroups and several characterizations related to χ-single valued neutrosophic subgroups are suggested.</p>

Group decision making method for residents to choose livable cities depicted by n-intuitionistic polygonal fuzzy sets1

2020 ◽  
Vol 39 (3) ◽  
pp. 3503-3518
Author(s):  
Guijun Wang ◽  
Jie Zhou
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Arithmetic Operation ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Fuzzy Information ◽  
Decision Matrix ◽  
Arithmetic Average

The polygonal fuzzy set is an effective tool to express a class of fuzzy information with the help of finite ordered real numbers. It can not only guarantee the closeness of arithmetic operation of the polygonal fuzzy sets, but also has good linearity and intuitiveness. Firstly, the concept of the n-intuitionistic polygonal fuzzy set (n-IPFS) is proposed based on the intuitionistic fuzzy set and the polygonal fuzzy set. The ordered representation and arithmetic operation of n-IPFS are given by an example. Secondly, a new aggregation method for multi attribute fuzzy information is given based on the n-IPFS operations and the weighted arithmetic average operator, and the ranking criteria of n-IPFS are obtained by using the score function and the accuracy function. Finally, a new group decision making method is proposed for urban residents to choose the livable city problem based on the decision matrix of the n-IPFS, and the effectiveness of the proposed method is explained by an actual example.

scholarly journals q-Rung Orthopair Fuzzy Geometric Aggregation Operators Based on Generalized and Group-Generalized Parameters with Application to Water Loss Management

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1236
Author(s):  
Muhammad Riaz ◽  
Ayesha Razzaq ◽  
Humaira Kalsoom ◽  
Dragan Pamučar ◽  
Hafiz Muhammad Athar Farid ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Water Loss ◽  
Intuitionistic Fuzzy Set ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Water Supply Systems ◽  
Pythagorean Fuzzy Set ◽  
Water Losses ◽  
Water Loss Management

The notions of fuzzy set (FS) and intuitionistic fuzzy set (IFS) make a major contribution to dealing with practical situations in an indeterminate and imprecise framework, but there are some limitations. Pythagorean fuzzy set (PFS) is an extended form of the IFS, in which degree of truthness and degree of falsity meet the condition 0≤Θ˘2(x)+K2(x)≤1. Another extension of PFS is a q´-rung orthopair fuzzy set (q´-ROFS), in which truthness degree and falsity degree meet the condition 0≤Θ˘q´(x)+Kq´(x)≤1,(q´≥1), so they can characterize the scope of imprecise information in more comprehensive way. q´-ROFS theory is superior to FS, IFS, and PFS theory with distinguished characteristics. This study develops a few aggregation operators (AOs) for the fusion of q´-ROF information and introduces a new approach to decision-making based on the proposed operators. In the framework of this investigation, the idea of a generalized parameter is integrated into the q´-ROFS theory and different generalized q´-ROF geometric aggregation operators are presented. Subsequently, the AOs are extended to a “group-based generalized parameter”, with the perception of different specialists/decision makers. We developed q´-ROF geometric aggregation operator under generalized parameter and q´-ROF geometric aggregation operator under group-based generalized parameter. Increased water requirements, in parallel with water scarcity, force water utilities in developing countries to follow complex operating techniques for the distribution of the available amounts of water. Reducing water losses from water supply systems can help to bridge the gap between supply and demand. Finally, a decision-making approach based on the proposed operator is being built to solve the problems under the q´-ROF environment. An illustrative example related to water loss management has been given to show the validity of the developed method. Comparison analysis between the proposed and the existing operators have been performed in term of counter-intuitive cases for showing the liability and dominance of proposed techniques to the existing one is also considered.

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 The Maximizing Deviation Method Based on Interval-Valued Pythagorean Fuzzy Weighted Aggregating Operator for Multiple Criteria Group Decision Analysis

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Wei Liang ◽  
Xiaolu Zhang ◽  
Manfeng Liu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Intuitionistic Fuzzy Set ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Maximizing Deviation Method ◽  
Interval Valued ◽  
Deviation Method

As a new extension of Pythagorean fuzzy set (also called Atanassov’s intuitionistic fuzzy set of second type), interval-valued Pythagorean fuzzy set which is parallel to Atanassov’s interval-valued intuitionistic fuzzy set has recently been developed to model imprecise and ambiguous information in practical group decision making problems. The aim of this paper is to put forward a novel decision making method for handling multiple criteria group decision making problems within interval-valued Pythagorean fuzzy environment based on interval-valued Pythagorean fuzzy numbers (IVPFNs). There are three key issues being addressed in this approach. The first is to introduce an interval-valued Pythagorean fuzzy weighted arithmetic averaging (IVPF-WAA) operator to aggregate the decision data in order to get the overall preference values of alternatives. Some desirable properties of the IVPF-WAA operator are also investigated. Based on the idea of the maximizing deviation method, the second is to establish an optimization model for determining the weights of criteria for each expert. The third is to construct a minimizing consistency optimal model to derive the weights of criteria for the group. Finally, an illustrating example is given to verify the proposed approach.

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