Two Centroid Point for SVTN-Numbers and SVTrN-Numbers

2020 ◽  
pp. 279-307
Author(s):  
Irfan Deli ◽  
Emel Kırmızı Öztürk
Keyword(s):  
Graph Theory ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Neutrosophic Set ◽  
Fuzzy Graph ◽  
Multiple Attribute ◽  
Centroid Point ◽  
Definition Of ◽  
Neutrosophic Number

In this chapter, some basic definitions and operations on the concepts of fuzzy set, fuzzy number, intuitionistic fuzzy set, single-valued neutrosophic set, single-valued neutrosophic number (SVN-number) are presented. Secondly, two centroid point are called 1. and 2. centroid point for single-valued trapezoidal neutrosophic number (SVTN-number) and single-valued triangular neutrosophic number (SVTrN-number) are presented. Then, some desired properties of 1. and 2. centroid point of SVTN-numbers and SVTrN-numbers studied. Also, based on concept of 1. and 2. centroid point of SVTrN-numbers, a new single-valued neutrosophic multiple-attribute decision-making method is proposed. Moreover, a numerical example is introduced to illustrate the availability and practicability of the proposed method. Finally, since centroid points of normalized SNTN-numbers or SNTrN-numbers are fuzzy values, all definitions and properties of fuzzy graph theory can applied to SNTN-numbers or SNTrN-numbers. For example, definition of fuzzy graph theory based on centroid points of normalized SVTN-numbers and SVTrN-numbers is given.

scholarly journals Multiple-attribute Decision-Making Method under a Single-Valued Neutrosophic Hesitant Fuzzy Environment

2015 ◽  
Vol 24 (1) ◽  
pp. 23-36 ◽  
Author(s):  
Jun Ye
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Neutrosophic Set ◽  
Fuzzy Environment ◽  
Cosine Measure ◽  
Multiple Attribute

AbstractOn the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set (SVNHFS) as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single-valued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, we introduce the basic operational relations and cosine measure function of SVNHFSs. Also, we develop a single-valued neutrosophic hesitant fuzzy weighted averaging (SVNHFWA) operator and a single-valued neutrosophic hesitant fuzzy weighted geometric (SVNHFWG) operator and investigate their properties. Furthermore, a multiple-attribute decision-making method is established on the basis of the SVNHFWA and SVNHFWG operators and the cosine measure under a single-valued neutrosophic hesitant fuzzy environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.

scholarly journals New Distance Measures for Dual Hesitant Fuzzy Sets and Their Application to Multiple Attribute Decision Making

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 191
Author(s):  
Wang ◽  
Li ◽  
Zhang ◽  
Han
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Distance Measures ◽  
Hesitant Fuzzy Set ◽  
Hesitant Fuzzy Sets ◽  
Attribute Weights ◽  
Multiple Attribute

Multiple attribute decision making (MADM) is full of uncertainty and vagueness due to intrinsic complexity, limited experience and individual cognition. Representative decision theories include fuzzy set (FS), intuitionistic fuzzy set (IFS), hesitant fuzzy set (HFS), dual hesitant fuzzy set (DHFS) and so on. Compared with IFS and HFS, DHFS has more advantages in dealing with uncertainties in real MADM problems and possesses good symmetry. The membership degrees and non-membership degrees in DHFS are simultaneously permitted to represent decision makers’ preferences by a given set having diverse possibilities. In this paper, new distance measures for dual hesitant fuzzy sets (DHFSs) are developed in terms of the mean, variance and number of elements in the dual hesitant fuzzy elements (DHFEs), which overcomes some deficiencies of the existing distance measures for DHFSs. The proposed distance measures are effectively applicable to solve MADM problems where the attribute weights are completely unknown. With the help of the new distance measures, the attribute weights are objectively determined, and the closeness coefficients of each alternative can be objectively obtained to generate optimal solution. Finally, an evaluation problem of airline service quality is conducted by using the distance-based MADM method to demonstrate its validity and applicability.

MODELS FOR MULTIPLE ATTRIBUTE DECISION MAKING WITH INTUITIONISTIC FUZZY INFORMATION

2007 ◽  
Vol 15 (03) ◽  
pp. 285-297 ◽  
Author(s):  
Z. S. XU
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Fuzzy Information ◽  
Attribute Weights ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute

The intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, was introduced by Atanassov [K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems 20 (1986) 87–96] as a generalization of Zadeh' fuzzy set [L. A. Zadeh, "Fuzzy Sets", Information and Control 8 (1965) 338–353] to deal with fuzziness and uncertainty. In this paper, we investigate the multiple attribute decision making (MADM) problems, in which the information about attribute weights is incomplete, and the attribute values are expressed in intuitionistic fuzzy numbers (IFNs). We first define the concept of intuitionistic fuzzy ideal solution (IFIS), and then, based on the IFIS and the distance measure, we establish some optimization models to derive the attribute weights. Furthermore, based on the developed models, we develop some procedures for the rankings of alternatives under different situations, and extend the developed models and procedures to handle the MADM problems with interval-valued intuitionistic fuzzy information. Finally, we give some illustrative examples to verify the effectiveness and practicability of the developed models and procedures.

scholarly journals Three-Way Multi-Attribute Decision Making Based on Outranking Relations under Intuitionistic Fuzzy Environments

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1384
Author(s):  
Zengtai Gong ◽  
Le Fan
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Decision Makers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Multiple Attribute ◽  
Multi Attribute Decision Making ◽  
Supplier Selection Problem

With the increasing complexity of the human social environment, it is impossible to describe each object in detail with accurate numbers when solving multiple attribute decision-making (MADM) problems. Compared with the fuzzy set (FS), the intuitionistic fuzzy set (IFS) not only has obvious advantages in allocating ambiguous values to the object to be considered, but also takes into account the degree of membership and non-membership, so it is more suitable for decision makers (DMs) to deal with complex realistic problems. Therefore, it is of great significance to propose a MADM method under an intuitionistic fuzzy environment. Moreover, compared with the traditional 2WD, by putting forward the option of delay, the decision-making risk can be effectively reduced using three-way decision (3WD). In addition, the binary relations between objects in the decision-making process have been continuously generalized, such as equivalence relation which have symmetrical relationship, dominance relation and outranking relation, which are worthy of study. In this paper, we propose 3WD-MADM method based on IF environment and the objective IFS is calculated by using the information table. Then, the hybrid information table is used to solve the supplier selection problem to demonstrate the effectiveness of the proposed method.

An Approach to Solve the Linear Programming Problem Using Single Valued Trapezoidal Neutrosophic Number

2020 ◽  
pp. 54-66
Author(s):  
Tuhin Bera ◽  
◽  
◽  
Nirmal Kumar Mahapatra
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Set Theory ◽  
Fuzzy Set ◽  
Linear Programming Problem ◽  
Intuitionistic Fuzzy Set ◽  
Neutrosophic Set ◽  
Real Field ◽  
Trapezoidal Neutrosophic Number ◽  
Neutrosophic Number

While making a decision, the neutrosophic set theory includes the uncertainty part beside certainty part (i.e., Yes or No). In the present uncertain socio-economic fashion, this pattern is highly acceptable and hence, the limitations of fuzzy set and intuitionistic fuzzy set are overcome with neutrosophic set theory. The present study provides a modified structure of linear programming problem (LP-problem) and its solution approach in neutrosophic sense. A special type of neutrosophic set defined over the set of real number, viz., single valued trapezoidal neutrosophic number (SVTN-number) is adopted here as the coefficients of the objective function, right-hand side coefficients and decision variables itself of an LP-problem. In order to solve such problem, a parameter based ranking function of SVTN-number is newly constructed from the geometrical configuration of the trapezium. It plays a key role in the development of the solution algorithm. An LP-problem is normally solved under the asset of some given constraints. Besides that, there may be some hidden parameters (e.g., awareness level of nearer society for the smooth run of a clinical pharmacy, ruined structure of road to be met a profit from a bus, etc) of an LP-problem and these affect the solution badly when experts ignore them. This study makes an attempt to solve an LP-problem by giving importance to all these to attain a fair outcome. The efficiency of the proposed concept is illustrated in a real field. A real example is stated and is solved numerically under the present view.

scholarly journals Coloring picture fuzzy graphs through their cuts and its computation

2021 ◽  
Vol 7 (1) ◽  
pp. 63
Author(s):  
Isnaini Rosyida ◽  
Suryono Suryono
Keyword(s):  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Fuzzy Graph ◽  
Chromatic Numbers ◽  
The Third ◽  
Fuzzy Graphs ◽  
Picture Fuzzy Set ◽  
Definition Of ◽  
Fuzzy Vertex ◽  
Matlab Programming

In a fuzzy set (FS), there is a concept of alpha-cuts of the FS for alpha in [0,1]. Further, this concept was extended into (alpha,delta)-cuts in an intuitionistic fuzzy set (IFS) for delta in [0,1]. One of the expansions of FS and IFS is the picture fuzzy set (PFS). Hence, the concept of (alpha,delta)-cuts was developed into (alpha,delta,beta)-cuts in a PFS where beta is an element of [0,1]. Since a picture fuzzy graph (PFG) consists of picture fuzzy vertex or edge sets or both of them, we have an idea to construct the notion of the (alpha,delta,beta)-cuts in a PFG. The steps used in this paper are developing theories and algorithms. The objectives in this research are to construct the concept of (alpha,delta,beta)-cuts in picture fuzzy graphs (PFGs), to construct the (alpha,delta,beta)-cuts coloring of PFGs, and to design an algorithm for finding the cut chromatic numbers of PFGs. The first result is a definition of the (alpha,delta,beta)-cut in picture fuzzy graphs (PFGs) where (alpha,delta,beta) are elements of a level set of the PFGs. Further, some properties of the cuts are proved. The second result is a concept of PFG coloring and the chromatic number of PFG based on the cuts. The third result is an algorithm to find the cuts and the chromatic numbers of PFGs. Finally, an evaluation of the algorithm is done through Matlab programming. This research could be used to solve some problems related to theories and applications of PFGs.

scholarly journals Power Improved Generalized Heronian Mean Operators Utilizing Hamacher Operations with Picture Fuzzy Information

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-25
Author(s):  
Baolin Li ◽  
Lihua Yang
Keyword(s):  
Fuzzy Set ◽  
Hamming Distance ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Fuzzy Information ◽  
Multiple Attribute ◽  
Picture Fuzzy Set ◽  
Einstein Operations ◽  
The Impact ◽  
Heronian Mean

In multiple attribute decision-making (MADM), to better denote complicated preference information of decision-makers (DMs), picture fuzzy set (PFS) as an expansion of intuitionistic fuzzy set (IFS) has become a powerful tool in the recent years. Meanwhile, to remove the impact of abnormal data and capture the correlations among attributes in MADM issue, we propose the power improved generalized Heronian mean (PIGHM) operators in this paper, which have the merits of both power average (PA) operator and improved generalized Heronian mean (IGHM) operator. Additionally, Hamacher operations as a generalization of Algebraic operations and Einstein operations demonstrate good smooth approximate. Motivated by these, the main purpose is to explore PIGHM operators utilizing Hamacher operations to cope with MADM issue with picture fuzzy information. First, we introduce the Hamacher operations, the normalized hamming distance, and similarity measure of picture fuzzy numbers (PHNs). Second, based on these, two new picture fuzzy aggregating operators (AOs), the picture fuzzy Hamacher weighted power improved generalized Heronian mean (PFHWPIGHM) operator and the picture fuzzy Hamacher weighted geometric power improved generalized Heronian mean (PFHWGPIGHM) operator, are put forward, and some properties and special instances of proposed AOs are also investigated. Third, a new MADM model in terms of the PIGHM AOs is developed. Eventually, a practical MADM example, together with sensitivity analysis and comparative analysis, is conducted to verify the credibility and superiority of the new MADM model.

scholarly journals A Novel Approached Based on T-Spherical Fuzzy Schweizer-Sklar Power Heronian Mean Operator for Evaluating Water Reuse Applications under Uncertainty

2021 ◽  
Vol 13 (13) ◽  
pp. 7108
Author(s):  
Qaisar Khan ◽  
Jeonghwan Gwak ◽  
Muhammad Shahzad ◽  
Muhammad Kamran Alam
Keyword(s):  
Fuzzy Set ◽  
Water Reuse ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Mathematical Tool ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Picture Fuzzy Set ◽  
The City ◽  
Heronian Mean

The T-Spherical Fuzzy set (T-SPHFS) is one of the core simplifications of quite a lot of fuzzy concepts such as fuzzy set (FS), intuitionistic fuzzy set (ITFS), picture fuzzy set (PIFS), Q-rung orthopair fuzzy set (Q-RUOFS), etc. T-SPHFS reveals fuzzy judgment by the degree of positive membership, degree of abstinence, degree of negative membership, and degree of refusal with relaxed conditions, and this is a more powerful mathematical tool to pair with inconsistent, indecisive, and indistinguishable information. In this article, several novel operational laws for T-SPFNs based on the Schweizer–Sklar t-norm (SSTN) and the Schweizer–Sklar t-conorm (SSTCN) are initiated, and some desirable characteristics of these operational laws are investigated. Further, maintaining the dominance of the power aggregation (POA) operators that confiscate the ramifications of the inappropriate data and Heronian mean (HEM) operators that consider the interrelationship among the input information being aggregated, we intend to focus on the T-Spherical fuzzy Schweizer–Sklar power Heronian mean (T-SPHFSSPHEM) operator, the T-Spherical fuzzy Schweizer–Sklar power geometric Heronian mean (T-SPHFSSPGHEM) operator, the T-Spherical fuzzy Schweizer–Sklar power weighted Heronian mean (T-SPHFSSPWHEM) operator, the T-Spherical fuzzy Schweizer–Sklar power weighted geometric Heronian mean (T-SPHFSSPWGHEM) operator, and their core properties and exceptional cases in connection with the parameters. Additionally, deployed on these newly initiated aggregation operators (AOs), a novel multiple attribute decision making (MADM) model is proposed. Then, the initiated model is applied to the City of Penticton (British Columbia, Canada) to select the best choice among the accessible seven water reuse choices to manifest the practicality and potency of the preferred model and a comparison with the proffered models is also particularized.

A Hesitant Intuitionistic Fuzzy Set Approach to Study Ideals of Semirings

2021 ◽  
Vol 10 (3) ◽  
pp. 1-17
Author(s):  
Debabrata Mandal
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Cartesian Product ◽  
Intuitionistic Fuzzy Set ◽  
Ideal Theory ◽  
Hesitant Fuzzy Set ◽  
Neutrosophic Set ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
The Ideal

The classical set theory was extended by the theory of fuzzy set and its several generalizations, for example, intuitionistic fuzzy set, interval valued fuzzy set, cubic set, hesitant fuzzy set, soft set, neutrosophic set, etc. In this paper, the author has combined the concepts of intuitionistic fuzzy set and hesitant fuzzy set to study the ideal theory of semirings. After the introduction and the priliminary of the paper, in Section 3, the author has defined hesitant intuitionistic fuzzy ideals and studied several properities of it using the basic operations intersection, homomorphism and cartesian product. In Section 4, the author has also defined hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals of a semiring and used these to find some characterizations of regular semiring. In that section, the author also has discussed some inter-relations between hesitant intuitionistic fuzzy ideals, hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals, and obtained some of their related properties.

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