Hydrodynamic and hydromagnetic stability

As the extension of fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, and picture fuzzy set, the spherical fuzzy set is characterized by three functions expressing the positive-membership degree, the neutral-membership degree and the negative-membership degree which the sum squares of them is equal or less than 1. In this work, we shall present some novel Dice similarity measures of spherical fuzzy sets and the generalized Dice similarity measures of spherical fuzzy sets and indicates that the Dice similarity measures and asymmetric measures (projection measures) are the special cases of the generalized Dice similarity measures in some parameter values. Then, we propose the generalized Dice similarity measures-based multiple attribute group decision making models with spherical fuzzy information. Then, we apply the generalized Dice similarity measures between spherical fuzzy sets to multiple attribute group decision making. Finally, an illustrative example is given to demonstrate the efficiency of the similarity measures for selecting the desirable ERP system.

https://informatica.vu.lt/journal/INFORMATICA/article/875/file/pdf

The Generalized Dice Similarity Measures for Picture Fuzzy Sets and Their Applications

Abstract Heronian mean (HM) operator has the advantages of considering the interrelationships between parameters, and linguistic intuitionistic fuzzy number (LIFN), in which the membership and non-membership are expressed by linguistic terms, can more easily describe the uncertain and the vague information existing in the real world. In this paper, we propose the partitioned Heronian mean (PHM) operator which assumes that all attributes are partitioned into several parts and members in the same part are interrelated while in different parts there are no interrelationships among members, and develop some new operational rules of LIFNs to consider the interactions between membership function and non-membership function, especially when the degree of non-membership is zero. Then we extend PHM operator to LIFNs based on new operational rules, and propose the linguistic intuitionistic fuzzy partitioned Heronian mean (LIFPHM) operator, the linguistic intuitionistic fuzzy weighted partitioned Heronian mean (LIFWPHM) operator, the linguistic intuitionistic fuzzy partitioned geometric Heronian mean (LIFPGHM) operator and linguistic intuitionistic fuzzy weighted partitioned geometric Heronian mean (LIFWPGHM) operator. Further, we develop two methods to solve multi-attribute group decision making (MAGDM) problems with the linguistic intuitionistic fuzzy information. Finally, we give some examples to verify the effectiveness of two proposed methods by comparing with the existing

Partitioned Heronian Means Based on Linguistic Intuitionistic Fuzzynumbers for Dealing with Multi-Attribute Group Decision Making

Thin film arises in various applications from electrochemistry to nano devices, many mathematical tools were adopted to study the problem, e.g. Lie symmetries and conservation laws, however, the variational approach is rare. This paper shows that the semi-inverse method is an effective approach to establishment of a variational formulation for the thin film equation. A detailed derivation process is given, a special skill for construction of a heuristic trial-functional is elucidated.

A variational principle for a thin film equation

Spherical fuzzy sets (SFSs), recently proposed by Ashraf, is one of the most important concept to describe the fuzzy information in the process of decision making. In SFSs the sum of the squares of memberships grades lies in close unit interval and hence accommodate more uncertainties. Thus, this set outperforms over the existing structures of fuzzy sets. In real decision making problems, there is often a treat regarding a neutral character towards the membership and non-membership degrees expressed by the decision-makers. To get a fair decision during the process, in this paper, we define some new operational laws by Dombi t-norm and t-conorm. In the present study, we propose Spherical fuzzy Dombi weighted averaging (SFDWA), Spherical fuzzy Dombi ordered weighted averaging (SFDOWA), Spherical fuzzy Dombi hybrid weighted averaging (SFDHWA), Spherical fuzzy Dombi weighted geometric (SFDWG), Spherical fuzzy Dombi ordered weighted geometric (SFDOWG) and Spherical fuzzy Dombi hybrid weighted geometric (SFDHWG) aggregation operators and discuss several properties of these aggregation operators. These aforesaid operators are enormously used to help a successful solution of the decision problems. Then an algorithm by using spherical fuzzy set information in decision-making matrix is developed and applied the algorithm to decision-making problem to illustrate its applicability and effectiveness. Through this algorithm, we proved that our proposed approach is practical and provides decision makers a more mathematical insight before making decisions on their options. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantages of our method. Results indicate that the proposed method is suitable and effective for decision process to evaluate their best alternative.

Spherical fuzzy Dombi aggregation operators and their application in group decision making problems

Spherical fuzzy sets and their applications in multi-attribute decision making problems

Triangular cubic linguistic hesitant fuzzy aggregation operators and their application in group decision making

In recent decades, there has been a massive growth towards the prime interest of the hydrogen energy industry in automobile transportation fuel. Hydrogen is the most plentiful component and a perfect carrier of energy. Generally, evaluating a suitable hydrogen power plant site is a complex selection of multi-criteria decision-making (MCDM) problem concerning proper location assessment based on numerous essential criteria, the decision-makers expert opinion, and other qualitative/quantitative aspects. This paper presents the novel single-valued neutrosophic (SVN) multi-attribute decision-making method to help decision-makers choose the optimal hydrogen power plant site. At first, novel operating laws based on sine trigonometric function for single-valued neutrosophic sets (SVNSs) are introduced. The well-known sine trigonometry function preserves the periodicity and symmetric in nature about the origin, and therefore it satisfies the decision-maker preferences over the multi-time phase parameters. In conjunction with these properties and laws, we define several new aggregation operators (AOs), called SVN weighted averaging and geometric operators, to aggregate SVNSs. Subsequently, on the basis of the proposed AOs, we introduce decision-making technique for addressing multi-attribute decision-making (MADM) problems and provide a numerical illustration of the hydrogen power plant selection problem for validation. A detailed comparative analysis, including a sensitivity analysis, was carried out to improve the understanding and clarity of the proposed methodologies in view of the existing literature on MADM problems.

https://www.mdpi.com/2073-8994/12/2/298/pdf

Fuzzy Decision Support Modeling for Hydrogen Power Plant Selection Based on Single Valued Neutrosophic Sine Trigonometric Aggregation Operators

The objective of this manuscript is to present the notion of probabilistic hesitant fuzzy rough (PHFR) set and their basic operations. As a generalization of the sets, PHFR set is a more profitable way to express the uncertainties in the data. For it, firstly, we define the basic operational laws like, the union, intersection and the composition of probabilistic hesitant fuzzy approximation spaces with some basic properties are discussed in details. Secondly, presented the novel decision-making technique based on the PHFR sets over two nonempty fixed sets to deal with uncertainty in decision-making problems. Finally, two numerical examples are provided with some comparative study to validate the proposed approach.

Applications of probabilistic hesitant fuzzy rough set in decision support system

This paper contributes to cubic aggregation operator and applications in decision-making problem. In this paper, we use Dombi operational laws and Heronian mean operators, to develop a new concept of cubic fuzzy Heronian mean Dombi aggregation operators, i.e., cubic fuzzy Heronian mean Dombi aggregation (CFHMDA), cubic fuzzy weighted Heronian mean Dombi aggregation (CFWHMDA), cubic fuzzy geometric Heronian mean Dombi aggregation (CFGHMDA), and cubic fuzzy weighted geometric Heronian mean Dombi aggregation (CFWGHMDA) operators. The proposed operators are not deal single aspect, but also deal with the relation between multi-aspects making them more effectively solving decision-making (MADM) problems. We proposed a new algorithm to solve a multi-attribute decision-making problem based on the developed operators. Finally, we solved a MADM problems with the cubic fuzzy Heronian mean Dombi aggregation operators.

Fazal Ghani

Papers

Spherical fuzzy sets and their applications in multi-attribute decision making problems

Triangular cubic linguistic hesitant fuzzy aggregation operators and their application in group decision making

Fuzzy Decision Support Modeling for Hydrogen Power Plant Selection Based on Single Valued Neutrosophic Sine Trigonometric Aggregation Operators

Applications of probabilistic hesitant fuzzy rough set in decision support system

Cubic fuzzy Heronian mean Dombi aggregation operators and their application on multi-attribute decision-making problem