Some single-valued neutrosophic power muirhead mean operators and their application to group decision making

Application of evidence reasoning algorithm and QUALIFLEX with single-valued neutrosophic set for MCDM

Multi-criteria decision-making methods often include attributes with uncertain nature in practical applications, single-valued neutrosophic set is an important approach to solve above problem. QUALIFLEX method is a traditional decision method that makes decision by comparing different permutations of alternatives. In this paper, QUALIFLEX method is developed to solve the MCDM problem with the element of decision matrix is the single-valued neutrosophic number. Besides, since the defects of the original QUALIFLEX method about fusing information of different attributes, this paper uses Dempster-Shafer theory of evidence to integrate the information about weight and alternatives. Finally, by comparing the result with other MCDM methods, we find that the new method can not only obtain reasonable results, but also explain the decision results by probability theory. This paper not only develops the traditional MCDM method, but also a meaningful attempt to apply AI algorithm in MCDM method.

Power Muirhead mean in spherical normal fuzzy environment and its applications to multi-attribute decision-making: Spherical normal fuzzy power Muirhead mean

This study aims to propose the power Muirhead mean (PMM) operator in the spherical normal fuzzy sets (SNoFS) environment to solve multiple attribute decision-making problems. Spherical normal fuzzy sets better characterize real-world problems. On the other hand, the Muirhead mean (MM) considers the relationship between any number of criteria of the operator. Power aggregation (PA) reduces the negative impact of excessively high or excessively low values on aggregation results. This article proposes two new aggregation methods: spherical normal fuzzy power Muirhead mean (SNoFPMM) and spherical normal fuzzy weighted power Muirhead mean (SNoFWPMM). Also, these operators produce effective results in terms of their suitability to real-world problems and the relationship between their criteria. The proposed operators are applied to solve the problems in choosing the ideal mask for the COVID-19 outbreak and investment company selection. However, uncertainty about the effects of COVID-19 complicates the decision-making process. Spherical normal fuzzy sets can handle both real-world problems and situations involving uncertainty. Our approach has been compared with other methods in the literature. The superior aspects and applicability of our strategy are also mentioned.

Interval complex neutrosophic soft relations and their application in decision-making

Interval complex neutrosophic soft sets (I-CNSSs) are interval neutrosophic soft sets (I-NSSs) described by three two-dimensional independent membership functions which are uncertainty interval, indeterminacy interval, and falsity interval respectively. Relation is a tool that helps in describing consistency and agreement between objects. Throughout this paper, we insert and discuss the interval complex neutrosophic soft relation (simply denoted by I-CNSR) that is a novel soft computing technique used to examine the degree of interaction between two corresponding models called I-CNSSs. We present the definition of the Cartesian product of I-CNSSs followed by the definition of I-CNSR. Further, the definitions and some theorems and properties related to the composition, inverse, and complement of I-CNSR are provided. The notions of symmetric, reflexive, transitive, and equivalent of I-CNSRs are proposed and the algebraic properties of these concepts are verified. Additionally, we point the contribution of our concept to real life problems by presenting a proposed algorithm to solve a real-life decision-making problem. Finally, a comparison between the proposed model and the existing relations is conducted to clarify the importance of this model.

Multiple attribute group decision-making based on interval-valued q-rung orthopair uncertain linguistic power Muirhead mean operators and linguistic scale functions

Fuzzy set theory and its extended form have been widely used in multiple-attribute group decision-making (MAGDM) problems, among which the interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs) got a lot of attention for its ability of capturing information denoted by interval values. Based on the previous studies, to find a better solution for fusing qualitative quantization information with fuzzy numbers, we propose a novel definition of interval-valued q-rung orthopair uncertain linguistic sets (IVq-ROULSs) based on the linguistic scale functions, as well as its corresponding properties, such as operational rules and the comparison method. Furthermore, we utilize the power Muirhead mean operators to construct the information fusion method, and provide a variety of aggregation operators based on the proposed information description environment. A model framework is constructed for solving the MAGDM problem utilizing the proposed method. Finally, we illustrate the performance of the new method and investigate its advantages and superiorities through comparative analysis.

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

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.

Q-Rung Probabilistic Dual Hesitant Fuzzy Sets and Their Application in Multi-Attribute Decision-Making

The probabilistic dual hesitant fuzzy sets (PDHFSs), which are able to consider multiple membership and non-membership degrees as well as their probabilistic information, provide decision experts a flexible manner to evaluate attribute values in complicated realistic multi-attribute decision-making (MADM) situations. However, recently developed MADM approaches on the basis of PDHFSs still have a number of shortcomings in both evaluation information expression and attribute values integration. Hence, our aim is to evade these drawbacks by proposing a new decision-making method. To realize this purpose, first of all a new fuzzy information representation manner is introduced, called q-rung probabilistic dual hesitant fuzzy sets (q-RPDHFSs), by capturing the probability of each element in q-rung dual hesitant fuzzy sets. The most attractive character of q-RPDHFSs is that they give decision experts incomparable degree of freedom so that attribute values of each alternative can be appropriately depicted. To make the utilization of q-RPDHFSs more convenient, we continue to introduce basic operational rules, comparison method and distance measure of q-RPDHFSs. When considering to integrate attribute values in q-rung probabilistic dual hesitant fuzzy MADM problems, we propose a series of novel operators based on the power average and Muirhead mean. As displayed in the main text, the new operators exhibit good performance and high efficiency in information fusion process. At last, a new MADM method with q-RPDHFSs and its main steps are demonstrated in detail. Its performance in resolving practical decision-making situations is studied by examples analysis.

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

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.