An extended Pythagorean fuzzy VIKOR method with risk preference and a novel generalized distance measure for multicriteria decision-making problems

VIKOR and TOPSIS framework with a truthful-distance measure for the (t, s)-regulated interval-valued neutrosophic soft set

This article introduces the structure of the ( t , s ) -regulated interval-valued neutrosophic soft set (abbr. ( t , s ) -INSS). The structure of ( t , s ) -INSS is shown to be capable of handling the sheer heterogeneity and complexity of real-life situations, i.e. multiple inputs with various natures (hence neutrosophic), uncertainties over the input strength (hence interval-valued), the existence of different opinions (hence soft), and the perception at different strictness levels (hence ( t , s ) -regulated). Besides, a novel distance measure for the ( t , s ) -INSS model is proposed, which is truthful to the nature of each of the three membership (truth, indeterminacy, falsity) values present in a neutrosophic system. Finally, a Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and a Viekriterijumsko Kompromisno Rangiranje (VIKOR) algorithm that works on the ( t , s ) -INSS are introduced. The design of the proposed algorithms consists of TOPSIS and VIKOR frameworks that deploy a novel distance measure truthful to its intuitive meaning. The conventional method of TOPSIS and VIKOR will be generalized for the structure of ( t , s ) -INSS. The parameters t and s in the ( t , s ) -INSS model take the role of strictness in accepting a collection of data subject to the amount of mutually contradicting information present in that collection of data. The proposed algorithm will then be subjected to rigorous testing to justify its consistency with human intuition, using numerous examples which are specifically made to tally with the various human intuitions. Both the proposed algorithms are shown to be consistent with human intuitions through all the tests that were conducted. In comparison, all other works in the previous literature failed to comply with all the tests for consistency with human intuition. The ( t , s ) -INSS model is designed to be a conclusive generalization of Pythagorean fuzzy sets, interval neutrosophic sets, and fuzzy soft sets. This combines the advantages of all the three previously established structures, as well as having user-customizable parameters t and s , thereby enabling the ( t , s ) -INSS model to handle data of an unprecedentedly heterogeneous nature. The distance measure is a significant improvement over the current disputable distance measures, which handles the three types of membership values in a neutrosophic system as independent components, as if from a Euclidean vector. Lastly, the proposed algorithms were applied to data relevant to the ongoing COVID-19 pandemic which proves indispensable for the practical implementation of artificial intelligence.

Blockchain knowledge selection under the trapezoidal fermatean fuzzy number

Blockchain knowledge signifies a useful fundamental knowledge to safeguard faith in transboundary transmittals for main banks and financial institutions. In the study of group decision-making, the most important issue is how to coordinate opinions from different blockchains to reach a compromise under uncertainty. To tackle uncertainties surrounding multi-attribute group decision-making (MAGDM) problems in real-life scenes, we introduce a trapezoidal fermatean fuzzy set which generalizes trapezoidal fuzzy sets and fermatean fuzzy sets. The trapezoidal fermatean fuzzy model enables the degrees of membership, abstention, and non-membership to be expressed by linguistic terms. We define the operational laws of trapezoidal fermatean fuzzy numbers, and Einstein aggregation operator based on the trapezoidal fermatean fuzzy number. This makes it more flexible and descriptive to model the attitudes of Blockchain knowledge in MAGDM applications. Since multi-input arguments are interconnected and Blockchain knowledge has a lot of options perception, we also define the TOPSIS technique to facilitate the fusion of trapezoidal fermatean fuzzy information. With the aid of the trapezoidal fermatean fuzzy-TOPSIS technique, the main goal of this research is to present a general MAGDM framework by integrating the step with the complex proportional assessment. A trapezoidal fermatean positive ideal solution always wants the maximum value of the benefit criteria and the minimum value of the cost criteria. On the other hand, the trapezoidal fermatean negative ideal solution always wants the maximum value of the cost criteria and the minimum value of the benefit criteria. An integrated trapezoidal fermatean fuzzy-TOPSIS framework is established. In the proposed decision framework, the trapezoidal fermatean fuzzy-TOPSIS method is utilized to identify the subjective weights of decision attributes, and the trapezoidal fermatean fuzzy-TOPSIS approach is used to rank alternatives. Lastly, a case study concerning blockchain knowledge assessment is presented to demonstrate that the suggested scheme is feasible and effective. Furthermore, sensitivity and comparison analyses are conducted to show the robustness and superiority of the proposed method.

Multi-criteria Optimization Technique with Complex Pythagorean Fuzzy N-soft Information

The main objective of this article is to lay the foundations of a novel multi-criteria optimization technique, namely, the complex Pythagorean fuzzy N-soft VIKOR (CPFNS-VIKOR) method that is highly proficient to express a great deal of linguistic imprecision and vagueness inherent in human assessments. This strategy provides a versatile decision-making tool for the ranking-based fuzzy modeling of two-dimensional parameterized data. The CPFNS-VIKOR method integrates the ground-breaking specialities of the VIKOR method with the outstanding parametric structure of the complex Pythagorean fuzzy N-soft model. It is exclusively designed for the specification of a compromise optimal solution having maximum group utility and minimum individual regret of the opponent by analyzing their weighted proximity from ideal solutions. The developed strategy factually permits specific linguistic terms to demystify the individual perspectives of the decision-making experts regarding the efficacy of the alternatives and the priorities of the applicable criteria. We comprehensively assemble these independent appraisals of all the experts using the complex Pythagorean fuzzy N-soft weighted averaging operator. Moreover, we calibrate the ranking measure by utilizing group utility measure and regret measure in order to specify the hierarchical outranking of the feasible alternatives. We demonstrate the systematic methodology and framework of the proposed method with the assistance of an explicative flow chart. We skilfully investigate an empirical analysis related to selection of constructive industrial robots for the modernization of a manufacturing industry which really justifies the remarkable accountability of the proposed strategy. Furthermore, we validate this technique by a comparative study with the existing complex Pythagorean fuzzy TOPSIS (CPF-TOPSIS) method, complex Pythagorean fuzzy VIKOR (CPF-VIKOR) method and Pythagorean fuzzy TOPSIS (PF-TOPSIS) method. The comparative study is exemplified with an illustrative bar chart that visually endorses the rationality of the proposed methodology by interpreting highly compatible and accurate final outcomes. Finally, we holistically analyze the functionality of the developed strategy to enlighten its merits and prominence over other available competent approaches.

Risk Attitude in Multicriteria Decision Analysis: A Compromise Approach

In fields on which decisions need to be taken including health, as we are seeing nowadays in the COVID-19 crisis, decision-makers face multiple criteria and results with a random component. In stochastic multicriteria decision-making models, the risk attitude of the decision maker is a relevant factor. Traditionally, the shape of a utility function is the only element that represents the decision maker's risk attitude. The eduction process of multi-attribute utility functions implies some operational drawbacks, and it is not always easy. In this paper, we propose a new element with which the decision maker's risk attitude can be implemented: the selection of the stochastic efficiency concept to be used during a decision analysis. We suggest representing the risk attitude as a conflict between two poles: risk neutral attitude, associated with best expectations, and risk aversion attitude, associated with a lower uncertainty. The Extended Goal Programming formulation has inspired the parameter that is introduced in a new risk attitude formulation. This parameter reflects the trade-off between the two classical poles with respect to risk attitude. Thus, we have produced a new stochastic efficiency concept that we call Compromise Efficiency.