An interval-valued Pythagorean prioritized operator-based game theoretical framework with its applications in multicriteria group decision making

Distance and similarity measures on belief and plausibility under q-rung orthopair fuzzy sets with applications

Belief and plausibility functions based on evidence theory (ET) have been widely used in managing uncertainty. Various generalizations of ET to fuzzy sets (FSs) have been reported in the literature, but no generalization of ET to q-rung orthopair fuzzy sets (q-ROFSs) has been made yet. Therefore, this paper proposes a novel, simple, and intuitive approach to distance and similarity measures for q-ROFSs based on belief and plausibility functions within the framework of ET. This research addresses a significant research gap by introducing a comprehensive framework for handling uncertainty in q-ROFSs using ET. Furthermore, it acknowledges the limitations inherent in the current state of research, notably the absence of generalizations of ET to q-ROFSs and the challenges in extending belief and plausibility measures to certain aggregation operators and other generalizations including Hesitant fuzzy sets, Bipolar fuzzy sets, Fuzzy soft sets etc. Our contribution lies in the proposal of a novel approach to distance and similarity measures for q-ROFSs under ET, utilizing Orthopairian belief and plausibility intervals (OBPIs). We establish new similarity measures within the generalized ET framework and demonstrate the reasonability of our method through useful numerical examples. Additionally, we construct Orthopairian belief and plausibility GRA (OBP-GRA) for managing daily life complex issues, particularly in multicriteria decision-making scenarios. Numerical simulations and results confirm the usability and practical applicability of our proposed method in the framework of ET.

Research on expert group decision-making and conflict resolution in complex engineer-ing consulting process

Expert group decision-making in the process of engineering consulting is an important part of the smooth development of engineering projects. Whether the conceptual design scheme of the project is reasonable or not will directly affect the construction quality of the project. After the preliminary selection of a river ecological governance project, four conceptual design schemes were obtained. The owner invited 20 experts in relevant fields to make decisions on the four schemes collected in the early stage. The experts gave preference information for each scheme after reading the relevant materials of the project and clarifying the actual needs of the project. Based on this background, this paper uses a combination of quantitative and qualitative methods to construct a model for group decision-making and conflict resolution in the engineering consulting process. We use the preference relationship to reflect the degree of experts’ preference for the scheme, cluster them through similarity calculation, calculate the conflict degree of group preference and personal preference respectively, and comprehensively use the sequence difference method and personal preference correction method to resolve the conflict, so that their opinions can be quickly agreed within the specified time. The results calculated by model are consistent with the actual situation of the project, which verifies the effectiveness of the model proposed in this paper, which can provide a reference for similar project decision-making and conflict resolution process.

Cooperative Game Approach to Robust Control Design for Fuzzy Dynamical Systems

There is uncertainty in the system, and we consider that uncertainty is (possibly fast) time varying, but with definite bound. Fuzzy set theory is used to describe the inexact boundary and then the problem of robust control of uncertain dynamical systems is studied. Based on two adjustable design parameters, a robust control method for general mechanical systems is proposed. The control is deterministic, not the conventional IF-THEN rule based. By using the Lyapunov minimax approach, it is proved that the proposed control can guarantee system performance to be uniformly bounded and uniformly ultimately bounded. In order to find the optimal solution in the prescribed range, a two-player cooperative game is used. To reduce costs while ensuring control performance, two performance indices are developed, each of which is controlled by an adjustable parameter (i.e., player). Both necessary and sufficient conditions for Pareto-optimality are established. Using these conditions, the Pareto-optimal solution can be obtained. The effectiveness of the control design is demonstrated by the simulation of the two-body pendulum.

An enhanced VIKOR method for multi-criteria group decision-making with complex Fermatean fuzzy sets

This paper aims to propose a new decision-making approach retaining the fascinating traits of the conventional VIKOR method in the context of the enrich multidimensional complex Fermatean fuzzy $ N $-soft set. The VIKOR technique is contemplated as the most reliable decision-making approach among others which employs a strategy to identify the compromise solution with advantageous distance from the positive ideal solution possesses maximum majority utility and minimum individual regret. At the same time, the paramount characteristic of the complex Fermatean fuzzy $ N $-soft set considers the proclivity to capture two-dimensional uncertain and imprecise information along with the multi-valued parameters. This article expands the literature to handle the multi-attribute group decision-making strategy by introducing a technique, namely, the complex Fermatean fuzzy $ N $-soft VIKOR method that amalgamates the unconventional traits of complex Fermatean fuzzy $ N $-soft with the capability of the VIKOR method. The proposed technique permits the assignment of the $ N $-soft grades to the decision-makers, alternatives, and attributes based on their performances. Firstly, we unify these individual opinions of all decision-makers about the alternatives by employing the complex Fermatean fuzzy $ N $-soft weighted average operator. After that, all entities of the aggregated decision matrix are converted into crisp data by utilizing the score function. Furthermore, we calculate the ranking measures of the group utility and the individual regret by assigning the weight of strategy belongs to the interval $ [0, 1]. $ To find the compromise solution, we arrange the ranking measures in ascending order, and the alternative that possesses the conditions of compromise solution is selected. We demonstrate the presented multi-attribute group decision-making technique by selecting the best location for a nuclear power plant. We conduct the comparative analysis of the presented technique with Fermatean fuzzy TOPSIS to endorse the veracity and accuracy of our method. Finally, we explain the merits and limitations of our strategy and give some concluding remarks.

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.

An approach to decision making with interval-valued complex Pythagorean fuzzy model for evaluating personal risk of mental patients

It is prominent important for managers to assess the personal risk of mental patients. The evaluation process refers to numerous indexes, and the evaluation values are general portrayed by uncertainty information. In order to conveniently model the complicated uncertainty information in realistic decision making, interval-valued complex Pythagorean fuzzy set is proposed. Firstly, with the aid of Einstein t-norm and t-conorm, four fundamental operations for interval-valued complex Pythagorean fuzzy number (IVCPFN) are constructed along with some operational properties. Subsequently, according to these proposed operations, the weighted average and weighted geometric forms of aggregation operators are initiated for fusing IVCPFNs, and their anticipated properties are also examined. In addition, a multiple attribute decision making issue is examined under the framework of IVCPFNs when employing the novel suggested operators. Ultimately, an example regarding the assessment on personal risk of mental patients is provided to reveal the practicability of the designed approach, and the attractiveness of our results is further found through comparing with other extant approaches.The main novelty of the coined approach is that it not only can preserve the original assessment information adequately by utilizing the IVCPFNs, but also can aggregate IVCPFNs effectively.

An improved OWA-Fuzzy AHP decision model for multi-attribute decision making problem

Multi-attribute decision-making (MADM) is an important part of modern decision-making science. Fuzzy Analytic Hierarchy Process (Fuzzy AHP) is a popular model to deal with the issue of MADM for its flexible and effective advantages. However, The traditional Fuzzy AHP with some limitations does not consider the preference (attitude) of decision makers (DMs). In addition, some ideas of combining Ordered Weighted Average (OWA) and Fuzzy AHP don’t investigated the MADM well. Some programs are only applicable to a few examples, and more general cases do not result in effective decision making. Considering these shortcomings, an OWA-Fuzzy AHP decision model using OWA weights and Fuzzy AHP is proposed in this paper. Our contribution is that the proposed method can handle situations where the degree of fuzzy synthesis is not intersected. Moreover, the loss of information can be reduced in the process of applying the proposed method, so that the decision result is more reasonable than the previous methods. Several examples and comparative experimental simulation are given to illustrate the effectiveness and superiority of the proposed model.

Evidence combination based on prospect theory for multi-sensor data fusion

Multi-sensor data fusion (MSDF) is an efficient technology to enhance the performance of the system with the involvement of different kinds of sensors, which are broadly utilized in many fields at present. However, the data obtained from multi-sensors may have different degrees of uncertainty in the practical applications. Evidence theory is very useful to convey and manage uncertainty without a priori probability, so that it has been proverbially adopted in the information fusion fields. However, in the face of conflicting evidences, it has the possibility of producing counterintuitive results via conducting the Dempster's combination rule (DCR). To solve the above-mentioned issue, a hybrid MSDF method is exploited through integrating a newly defined evidential credibility measure of evidences based on prospect theory and the evidence theory. More specifically, a series of concepts for the evidential credibility measure are first presented, including the local credibility degree, global credibility degree, evidential credibility estimation and credibility prospect value function to comprehensively describe the award and punish grades in terms of credible evidence and incredible evidence, respectively. Based on the above researches, an appropriate weight for each evidence can be obtained. Ultimately, the weight of each evidence is leveraged to amend the primitive evidences before conducting DCR. The results attained in the experiments demonstrate that the hybrid MSDF approach is efficient and superior to handle conflict evidences as well as the application in data fusion problems.

A GMCDM approach with linguistic Z-numbers based on TOPSIS and Choquet integral considering risk preference

Group multi-criteria decision-making (GMCDM) is an important part of decision theory, which is aimed to assess alternatives according to multiple criteria by collecting the wisdom of experts. However, in the process of evaluating, because of the limitation of human knowledge and the complexity of problems, an efficient GMCDM approach under uncertain environment still need to be further explored. Thus, in this paper, a novel GMCDM approach with linguistic Z-numbers based on TOPSIS and Choquet integral is proposed. Firstly, since linguistic Z-numbers performs better in coping with uncertain information, it is used to express the evaluation information. Secondly, TOPSIS, one of the most useful and systematic multi-criteria decision-making (MCDM) method, is adopted as the framework of the proposed approach. Thirdly, frequently it exists interaction between criteria, so Choquet integral is introduced to capture this kind of influence. What’s more, viewing that decision makers (DMs) show different preferences for uncertainty, the risk preference is regarded as a vital parameter when calculating the score of linguistic Z-numbers. An application in supplier selection is illustrated to demonstrate the effectiveness of the proposed approach. Finally, a further comparison and discussion of the proposed GMCDM method is given.

Negation of Pythagorean Fuzzy Number Based on a New Uncertainty Measure Applied in a Service Supplier Selection System

The Pythagorean fuzzy number (PFN) consists of membership and non-membership as an extension of the intuitionistic fuzzy number. PFN has a larger ambiguity, and it has a stronger ability to express uncertainty. In the multi-criteria decision-making (MCDM) problem, it is also very difficult to measure the ambiguity degree of a set of PFN. A new entropy of PFN is proposed based on a technique for order of preference by similarity to ideal solution (Topsis) method of revised relative closeness index in this paper. To verify the new entropy with a good performance in uncertainty measure, a new Pythagorean fuzzy number negation approach is proposed. We develop the PFN negation and find the correlation of the uncertainty measure. Existing methods can only evaluate the ambiguity of a single PFN. The newly proposed method is suitable to systematically evaluate the uncertainty of PFN in Topsis. Nowadays, there are no uniform criteria for measuring service quality. It brings challenges to the future development of airlines. Therefore, grasping the future market trends leads to winning with advanced and high-quality services. Afterward, the applicability in the service supplier selection system with the new entropy is discussed to evaluate the service quality and measure uncertainty. Finally, the new PFN entropy is verified with a good ability in the last MCDM numerical example.

The Evaluation Method of Low-Carbon Scenic Spots by Combining IBWM with B-DST and VIKOR in Fuzzy Environment

With the concept of sustainability gaining popularity, low-carbon tourism has been widely considered. In this paper, a multicriteria group decision making (MCGDM) process based on an uncertain environment is proposed to study the evaluation problem of low-carbon scenic spots (LSSs). In order to minimize the influence of subjective and objective factors, the traditional Vlse Kriterjumska Optimizacija I Kompromisno Resenje (VIKOR) method is expanded, using the improved best and worst method (IBWM) and Bayes approximation method, based on Dempster-Shafer Theory (B-DST). First, in order to make the evaluation process more professional, a number of evaluation criteria are established as effective systems, followed by the use of triangular intuitionistic fuzzy numbers (TIFNs) to evaluate alternatives of LSSs. Next, according to the evaluation results, the weights of the criteria are determined by the IBWM method, and the weights of the expert panels (Eps) are determined by B-DST. Finally, a weighted averaging algorithm of TIFN is used to integrate the above results to expand the traditional VIKOR and obtain the optimal LSS. The applicability of this method is proven by example calculation. The main conclusions are as follows: tourist facilities and the eco-environment are the two most important factors influencing the choice of LSSs. Meanwhile, the roles of management and participant attitudes in LSS evaluations cannot be ignored.

An Optimization-Based Approach to Social Network Group Decision Making with an Application to Earthquake Shelter-Site Selection

The social network has emerged as an essential component in group decision making (GDM) problems. Thus, this paper investigates the social network GDM (SNGDM) problem and assumes that decision makers offer their preferences utilizing additive preference relations (also called fuzzy preference relations). An optimization-based approach is devised to generate the weights of decision makers by combining two reliable resources: in-degree centrality indexes and consistency indexes. Based on the obtained weights of decision makers, the individual additive preference relations are aggregated into a collective additive preference relation. Further, the alternatives are ranked from best to worst according to the obtained collective additive preference relation. Moreover, earthquakes have occurred frequently around the world in recent years, causing great loss of life and property. Earthquake shelters offer safety, security, climate protection, and resistance to disease and ill health and are thus vital for disaster-affected people. Selection of a suitable site for locating shelters from potential alternatives is of critical importance, which can be seen as a GDM problem. When selecting a suitable earthquake shelter-site, the social trust relationships among disaster management experts should not be ignored. To this end, the proposed SNGDM model is applied to evaluate and select earthquake shelter-sites to show its effectiveness. In summary, this paper constructs a novel GDM framework by taking the social trust relationship into account, which can provide a scientific basis for public emergency management in the major disasters field.