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In any conflict analysis model, agents are decision-makers (DMs). In reality, the regret psychology of DMs often influence decision outcomes due to uncertain risks. However, the existing conflict analysis model avoids DMs' regret psychology. The q-rung orthopair fuzzy information (q-ROFIS) with regret theory (RT)-based conflict analysis in detail is a primary aim of this study to solve more complex and uncertain-conflict problems than possible within the confinement of current knowledge. First, we define RT-based q-rung orthopair fuzzy conflict distance (q-ROFCD) in a pair and show that our q-ROFCD holds symmetry and triangular inequality. Using q-ROFCD, we have studied pre-defined parameters and three-way decision (3WD) theory-based conflict analysis. In pre-defined parameters-based conflict analysis, we trisect the agents according to single and multiple issues, define q-rung orthopair fuzzy conflict of each issue and issue set, trisect issues, provide a feasible strategy for a conflict situation, define the conflict degree of each agent and agent set, and finally find out the intrinsic reasons for the conflict are. In 3WD theory based-conflict analysis, we trisect the agents according to single and multiple issues using Bayesian minimum cost theory, define conflict region, rank the issues, introduce three-way coalitions of agents and finally define maximal coalition of agents. At last, the stability and validity of the proposed model are verified via an application, sensitive analysis and comparative analysis with similar studies. [ABSTRACT FROM AUTHOR]

This paper introduces the notion of k-fuzzy metric spaces, which generalizes and extends the concept of fuzzy metric spaces due to George and Veeramani in [A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), 395-399.] for the fuzzy sets involving more than one (k) parameters. It is shown that the topology generated by the k-fuzzy metric is first countable, and the k-fuzzy metric space is Hausdorff. Finally, we prove a fixed point theorem, which generalizes and extends the results of Grabiec [M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389.] into k-fuzzy metric spaces. [ABSTRACT FROM AUTHOR]

Aiming of this paper is to introduce large-scale group decision-making (LSGDM) into three-way decisions (3WDs) with decision-theoretic rough sets (DTRSs) and propose LSGDM based 3WDs under linguistic assessments. There are two parameters involved of the 3WDs with DTRSs such as conditional probability and loss functions. Here we mainly focus on the calculation of loss function using LSGDM approach. LSGDM problem is characterized by a large number of experts, multiple clusters and a mass of evaluation data given by the experts. In some cases, experts are unwilling to revise their opinions to reach a consensus. So, the proper management of experts opinions and their non-cooperative behaviors (NCBs) is necessary to establish a consensus model. An appropriate adjustment of the credibility information is also essential. Using the clustering method, the proposed model divides the experts with similar evaluations into a subgroup. In each cluster, the experts' opinions are then aggregate. In order to measure the level of consensus among clusters, the cluster consensus index (CCI) and group consensus index (GCI) have been developed. Then, using a tool for managing the NCBs of clusters includes two components: (1) for identifying the NCBs of clusters, NCB degree has defined using CCI and GCI; (2) for consensus improvement, implemented the weight punishment mechanism to NCBs clusters. Finally, we have designed a rule for classifying the objects into three regions, and the associated cost of each object is derived for ranking the objects in each region. An example is offered for selection of the Energy project to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In the real-world scenario, one has to find a dominating person in a social network, conferences, meetings or any group discussion. The fuzzy graph (network) is one of the most powerful tools to find the strongest influential person in a network. This paper aims to develop a concept of fuzzy graphs (FGs) in the setup of bipolar-valued hesitant fuzzy sets (BVHFs). The concept of bipolar-valued hesitant fuzzy graph (BVHFG) is different from the concept of bipolar fuzzy graph (BFG). BVHFG is the generalization of hesitant fuzzy graph (HFG), which not only considers the satisfaction degree of units in a network but also considers the satisfaction degree to some implicit counter property of units with several bipolar fuzzy values. We first introduce the definition of BVHFG, represented by another class of imprecise membership grades that refers to BVHF membership grades. We shall subsequently see the scope of BVHF membership grades in BVHFG is greater than the scope of bipolar-valued membership grades in BFG. In addition, we also discuss the basic operations and functional properties of BVHFGs. Finally, we propose a numerical method to find the most dominating person using our proposed work. As the proposed method of ranking considers the degree of hesitation as well as bipolarity, this method has the edge over earlier work. To establish the importance of our method, we also find domination degrees for HFG and BVHFG using the same example and show that there is a significant change in the ranking of dominating persons. [ABSTRACT FROM AUTHOR]

Multi-granulation rough sets (MGRSs) and decision-theoretic rough sets (DTRSs) are two important and popular generalizations of classical rough sets. The combination of two generalized rough sets have been investigated by numerous researchers in different extensions of fuzzy settings such as interval-valued fuzzy sets (IVFSs), intuitionistic fuzzy sets (IFSs), bipolar-valued fuzzy sets (BVFSs), etc. Pythagorean fuzzy (PF) set is another extension of fuzzy set, which is more capable in comparison to IFS handle vagueness in real world. However, few studies have focused on the combination of the two rough sets in PF settings. In this study, we combine the two generalized rough sets in PF settings. First, we introduce a type of PF subset (of subset of the given universe) of the PF Set (of the given universe). Then we establish two basic models of multi-granulation PF DTRS (MG-PF-DTRS) of PF subset of the PF set based on PF inclusion measure within the framework of multi-granulation PF approximation space. One model is based on a combination of PF relations (PFRs) and the construction of approximations with respect to the combined PFR. By combining PFRs through intersection and union, respectively, we construct two models. The other model is based on the construction of approximations from PFRs and a combination of the approximations. By using intersection and union to combine the approximations, respectively, we again get two models. As a result, we have total four models. Further for different constraints on parameters, we obtain three kinds of each model of the MG-PF-DTRSs. Then, their principal structure, basic properties and uncertainty measure methods are investigated as well. Second, we give a way to compute PF similarity degrees between two objects and also give a way to compute PF decision-making objects from incomplete multi-source information systems (IMSISs). Then we design an algorithm for decision-making to IMSISs using MG-PFDTRSs and their uncertainty measure methods. Finally, an example about the mutual funds investment is included to show the feasibility and potential of the theoretic results obtained. [ABSTRACT FROM AUTHOR]

Preference analysis is a class of important issues in multi-criteria decision making. The rough set theory is a powerful approach to handle preference analysis. In order to solve the multi-criteria preference analysis, this work improves the fuzzy multi-granulation decision-theoretic rough set model with additive consistent fuzzy preference relation, and it is used to analyze data from different sources, i.e., multi-source (fuzzy) information system. More specifically, we introduce the models of optimistic and pessimistic fuzzy preference relation multi-granulation decision-theoretic rough sets. Then, their principal structure, basic properties and several kinds of uncertainty measure methods are investigated as well. An example is employed to illustrate the effectiveness of the proposed models, and comparisons are also offered according to different measures of our models and existing models. [ABSTRACT FROM AUTHOR]

This article introduces general framework of multi-granulation bipolar-valued fuzzy (BVF) probabilistic rough sets (MG-BVF-PRSs) models in multi-granulation BVF probabilistic approximation space over two universes. Four types of MG-BVF-PRSs are established, by the four different conditional probabilities of BVF event. For different constraints on parameters, we obtain four kinds of each type MG-BVF-PRSs over two universes. To find a suitable way of explaining and determining these parameters in each kind of each type MG-BVF-PRS, three-way decisions (3WDs) are studied based on Bayesian minimum-risk procedure, i.e., the multi-granulation BVF decision-theoretic rough set (MG-BVF-DTRS) approach. The main contribution of this paper is twofold. One is to extend the fuzzy probabilistic rough set (FPRS) to MG-BVF-PRS model over two universes. Another is to present an approach to select parameters in MG-BVF-PRS modeling by using the process of decision making under conditions of risk. [ABSTRACT FROM AUTHOR]

This paper describes the usefulness of FEM for exploring the parameter sensitive analysis. Using 2D axisymmetric analysis, the critical performance parameters are examined by varying the thickness and material properties of different layers of flexible pavement. Hypothetical pavement sections are also analyzed with a view to check the sensitivity of horizontal axisymmetric extent and refinement of mesh. The developed computer program after validation is used to calculate the horizontal tensile strain at the bottom of the bituminous layer (BL) and the vertical compressive strain at the top of the subgrade. These computed strains are incorporated in the fatigue and rutting criteria recommended in Indian Road Congress (IRC: 37-2012) to estimate the pavement life for various hypothetical conditions. Tensile strain at the bottom of BL and compressive strain on top of the subgrade decreases with an increase in the thickness of BL, which results in increase of fatigue and rutting lives. An increase in thickness of the base layer and the increase in its elastic modulus reduces the damage due to rutting, while it has less effect on damage due to fatigue. Such type of analysis proves beneficial for designing a pavement, keeping equilibrium between fatigue and rutting lives. [ABSTRACT FROM AUTHOR]