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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]

Summary: Cloud computing technologies have been prospering in recent years and have opened an avenue for a wide variety of forms of adaptable data sharing. Taking advantage of these state‐of‐the‐art innovations, the cloud storage data owner must, however, use a suitable identity‐based cryptographic mechanism to ensure the safety prerequisites while sharing data to large numbers of cloud data users with fuzzy identities. As a successful way to guarantee secure fuzzy sharing of cloud data, the identity‐based cryptographic technology still faces an effectiveness problem under multireceiver configurations. The chaos theory is considered a reasonable strategy for reducing computational complexity while meeting the cryptographic protocol's security needs. In an identity‐based cryptographic protocol, public keys for individual clients are distributed, allowing the clients to separately select their own network identities or names as their public keys. In fact, in a public‐key cryptographic protocol, it is for the best that the confirmation of the public key is done in a safe, private manner, because this way the load of storage on the server's side can be considerably relieved. The objective of this paper is to outline and examine a conversion process that can transfer cryptosystems using Chebyshev's chaotic maps over the Galois field to a subtree‐based protocol in the cloud computing setting for fuzzy user data sharing, as opposed to reconcocting a different structure. Furthermore, in the design of our conversion process, no adjustment of the original cryptosystem based on chaotic maps is needed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new type of fuzzy set, called Pythagorean linguistic sets (PLSs), to address the preferred and nonpreferred degrees of linguistic variables. Moreover, it allows decision makers to offer effectively handle uncertain information more flexible than intuitionistic linguistic sets (ILSs) when one compares two alternatives in the process of decision making. Some of the fundamental operational laws, score, accuracy, and aggregation operators are defined, and their properties are investigated. Preference relation (PR) is a useful and efficient tool for decision making that only requires the decision makers to compare two alternatives at one time. Taking the advantages of PLSs and PRs, this paper also introduces Pythagorean linguistic preference relations (PLPRs) and studies their application. We propose an approach for group decision making using group recommendations based on consistency matrices and feedback mechanism. First, the proposed method constructs the collective consistency matrix, the weight collective PRs, and the group collective PRs. Then, it constructs a consensus relation for each expert and determines the group consensus degree (GCD) for all experts. If the GCD is smaller than a predefined threshold value, then a feedback mechanism is activated to update the PLPRs. Finally, after the GCD is greater than or equal to the predefined threshold value, we calculate the arithmetic mathematical average values of the updated group collective PR to select the most appropriate alternative. [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]

Abstract: Decision‐theoretic rough sets (DTRSs), which provide a classical model of three‐way decisions (3WDs), play an important role in risk decision‐making problems. The risk is associated with the loss function of DTRSs, which is evaluated by the decision makers. As a new extension of fuzzy sets, Pythagorean fuzzy sets can handle uncertain information more flexibly than intuitionistic fuzzy sets in the process of decision making and it gives a new measure for the determination of loss functions of DTRSs. More specifically, we take into account the loss functions of DTRSs with Pythagorean fuzzy numbers and propose a Pythagorean fuzzy decision‐theoretic rough set (PFDTRS) model. Some properties of the expected losses are carefully investigated. Then we further design three approaches for deriving 3WDs with the PFDTRS model. The group decision making (GDM) based on the PFDTRS model is also discussed. It provides a novel interpretation for the determination of loss functions. With the aid of the Pythagorean fuzz weighted averaging operator, we aggregate the loss functions, as suggested by the all experts, which support a coherent way of designing information granules in the presence of numerics. An algorithm for 3WDs in GDM based on the PFDTRS model is designed. Then, an example is presented to elaborate on 3WDs with the PFDTRS model. [ABSTRACT FROM AUTHOR]