Decision making under measure-based granular uncertainty with intuitionistic fuzzy sets

Archimedean Aggregation Operators Based on Complex Pythagorean Fuzzy Sets Using Confidence Levels and Their Application in Decision Making

The diagnosed complex Pythagorean fuzzy (CPF) set is a more valuable and dominant tool than the Pythagorean and intuitionistic fuzzy sets to describe awkward and unreliable information more effectively. Further, Archimedean t-norm and t-conorm have a significant influence to depict the relation among aggregated values. To take advantage of the CPF set and Archimedean t-norm and t-conorm, and assume the relation among Archimedean norms and algebraic, Einstein, Hamacher, and frank norms at the same time, in this analysis, first, we proposed the fundamental Archimedean operational laws. Second, based on these laws, we developed confidence CPF Archimedean-weighted averaging (CCPFSAWA), confidence CPF Archimedean-ordered weighted averaging (CCPFSAOWA), confidence CPF Archimedean-weighted geometric (CCPFSAWG), confidence CPF Archimedean-ordered weighted geometric (CCPFSAOWG) operators and implemented their valuable results and properties. We know that Archimedean t-norm and t-conorm are the general form of the all-aggregation operators, so by using different values of t-norm and t-conorm, we explored the confidence CPF-weighted averaging (CCPFWA), confidence CPF-ordered weighted averaging (CCPFOWA), confidence CPF Einstein-weighted averaging (CCPFEWA), confidence CPF Einstein-ordered weighted averaging (CCPFEOWA), confidence CPF Hamacher-weighted averaging (CCPFHWA), confidence CPF Hamacher-ordered weighted averaging (CCPFHOWA), confidence CPF frank-weighted averaging (CCPFFWA), confidence CPF frank-ordered weighted averaging (CCPFFOWA), confidence CPF-weighted geometric (CCPFWG), confidence CPF-ordered weighted geometric (CCPFOWG), confidence CPF Einstein-weighted geometric (CCPFEWG), confidence CPF Einstein-ordered weighted geometric (CCPFEOWG), confidence CPF Hamacher-weighted geometric (CCPFHWG), confidence CPF Hamacher-ordered weighted geometric (CCPFHOWG), confidence CPF frank-weighted geometric (CCPFFWG), and confidence CPF frank-ordered weighted geometric (CCPFFOWG) operators. Then, we developed a multi-attribute decision-making (MADM) method based on the proposed operators. Finally, many examples are used to do comparative analysis among proposed and existing methods to show the validation of the new approaches.

Uncover the reasons for performance differences between measurement functions (Provably)

Recently, an exciting experimental conclusion in Li et al. (Knowl Inf Syst 62(2):611-637, 1) about measures of uncertainty for knowledge bases has attracted great research interest for many scholars. However, these efforts lack solid theoretical interpretations for the experimental conclusion. The main limitation of their research is that the final experimental conclusions are only derived from experiments on three datasets, which makes it still unknown whether the conclusion is universal. In our work, we first review the mathematical theories, definitions, and tools for measuring the uncertainty of knowledge bases. Then, we provide a series of rigorous theoretical proofs to reveal the reasons for the superiority of using the knowledge amount of knowledge structure to measure the uncertainty of the knowledge bases. Combining with experiment results, we verify that knowledge amount has much better performance for measuring uncertainty of knowledge bases. Hence, we prove an empirical conclusion established through experiments from a mathematical point of view. In addition, we find that for some knowledge bases that cannot be classified by entity attributes, such as ProBase (a probabilistic taxonomy), our conclusion is still applicable. Therefore, our conclusions have a certain degree of universality and interpretability and provide a theoretical basis for measuring the uncertainty of many different types of knowledge bases, and the findings of this study have a number of important implications for future practice.

Matrix games involving interval-valued hesitant fuzzy linguistic sets and its application to electric vehicles

Game theory has been successfully applied in a variety of domains to deal with competitive environments between individuals or groups. The matrix games involving fuzzy, interval fuzzy, and intuitionistic fuzzy numbers exclusively examine the numeric components of an issue. However, several researchers have also examined various extensions of conventional game theory, considering the ambiguous situations for payoffs and goals. In many real-life scenarios, qualitative information is often critical in expressing the payoffs of a matrix game. Thus, the present work contributes to the field of matrix games where the payoffs have been quantified via qualitative variables, termed interval-valued hesitant fuzzy linguistic sets. The mathematical formulation and solution concept for matrix games involving interval-valued hesitant fuzzy linguistic numbers is designed by utilizing an aggregation operator supported by linguistic scale function and solving them by employing score function. Finally, the proposed approach is validated by applying it to electric vehicle sales.

A Method Converting Multi-Properties Objective Reachability Problems to Multi-Objective Sets Reachability Problems over FKS

In this paper, we focus on the symmetrical relationship between multi-properties objective reachability problems and multi-objective sets reachability problems over FKS based on Zadeh logic. First, we give the formal definitions of those two problems. Then, we study their relationships and find that a multi-properties objective reachability problem and a special case of multi-objective sets reachability problems have symmetry. Finally, we give a polynomial time algorithm based on this symmetry to convert a multi-properties objective reachability problem to a multi-objective sets reachability problem. In addition, an illustrative example is listed to express some possible application methods based on our work.

A novel approach for ranking intuitionistic fuzzy numbers and its application to decision making

Ranking intuitionistic fuzzy numbers is an important issue in the practical application of intuitionistic fuzzy sets. Many scholars rank intuitionistic fuzzy numbers by defining different measures. These measures do not comprehensively consider the fuzzy semantics expressed by membership degree, nonmembership degree, and hesitancy degree. As a result, the ranking results are often counterintuitive, such as the indifference problems, the non-robustness problems, etc. In this paper, according to geometrical representation, a novel measure for intuitionistic fuzzy numbers is defined, which is called the ideal measure. After that, a new ranking approach is proposed. It’s proved that the ideal measure satisfies the properties of weak admissibility, membership degree robustness, nonmembership degree robustness, and determinism. A numerical example is applied to illustrate the effectiveness and feasibility of this method. Finally, using the presented approach, the optimal alternative can be acquired in multi-attribute decision-making problems. Comparison analysis shows that the ideal measure is more effective and simple than other existing methods.

Model Checking Fuzzy Computation Tree Logic Based on Fuzzy Decision Processes with Cost

In order to solve the problems in fuzzy computation tree logic model checking with cost operator, we propose a fuzzy decision process computation tree logic model checking method with cost. Firstly, we introduce a fuzzy decision process model with cost, which can not only describe the uncertain choice and transition possibility of systems, but also quantitatively describe the cost of the systems. Secondly, under the model of the fuzzy decision process with cost, we give the syntax and semantics of the fuzzy computation tree logic with cost operators. Thirdly, we study the problem of computation tree logic model checking for fuzzy decision process with cost, and give its matrix calculation method and algorithm. We use the example of medical expert systems to illustrate the method and model checking algorithm.

A theoretical development of improved cosine similarity measure for interval valued intuitionistic fuzzy sets and its applications

This study mainly focuses on developing a new flexible technique for interval-valued intuitionistic fuzzy cosine similarity measures, which significantly analyzes the strength of the relationship between two objects. Based on the notion of a cosine similarity measure between IVIFSs, the proposed measure is formulated. Then, the measure is demonstrated to satisfy some essential properties, which prepare the ground for applications in different areas. Finally, the study uses the proposed measure to solve real-world decision problems such as pattern recognition, medical diagnosis, and multi-criteria decision-making problems with interval-valued intuitionistic fuzzy information. The numerical examples of the mentioned applications are delivered to validate the effectiveness of the developed approach in solving real-life problems.

An Approach for the Analysis of Energy Resource Selection Based on Attributes by Using Dombi T-Norm Based Aggregation Operators

Dombi t-norm (DTN) and t-conorm (TCN) are among the most effective triangular norms in fuzzy systems for aggregation purposes. The environment of interval-valued intuitionistic fuzzy (IVIF) set gives us precision in expressing uncertain information by using a membership grade (MG) and non-membership grade (NMG) in the form of closed subintervals of 0, 1. The goal of this paper is to introduce DTN-based aggregation operators (AOs) for IVIF numbers (IVIFNs) and study their performance in the evaluation of the worth of energy recourses to be opted in Pakistan to deal with the energy crises situation. We first introduced some DTN and TCN-based operations for IVIFNs and developed two new AOs known as IVIF Dombi weighted averaging (IVIFDWA) and IVIF Dombi weighted geometric (IVIFDWG) operators. The validity and fitness of the proposed operators are tested. A case study is presented where the energy resources of Pakistan are discussed and the problem of the selection of sustainable energy resources in the context of Pakistan is investigated. The sensitivity analysis of the proposed IVIFDWA and IVIFDWG operators is studied and a comparative analysis of the current work with previous studies is established.