A decision variable-based combinatorial optimization approach for interval-valued intuitionistic fuzzy MAGDM

A new multi-attribute decision making approach based on new score function and hybrid weighted score measure in interval-valued Fermatean fuzzy environment

Interval-valued Fermatean fuzzy sets (IVFFSs) were introduced as a more effective mathematical tool for handling uncertain information in 2021. In this paper, firstly, a novel score function (SCF) is proposed based on IVFFNs that can distinguish between any two IVFFNs. And then, the novel SCF and hybrid weighted score measure were used to construct a new multi-attribute decision-making (MADM) method. Besides, three cases are used to demonstrate that our proposed method can overcome the disadvantages that the existing approaches cannot obtain the preference orderings of alternatives in some circumstances and involves the existence of division by zero error in the decision procedure. Compared with the two existing MADM methods, our proposed approach has the highest recognition index and the lowest error rate of division by zero. Our proposed method provides a better approach to dealing with the MADM problem in the interval-valued Fermatean fuzzy environment.

A multiattribute group decision-making method based on a new aggregation operator and the means and variances of interval-valued intuitionistic fuzzy values

The development of information measures associated with interval-valued intuitionistic fuzzy values (IVIFVs) has been an important research area over the past few decades. In the literature, the existing decision -making method using IVIFVs has some drawbacks, and the identification degree and information utilization suffer from a gap in the evaluation of alternatives. Therefore, the need for a reliable, useful, and comprehensive decision method is obvious. To obtain more accurate and reliable evaluation results, multiattribute group decision-making (MAGDM) problems, where the same attribute weights given by different decision-makers are different, are studied in this paper. First, the novel operational laws of IVIFVs and a new interval-valued intuitionistic fuzzy weighted arithmetic aggregation operator are defined to overcome the drawbacks of the IIFWA aggregation operator and avoid losing or distorting the original decision information in the process of aggregation. Second, the mean and variance of the possibility degrees of IVIFVs are defined based on the concept of a definite integral. Third, a novel MAGDM method based on the new aggregation operator and the mean and variance of the possibility degrees of IVIFVs is proposed to improve the identification of the evaluation results and ensure the effectiveness of the ranking order. Finally, the effectiveness and practicability of the proposed method are verified by an air combat training accuracy assessment example. This example can be used to assist decision-makers in evaluating air combat training hits in a timely and efficient manner, providing an objective, scientific basis for the realization and application of air combat training hit assessment and a new method and idea for MAGDM problems in an interval-valued intuitionistic fuzzy environment.

Analysis of Interval-Valued Intuitionistic Fuzzy Aczel–Alsina Geometric Aggregation Operators and Their Application to Multiple Attribute Decision-Making

When dealing with the haziness that is intrinsic in decision analysis-driven decision making procedures, interval-valued intuitionistic fuzzy sets (IVIFSs) can be quite effective. Our approach to solving the multiple attribute decision making (MADM) difficulties, where all of the evidence provided by the decision-makers is demonstrated as interval-valued intuitionistic fuzzy (IVIF) decision matrices, in which all of the components are distinguished by an IVIF number (IVIFN), is based on Aczel–Alsina operational processes. We begin by introducing novel IVIFN operations including the Aczel–Alsina sum, product, scalar multiplication, and exponential. We may then create IVIF aggregation operators, such as the IVIF Aczel–Alsina weighted geometric operator, the IVIF Aczel–Alsina ordered weighted geometric operator, and the IVIF Aczel–Alsina hybrid geometric operator, among others. We present a MADM approach that relies on the IVIF aggregation operators that have been developed. A case study is used to demonstrate the practical applicability of the strategies proposed in this paper. By contrasting the newly developed technique with existing techniques, the method is capable of demonstrating the advantages of the newly developed approach. A key result of this work is the discovery that some of the current IVIF aggregation operators are subsets of the operators reported in this article.

New Ranking Functions for Interval-Valued Intuitionistic Fuzzy Sets and Their Application to Multi-Criteria Decision-Making Problem

Many authors agree that the Interval-Valued Intuitionistic Fuzzy Set (IVIFS) theory generates as realistic as possible evaluation of real-life problems. One of the real-life problems where IVIFSs are often preferred is the Multi-Criteria Decision-Making (MCDM) problem. For this problem, the ranking of values obtained by fuzzing the opinions corresponding to alternatives is an important step, as a failure in ranking may lead to the selection of the wrong alternative. Therefore, the method used for ranking must have high performance. In this article, a new score function SKE and a new accuracy function HKE are developed to overcome the disadvantages of existing ranking functions for IVIFSs. Then, two illustrative examples of MCDM problems are presented to show the application of the proposed functions and to evaluate their effectiveness. Results show that the functions proposed have high performance and they are the eligibility for the MCDM problem.

Extended CPT-TODIM method for interval-valued intuitionistic fuzzy MAGDM and its application to urban ecological risk assessment

The urban ecological risk assessment is a new research field, which has been rising and developing with the change of environment management objectives and environment conception. The urban ecological risk assessment could be regarded as a classical multi-attribute group decision making (MAGDM) issue. The interval-valued intuitionistic fuzzy set (IVIFS) can fully describe the uncertain information for the urban ecological risk assessment. Furthermore, the classical TODIM (an acronym in Portuguese for Interactive Multi-Criteria Decision Making) is built on cumulative prospect theory (CPT), which is a selectable method in reflecting the DMs’ psychological behavior. Thus, in this paper, the TODIM method based on the CPT is proposed for MAGDM issue under IVIFS. At the same time, it is enhancing rationality to get the weight information of attributes by using the interval-valued intuitionistic fuzzy entropy weight method. And focusing on hot issues in contemporary society, this article applies the discussed method to urban ecological risk assessment, and demonstrates urban ecological risk assessment model based on the proposed method. Finally, through comparing the outcome of comparative analysis, we conclude that this improved approach is acceptable.

Application of a Fuzzy Decision Model to the Design of a Pillbox for Medical Treatment of Chronic Diseases

It is critical for medical systems to reduce waste from medical resources. One of the reasons why patients with chronic diseases create waste is that they often forget to take their medicine. Patients pay attention to the time and amount of medicine to take to different degrees. This negligence often affects when they take medicine or preventive drugs. The amount of medicine is also different for different patients. The evaluation model in this study utilizes the fuzzy analytic hierarchy process (FAHP) to obtain the degree (weight) of each evaluation item that is determined by each patient. After that, a more objective overall shape can be determined depending on the individual’s preference. In this study, the proposed package design serves as the case study. The results indicate that the evaluation model is feasible, and the research results of the case study are also valuable for follow-up designers. The design of a pillbox for patients with chronic diseases should consider the safety of taking the medicine; that is, the right person should take the right medicine at the right time at the right dose. Therefore, evaluating the feasibility of the pillbox for patients with chronic diseases is very important. The proposed evaluation model applies to products that have different compositions. Follow-up researchers or designers can apply this approach to different case designs.