A novel multi-criteria group decision-making approach using aggregation operators and weight determination method for supplier selection problem in hesitant Pythagorean fuzzy environment

Uncertainty is an important factor in the decision-making process. Hesitant Pythagorean fuzzy sets (HPFS), a combination of Pythagorean and hesitant fuzzy sets, proved as a significant tool to handle uncertainty. Well-defined operational laws and attribute weights play an important role in decision-making. Thus, the paper aims to develop new Trigonometric Operational Laws, a weight determination method, and a novel score function for group decision-making (GDM) problems in the HPF environment. The approach is presented in three phases. The first phase defines new operational laws with sine trigonometric function incorporating its special properties like periodicity, symmetricity, and restricted range hence compared with previously defined aggregation operators they are more likely to satisfy the decision maker preferences. Properties of trigonometric operational laws (TOL) are studied and various aggregation operators are defined. To measure the relationship between arguments, the operators are combined with the Generalized Heronian Mean operator. The flexibility of operators is increased by the use of a real parameter λ to express the risk preference of experts. The second phase defines a novel weight determination method, which separately considers the membership and non-membership degrees hence reducing the information loss and the third phase conquers the shortcomings of previously defined score functions by defining a novel score function in HPFS. To further increase the flexibility of defined operators they are extended in the environment with unknown or incomplete attribute weights. The effectiveness of the GDM model is verified with the help of a supplier selection problem. A detailed comparative analysis demonstrates the superiority, and sensitivity analysis verifies the stability of the proposed approach

New Types of Pythagorean Fuzzy Modules and Applications in Medical Diagnosis

In this article, we discuss several distinct categories of pythagorean fuzzy modules, study pythagorean fuzzy relations, and provide applications in the field of medical diagnosis. The concept of pythagorean fuzzy prime modules, along with its characteristics, is presented. In addition,an investigation is conducted into a pythagorean fuzzy multiplication module. Moreover, pythagorean fuzzy relations and pythagorean fuzzy homomorphisms are introduced. By making use of pythagorean fuzzy sets and pythagorean fuzzy relations., we propose a novel approach to the medical diagnosis process. This approach is achieved by pointing the smallest distance between the symptoms of the patients and the symptoms related to diseases

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches

Hybrid-fuzzy techniques with flexibility and attitudinal parameters for supporting early product design and reliability management

The main aim of the research work presented in this thesis is to define and develop novel Hybrid Fuzzy-based techniques for supporting aspects of product development engineering, specifically product reliability at the early phase of product design under the design for reliability philosophy and concept designs assessment problems when the required information is rough and incomplete. Thus, to achieve the above-stated aim, which has been formulated in the effort to filling the identified gaps in the literature which comprise of the need for a holistic, flexible and adjustable method to facilitate and support product design concept assessment and product reliability at the early product design phase. The need for the incorporation of the attitudinal character of the DMs into the product reliability and design concept assessment and finally, the need to account for the several interrelated complex attributes in the product reliability and design concept assessment process. A combination of research methods has been employed which includes an extensive literature review, multiple case study approach, and personal interview of experts, through which data were, collected that provided information for the real-life case study. With the new Hybrid Fuzzy-based techniques (i.e. the intuitionistic fuzzy TOPSIS model which is based on an exponential-related function (IF-TOPSISEF) and the Multi-attribute group decision-making (MAGDM) method which is based on a generalized triangular intuitionistic fuzzy geometric averaging (GTIFGA) operator), a more robust method for the product reliability and design concepts assessment respectively have been achieved as displayed in the comparative analysis in the thesis. The new methods have provided a more complete and a holistic view of the assessment process, by looking at the product reliability and design concept assessment from different scenario depending on the interest of the DMs. Using the above methods, the thesis has been able to evaluated some complex mechanical systems in literature and in real-life including Crawler Crane Machine and Forklift Truck for design change with the purpose of gaining appropriate reliability knowledge and information needed at the early product design phase, and that can subsequently aid and improve the product design concepts after all such useful information have been added into the new design. With the application of the new methods, and their proven feasibility and rationality as displayed in the assessment results of the complex mechanical systems in literature and that of the real-life case studies, this thesis, therefore, can conclude that the Hybrid Fuzzy-based techniques proposed, has provided a better and a novel alternative to existing product reliability and design concepts assessment methods

Uncertain Multi-Criteria Optimization Problems

Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relationships used when modeling optimization problems. Moreover, the notion of symmetry has appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better solution with respect to one objective may compromise other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories such as probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems have not yet been explored in depth, and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed in various uncertain frameworks with special emphasis on optimization problems

Multiple-Criteria Decision Making

Decision-making on real-world problems, including individual process decisions, requires an appropriate and reliable decision support system. Fuzzy set theory, rough set theory, and neutrosophic set theory, which are MCDM techniques, are useful for modeling complex decision-making problems with imprecise, ambiguous, or vague data.This Special Issue, “Multiple Criteria Decision Making”, aims to incorporate recent developments in the area of the multi-criteria decision-making field. Topics include, but are not limited to:- MCDM optimization in engineering;- Environmental sustainability in engineering processes;- Multi-criteria production and logistics process planning;- New trends in multi-criteria evaluation of sustainable processes;- Multi-criteria decision making in strategic management based on sustainable criteria