Q-rung orthopair normal fuzzy aggregation operators and their application in multi-attribute decision-making

© 2019 by the authors. Q-rung orthopair fuzzy set (q-ROFS) is a powerful tool to describe uncertain information in the process of subjective decision-making, but not express vast objective phenomenons that obey normal distribution. For this situation, by combining the q-ROFS with the normal fuzzy number, we proposed a new concept of q-rung orthopair normal fuzzy (q-RONF) set. Firstly, we defined the conception, the operational laws, score function, and accuracy function of q-RONF set. Secondly, we presented some new aggregation operators to aggregate the q-RONF information, including the q-RONF weighted operators, the q-RONF ordered weighted operators, the q-RONF hybrid operator, and the generalized form of these operators. Furthermore, we discussed some desirable properties of the above operators, such as monotonicity, commutativity, and idempotency. Meanwhile, we applied the proposed operators to the multi-attribute decision-making (MADM) problem and established a novel MADM method. Finally, the proposed MADM method was applied in a numerical example on enterprise partner selection, the numerical result showed the proposed method can effectively handle the objective phenomena with obeying normal distribution and complicated fuzzy information, and has high practicality. The results of comparative and sensitive analysis indicated that our proposed method based on q-RONF aggregation operators over existing methods have stronger information aggregation ability, and are more suitable and flexible for MADM problems

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

An extended Interval Type-2 Fuzzy VIKOR technique with equitable linguistic scales and Z-Numbers for solving water security problems in Malaysia

Interval Type-2 Fuzzy VIseKriterijumska Optimizacija I Kompromisno Resenje (IT2FVIKOR) technique is one of the techniques of Interval Type-2 Fuzzy Multi-Criteria Decision Making (IT2FMCDM), which was developed to solve problems involving conflicting and multiple objectives. Most of the IT2FVIKOR methods are created from linguistic variables based on Interval Type-2 Fuzzy Set (IT2FS) and its generalization, such as Interval Type-2 Fuzzy Numbers (IT2FNs). Recent literature suggests that equitable linguistic scales can offer a better alternative, particularly when IT2FSs have some limitations in handling uncertainty and imbalance. This paper proposes the extended IT2FVIKOR with an equitable linguistic scale and Z-Numbers, where its linguistic scale introduces an equitable balance of positive and negative scales added to the restriction and reliability approach. Different from the typical IT2FVIKOR, which directly utilizes IT2FNs with a positive membership, the proposed method introduces positive and negative membership where each side considers a restriction and reliability approach. Besides, this paper also offers objective weights using fuzzy entropy-based IT2FS to calculate the weights of the extended IT2FVIKOR. The obtained solutions would help decision makers (DMs) identify the best solution to enhance water security projects in terms of finding the best strategies for water supply security in Malaysia

Extension of aggregation operators to site selection for solid waste management under neutrosophic hypersoft set

With the fast growth of the economy and rapid urbanization, the waste produced by the urban population also rises as the population increases. Due to communal, ecological, and financial constrictions, indicating a landfill site has become perplexing. Also, the choice of the landfill site is oppressed with vagueness and complexity due to the deficiency of information from experts and the existence of indeterminate data in the decision-making (DM) process. The neutrosophic hypersoft set (NHSS) is the most generalized form of the neutrosophic soft set, which deals with the multi-sub-attributes of the alternatives. The NHSS accurately judges the insufficiencies, concerns, and hesitation in the DM process compared to IFHSS and PFHSS, considering the truthiness, falsity, and indeterminacy of each sub-attribute of given parameters. This research extant the operational laws for neutrosophic hypersoft numbers (NHSNs). Furthermore, we introduce the aggregation operators (AOs) for NHSS, such as neutrosophic hypersoft weighted average (NHSWA) and neutrosophic hypersoft weighted geometric (NHSWG) operators, with their necessary properties. Also, a novel multi-criteria decision-making (MCDM) approach has been developed for site selection of solid waste management (SWM). Moreover, a numerical description is presented to confirm the reliability and usability of the proposed technique. The output of the advocated algorithm is compared with the related models already established to regulate the favorable features of the planned study

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

New Challenges in Neutrosophic Theory and Applications

Neutrosophic theory has representatives on all continents and, therefore, it can be said to be a universal theory. On the other hand, according to the three volumes of “The Encyclopedia of Neutrosophic Researchers” (2016, 2018, 2019), plus numerous others not yet included in Encyclopedia book series, about 1200 researchers from 73 countries have applied both the neutrosophic theory and method. Neutrosophic theory was founded by Professor Florentin Smarandache in 1998; it constitutes further generalization of fuzzy and intuitionistic fuzzy theories. The key distinction between the neutrosophic set/logic and other types of sets/logics lies in the introduction of the degree of indeterminacy/neutrality (I) as an independent component in the neutrosophic set. Thus, neutrosophic theory involves the degree of membership-truth (T), the degree of indeterminacy (I), and the degree of non-membership-falsehood (F). In recent years, the field of neutrosophic set, logic, measure, probability and statistics, precalculus and calculus, etc., and their applications in multiple fields have been extended and applied in various fields, such as communication, management, and information technology. We believe that this book serves as useful guidance for learning about the current progress in neutrosophic theories. In total, 22 studies have been presented and reflect the call of the thematic vision. The contents of each study included in the volume are briefly described as follows. The first contribution, authored by Wadei Al-Omeri and Saeid Jafari, addresses the concept of generalized neutrosophic pre-closed sets and generalized neutrosophic pre-open sets in neutrosophic topological spaces. In the article “Design of Fuzzy Sampling Plan Using the Birnbaum-Saunders Distribution”, the authors Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam, and Abdur Razzaque Mughal discuss the use of probability distribution function of Birnbaum–Saunders distribution as a proportion of defective items and the acceptance probability in a fuzzy environment. Further, the authors Derya Bakbak, Vakkas Uluc¸ay, and Memet S¸ahin present the “Neutrosophic Soft Expert Multiset and Their Application to Multiple Criteria Decision Making” together with several operations defined for them and their important algebraic properties. In “Neutrosophic Multigroups and Applications”, Vakkas Uluc¸ay and Memet S¸ahin propose an algebraic structure on neutrosophic multisets called neutrosophic multigroups, deriving their basic properties and giving some applications to group theory. Changxing Fan, Jun Ye, Sheng Feng, En Fan, and Keli Hu introduce the “Multi-Criteria Decision-Making Method Using Heronian Mean Operators under a Bipolar Neutrosophic Environment” and test the effectiveness of their new methods. Another decision-making study upon an everyday life issue which empowered us to organize the key objective of the industry developing is given in “Neutrosophic Cubic Einstein Hybrid Geometric Aggregation Operators with Application in Prioritization Using Multiple Attribute Decision-Making Method” written by Khaleed Alhazaymeh, Muhammad Gulistan, Majid Khan, and Seifedine Kadry