Scores of hesitant fuzzy elements revisited: “Was sind und was sollen”

[EN] This paper revolves around the notion of score for hesitant fuzzy elements, the constituent parts of hesitant fuzzy sets. Scores allow us to reduce the level of uncertainty of hesitant fuzzy sets to classical fuzzy sets, or to rank alternatives characterized by hesitant fuzzy information. We propose a rigorous and normative definition capable of encapsulating the characteristics of the most important scores introduced in the literature. We systematically analyse different types of scores, with a focus on coherence properties based on cardinality and monotonicity. The hesitant fuzzy elements considered in this analysis are unrestricted. The inspection of the infinite case is especially novel. In particular, special attention will be paid to the analysis of hesitant fuzzy elements that are intervals

Study on Approaches to Interval-Valued Intuitionistic Fuzzy Multiple Attribute Decision Making with Incomplete Information

多属性决策可以描述为从有限个方案集中选择足够好的方案以获得最优目标的决策过程。可是，注意到大多数决策问题具有不确定性，并且对于不同的问题传统的决策方法通常是代价昂贵的和依赖数学上的近似方法(如非线性问题的线性化)，这样可能导致决策问题在性能方面的缺乏。因此，实用的有助决策的重要方面是提供处理不精确和模糊信息的能力。在这种情况下，模糊多属性决策方法通常比传统的多属性决策方法做得好，模糊多属性决策被Bellman和Zadeh视为目标或约束条件本质上是模糊的决策过程。从模糊数的结构来看，区间直觉模糊集作为模糊集的扩展来描述决策信息是一种非常有用的方式，因为区间直觉模糊集的隶属函数和非隶属函数是区间型...Multiple attribute decision making (MADM) may be characterised as a process of choosing or selecting 'sufficiently good' alternative(s) or course(s) of action, from a set of alternatives, to attain a goal. It should be noted, however, that much decision making involves uncertainty, and for difficult problems, conventional (nonfuzzy) methods are usually expensive and depend on mathematical approxim...学位：工学硕士院系专业：信息科学与技术学院自动化系_系统工程学号：2322006115257

Evaluation of learning management systems using interval valued intuitionistic fuzzy-z numbers

The use of online education tools has increased rapidly with the transition to distance education caused by the pandemic. The obligation to carry out all activities of face-to-face education online made it very important for the tools used in distance education to meet the increasing needs. In line with these needs, radical changes have occurred in the learning management systems used in distance education. Therefore, in this study, it is aimed to determine the features that the systems used in distance education should have and to compare the existing systems according to these features. For this purpose, a novel fuzzy extension, interval valued intuitionistic fuzzy Z-numbers, is defined for modeling uncertainty, and AHP and WASPAS methods using proposed fuzzy numbers are developed to determine the importance of decision criteria and compare alternatives.WOS:0010834495000112-s2.0-85173691458Emerging Sources Citation IndexArticleUluslararası işbirliği ile yapılmayan - HAYIRKasım2023YÖK - 2022-23Eki

Applications of Neutrosophic Bipolar Fuzzy Sets in HOPE Foundation for Planning to Build a Children Hospital with Different Types of Similarity Measures

In this paper we provide an application of neutrosophic bipolar fuzzy sets in daily life’s problem related with HOPE foundation that is planning to build a children hospital, which is the main theme of this paper. For it we first develop the theory of neutrosophic bipolar fuzzy sets which is a generalization of bipolar fuzzy sets

Interval-valued intuitionistic fuzzy ordered precise weighted aggregation operator and its application in group decision making

An important research topic related to the theory and application of the interval-valued intuitionistic fuzzy weighted aggregation operators is how to determine their associated weights. In this paper, we propose a precise weight-determined (PWD) method of the monotonicity and scale-invariance, just based on the new score and accuracy functions of interval-valued intuitionistic fuzzy number (IIFN). Since the monotonicity and scale-invariance, the PWD method may be a precise and objective approach to calculate the weights of IIFN and interval-valued intuitionistic fuzzy aggregation operator, and a more suitable approach to distinguish different decision makers (DMs) and experts in group decision making. Based on the PWD method, we develop two new interval-valued intuitionistic fuzzy aggregation operators, i.e. interval-valued intuitionistic fuzzy ordered precise weighted averaging (IIFOPWA) operator and interval-valued intuitionistic fuzzy ordered precise weighted geometric (IIFOPWG) operator, and study their desirable properties in detail. Finally, we provide an illustrative example. First published online: 24 Jan 201

The interval-valued intuitionistic fuzzy geometric choquet aggregation operator based on the generalized banzhaf index and 2-additive measure

Based on the operational laws on interval-valued intuitionistic fuzzy sets, the generalized Banzhaf interval-valued intuitionistic fuzzy geometric Choquet (GBIVIFGC) operator is proposed, which is also an interval-valued intuitionistic fuzzy value. It is worth pointing out that the GBIVIFGC operator can be seen as an extension of some geometric mean operators. Since the fuzzy measure is defined on the power set, it makes the problem exponentially complex. In order to overall reflect the interaction among elements and reduce the complexity of solving a fuzzy measure, we further introduce the GBIVIFGC operator w.r.t. 2-additive measures. Furthermore, if the information about weights of experts and attributes is incompletely known, the models of obtaining the optimal 2-additive measures on criteria set and expert set are given by using the introduced cross entropy measure and the Banzhaf index. Finally, an approach to pattern recognition and multi-criteria group decision making under interval-valued intuitionistic fuzzy environment is developed, respectively

Sustainability as a Multi-criteria Concept

Sustainability is a fairly old concept, born in the 18th century in the field of forestry, within a mono-functionality perspective. The concept has considerably evolved in the last few years towards a multi-functionality context, with applications reported in practically all areas of economic interest. On the other hand, modern sustainability is a complex problem, for two reasons: a) The multiplicity of functions of a very different nature involved in the process and b) The manner in which different segments of the society or stakeholders perceive the relative importance of these functions. For the above reasons, a realistic approach for dealing with the sustainability issue requires taking into consideration multiple criteria of different nature (economic, environmental and social), and in many cases within a participatory decision making framework. This book presents a collection of papers, dealing with different theoretical and applied issues of sustainability, with the help of a modern multi-criteria decision-making theory, with a single as well as several stakeholders involved in the decision-making process. Hopefully, this material will encourage academics and practitioners to alter their research in this hot and vital topic. After all, the sustainable management of the environment and its embedded resources is one of the most important, if not the major challenge of the 21st century

Improving the efficiency of production processes in the manufacturing industry based on methods of multicriteria analysis and metacheuristics

Problem procjene i rangiranja grešaka koje mogu dovesti do Lean gubitaka imaju presudan uticaj na efektivnost i pouzdanost proizvodnog kao i ostalih poslovnih procesa preduzeća. U ovoj doktorskoj disertaciji su razvijena dva nova fazi višekriterijumska modela optimizacije zasnovan na Analizi mogućih grešaka i efekata grešaka (prema eng. Failure Mode and Effect Analysis - FMEA), odnosno FMEA okviru za rangiranje grešaka na nivou svakog Lean gubitka. Na samom početku izvršena je identifikacija i grafički prikaz grešaka korišćenjem Išikava dijagrama. Ocjena identifikovanih grešaka vrši se u odnosu na tri faktora rizika (RF) definisana u FMEA metodi. Nedostaci FMEA metode, koje su sugerisani od strane drugih autora, su prevaziđeni kombinacijom ove metode sa pravilima fazi logike i metodama višekriterijumskog odlučivanja (prema eng. Multi Criteria Decision Making - MCDM). U prvom modelu relativna važnost RF i njihove vrijednosti opisani su unaprijed definisanim lingvističkim iskazima koji su modelirani sa trapezoidnim intuitivnim fazi brojevima (prema eng. Trapezoidal intuitionistic fuzzy numbers - TrIFN). Za određivanje vektora težine RF koristi se Analitički hijerarhijski proces proširen sa TrIFN (prema eng. Fuzzy Analytic Hierarchy Process with TrIFN - IFAHP). Rang identifikovanih grešaka daje se upotrebom predložene metode Višekriterijumskog kompromisnog rangiranja proširene sa TrIFN (prema eng. VIKOR with TrIFN - IF-VIKOR). Na kraju, urađena je analiza osjetljivosti koja pokazuje stabilnost predloženog pristupa. U drugom modelu, procjena i rangiranje grešaka koji dovode do Lean gubitaka daju se korišćenjem fazi MCDM metoda proširenih sa intervalnim intuitivnim fazi brojevima (prema eng. Interval valued intuitionistic fuzzy numbers - IVIFN). Relativna važnost RF i njihove vrijednosti opisani su unaprijed definisanim lingvističkim iskazima koji su modelirani sa IVIFN. Modifikovana fazi logika sa pravilima za IVIFN koristi se za određivanje nivoa rizika proizvodnog procesa. U drugom dijelu disertacije, predložen je hibridni model odlučivanja za ocjenu i izbor metoda/tehnika kvaliteta čija primjena dovodi do unaprjeđenja efektivnosti i pouzdanosti proizvodnih procesa u malim i srednjim preduzećima (MSP) prerađivačke industrije. Ovaj model kombinuje FMEA sa trougaoni intuitivni fazi brojevima (prema eng. Triangular intuitionistic fuzzy numbers – TIFN). Sve postojeće neizvjesnosti, relativna važnost RF, njihove vrijednosti, primjenljivost metoda kvaliteta, kao i troškovi primjene opisani su unaprijed definisanim jezičkim iskazima koji su modelirani TIFN. Izbor metoda kvaliteta naveden je kao KP problem, odnosno problem rastegljivog ranca koji se razlaže na potprobleme sa određenim brojem elemenata rješenja. Rješenje ovog problema pronalazi se korišćenjem genetskog algoritma (prema eng. Genetic algorithm - GA) (Gojković et al., 2021). Model je verifikovan kroz studiju slučaja sa podacima iz stvarnog života koji potiču od značajnog broja organizacija iz jednog regiona, čime je pokazan potencijal i primjenljivost razvijenih modela. Pokazano je da su predloženi modeli izuzetno pogodan kao alati za donošenje odluka za poboljšanje efektivnosti i pouzdanosti proizvodnog procesa u MSP prerađivačke industrije.The problem of evaluation and ranking failures that can lead to Lean waste has a critical effect on the safety and reliability of the manufacturing process, and other business processes of enterprises. In this doctoral dissertation, two new fuzzy multicriteria optimization models based on Failure Mode and Effect Analysis - FMEA have been developed to rank failures at the level of each Lean waste. At the beginning, failures were identified using the Ishikawa diagram. The evaluation of the identified failures is performed in relation to the three risk factors (RF) defined in the FMEA method. The disadvantages of the FMEA method, which have been suggested by other authors, have been overcome by combining this method with the fuzzy logic rols and the Multi Criteria Decision Making (MCDM). In the first model, the relative importance of RF and their values are described by predefined linguistic statements modeled with trapezoidal intuitionistic fuzzy numbers (TrIFN). The Fuzzy Analytic Hierarchy Process with TrIFN (IF-AHP) was used to determine the RF weight vector. The rank of identified failures is given using the proposed VIKOR with TrIFN (IF-VIKOR). Finally, a sensitivity analysis was performed showing the stability of the proposed approach. In the second model, estimation and ranking of failures leading to Lean waste are given using the fuzzy MCDM with interval valued intuitionistic fuzzy numbers (IVIFN). The relative importance of RF and their values are described by predefined linguistic statements modeled with IVIFN. A modified fuzzy logic ruls with IVIFN rules is used to determine the level of risk of the production process. In the second part of the dissertation, a hybrid decision-making model for evaluation and selection of quality methods/techniques is proposed, the application of which leads to the improvement of efficiency and reliability of production processes in small and medium enterprises (SMEs) of the manufacturing industry. This model combines FMEA with the triangular intuitionistic fuzzy numbers (TIFN). All existing uncertainties, the relative importance of RF, their values, the applicability of quality methods/techniques, as well as the costs of application are described by pre-defined linguistic statements modeled by TIFN. The choice of quality methods/techniques is stated as a KP problem. It is a Rubber Knapsack problem that decomposes into subproblems with a certain number of solution elements. The solution to this problem is found using a genetic algorithm (GA) (Gojković et al., 2021). The model was verified through a case study with real life data originating from a significant number of organizations from one region, showing the potential and applicability of the developed models. He showed that the proposed models are extremely suitable as decision-making tools for improving the efficiency and reliability of the production process in the SME manufacturing industry

Neutrosophic Theory and its Applications : Collected Papers - vol. 1

Neutrosophic Theory means Neutrosophy applied in many fields in order to solve problems related to indeterminacy. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every entity together with its opposite or negation and with their spectrum of neutralities in between them (i.e. entities supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel\u27s dialectics (the last one is based on and only). According to this theory every entity tends to be neutralized and balanced by and entities - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Hence, in one hand, the Neutrosophic Theory is based on the triad , , and . In the other hand, Neutrosophic Theory studies the indeterminacy, labelled as I, with In = I for n ≥ 1, and mI + nI = (m+n)I, in neutrosophic structures developed in algebra, geometry, topology etc. The most developed fields of the Neutrosophic Theory are Neutrosophic Set, Neutrosophic Logic, Neutrosophic Probability, and Neutrosophic Statistics - that started in 1995, and recently Neutrosophic Precalculus and Neutrosophic Calculus, together with their applications in practice. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic). In neutrosophic logic a proposition has a degree of truth (T), a degree of indeterminacy (I), and a degree of falsity (F), where T, I, F are standard or non-standard subsets of ]-0, 1+[. Neutrosophic Probability is a generalization of the classical probability and imprecise probability. Neutrosophic Statistics is a generalization of the classical statistics. What distinguishes the neutrosophics from other fields is the , which means neither nor . And , which of course depends on , can be indeterminacy, neutrality, tie (game), unknown, contradiction, vagueness, ignorance, incompleteness, imprecision, etc