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This paper sketches the antilogism of Christine Ladd-Franklin and historical advancement about antilogism, mainly constructs an axiomatic system Atl based on first-order logic with equality and the wholly-exclusion and not-wholly-exclusion relations abstracted from the algebra of Ladd-Franklin, with soundness and completeness of Atl proved, providing a simple and convenient tool on syllogistic reasoning. Atl depicts the empty class and the whole class differently from normal set theories, e.g. ZFC, revealing another perspective on sets and set theories. Two series of Dotterer and the theorem proved by Russinoff are re-characterized in antilogistic formulas corresponding to the square of opposition and twenty-four moods of syllogism. Then the restricted equivalence between two forms of antilogism and minimal inconsistency is built up, implying the internal connection between antilogisms and minimal inconsistency and leaving two related conjectures not proved. Besides, this paper provides a new explanation for the reason why contrariety, subcontrariety, and subalternation and the nine special moods require the non-empty assumption. [ABSTRACT FROM AUTHOR]

This study proposes a systematic approach based on axiomatic design incorporating lean and ergonomic principles within the proposed design. The contribution to the body of knowledge is to keep construction workers safe by fostering a secure construction environment. Axiomatic design and lean approaches are combined to address human factors and eliminate wastes that hinder a safe construction environment. The application of the proposed system is set in the context of the construction industry. The methodology provides the construction sector with a road map toward reducing the occurrence of accidents and serves as a complementary approach between lean and ergonomic principles. The design solution has been validated and partially applied in a metro construction firm. Results show that the design solution can improve the efficiency of the construction phases by adopting a value-maximization strategy and has the potential to improve the safety and ergonomics of construction projects. [ABSTRACT FROM AUTHOR]

In this paper, we take an axiomatic approach to the design of ecological footprint indices. Our focus is put on the heterogeneity of land with respect to types and regions, at the core of an inherent aggregation problem. We propose an axiomatic characterization of the ecological footprint index with two fundamentally new axioms, symmetry and independence, which can resolve the problem of land heterogeneity. It is shown that a unique index, up to an affine transformation, exists meeting the axiom system. This index simplifies the aggregation procedure considerably and avoids the need for a synthetic unit of measurement, like global hectares, as well as complex transformations of variables by means of weighting schemes. Our findings reveal differences with the Global Footprint Network (GFN) index, in particular with regard to the treatment of land heterogeneity. Finally, the axiomatic methodology employed may open up perspectives for the development of ecological measures in general, and especially of measures for sustainability and tipping points. [ABSTRACT FROM AUTHOR]

With the advantages of new technologies and rising demand from customers, it is necessary to improve the manufacturing process. This necessity was recognized by the industry; therefore, the concept of Industry 4.0 has been implemented in various areas of manufacturing and services. The backbone and main aspect of Industry 4.0 is digitalization and the implementation of technologies into processes. While this concept helps manufacturers with the modernization and optimization of many attributes of the processes, Industry 5.0 takes a step further and brings importance to the human factor of industry practice, together with sustainability and resilience. The concept of Industry 5.0 contributes to the idea of creating a sustainable, prosperous, and human-friendly environment within companies. The main focus of the article is to analyze the existing literature regarding what is missing from the successful implementation of human centricity into industry practice, namely in small and medium-sized factories (SMEs). These findings are then presented in the form of requirements and barriers for the implementation of human centricity into SME factories, which can serve as guidelines for implementing human-centered manufacturing using axiomatic design theory in SMEs, which can serve as a roadmap for practitioners. [ABSTRACT FROM AUTHOR]

During the configuration process of open architecture products (OAPs), adaptive change is inevitable to meet customers' personalised demands. However, the coupling between modules makes adaptive changes of open architecture products more difficult. For the coupling between modules in open architecture product design, an approach to analysing the coupling between modules is proposed. The implications of adaptive change for open architecture products are explained, and the interface relationships among the common platform, customised modules, and personalised modules are analysed. The coupling modes of three cases are discussed, i.e. the coupling between modules under the same branch, between modules under different branches with only functional collaboration, and between modules under different branches with function-structure correlation. The coupling degrees are calculated with consideration of the number of connections between modules and their comprehensive correlation degree. The structural complexity of the module is considered by development cost, development time, change cost, and change time, which is expressed with the information content in axiomatic design. Based on structural complexity, the dependency, and coupling degree between modules, the calculation method of change impact degree between modules is presented. The method on coupling analysis between modules in open architecture product design for personalised electric winches is illustrated. [ABSTRACT FROM AUTHOR]

This study aims to effectively support decision-makers in evaluating leading e-commerce companies in Vietnam from a sustainability perspective. In addition, this study evaluates and analyzes criteria that affect the performance of e-commerce companies in Vietnam to find the best practices for e-commerce implementation of managers. In this way, companies can save costs and increase marketing and promotion efficiency, helping to reach more customers. In doing so, an integrated framework based on MCDM is proposed for the first time in e-commerce industry assessment. In the first stage, the fuzzy decision making trial and evaluation Laboratory method is applied to determine the weights of 9 criteria based on collected data. This study lists prominent quantitative evaluation criteria, taking into account the sustainability aspect. In the second phase, ranking the top 12 e-commerce companies in Vietnam according to their performance based on these nine criteria was done by applying the neutrosophic fuzzy axiomatic design method. According to an analysis of the data, the external financial assistance coefficient (12.7%) is the most crucial factor determining how competitive international e-commerce businesses are. The results of this study can help underperforming companies make strategic decisions to improve their performance. Integrating these two techniques provides a new method for evaluating global trading companies that have hitherto remained unaddressed in the trading industry and, therefore, leave a gap that needs to be investigated. [ABSTRACT FROM AUTHOR]

Pollination is a crucial ecological process with far-reaching impacts on natural and agricultural systems. Approximately 85% of flowering plants depend on animal pollinators for successful reproduction. Over 75% of global food crops rely on pollinators, making them indispensable for sustaining human populations. Wind, water, insects, birds, bats, mammals, amphibians, and mollusks accomplish the pollination process. The design features of flowers and pollinators in angiosperms make the pollination process functionally effective and efficient. In this paper, we analyze the design aspects of the honeybee-enabled flower pollination process using the axiomatic design methodology. We tabulate functional requirements (FRs) of flower and honeybee components and map them onto nature-chosen design parameters (DPs). We apply the "independence axiom" of the axiomatic design methodology to identify couplings and to evaluate if the features of a flower and a honeybee form a good design (i.e., uncoupled design) or an underperforming design (i.e., coupled design). We also apply the axiomatic design methodology's "information axiom" to assess the pollination process's robustness and reliability. Through this exploration, we observed that the pollination process is not only a good design but also a robust design. This approach to assessing whether nature's processes are good or bad designs can be valuable for biomimicry studies. This approach can also inform design considerations for bio-inspired innovations such as microrobots. [ABSTRACT FROM AUTHOR]

In the era of rapid product iteration, companies need simple and effective methods to guide the entire process of product innovation design and enhance their product innovation capabilities. Most research focused on improving one or several steps in the product design process. Although some scholars have proposed methods that guided the entire process, they combined more than three different theories, which increased the difficulty of theoretical learning and the complexity of practical implementation. This paper proposed a product innovation design process composed of three theoretical methods: Kano, Axiomatic Design (AD), and Theory of the Solution of Inventive Problems (TRIZ). This new process guided the entire product design process with fewer theoretical methods, reducing the difficulty of learning and implementation. The paper demonstrated the effectiveness of this method through the design practice of a portable two-wheeled self-balancing vehicle. Additionally, the discussion section explored the method's potential from the design management perspective. [ABSTRACT FROM AUTHOR]

Maritime sector-based accidents are the source of major environmental disasters that place the sea environment at risk. It is critical to identify hazards and risk factors to avoid accidents and minimize losses. The importance of the Polar Regions in protecting the global ecosystem and nature has been identified as crucial. An environmental problem in the polar regions will affect the entire ecosystem. In this study, The Fuzzy-AHP approach was utilized to investigate the causes of the accidents and failures in polar regions. According to the findings, human error is the most crucial risk element, followed by technical, propulsion, radar detection failure, and improper watchkeeping technique risk factors. In the light of the findings, a suggested training course via an axiomatic design approach will reduce the ice navigation risk factors. [ABSTRACT FROM AUTHOR]

Francesco Berto proposed a logic for imaginative episodes. The logic establishes certain (in)validities concerning episodic imagination. They are not all equally plausible as principles of episodic imagination. The logic also does not model that the initial input of an imaginative episode is deliberately chosen. Stit-imagination logic models the imagining agent's deliberate choice of the content of their imagining. However, the logic does not model the episodic nature of imagination. The present paper combines the two logics, thereby modelling imaginative episodes with deliberately chosen initial input. We use a combination of stit-imagination logic and a content-sensitive variably strict conditional à la Berto, for which we give a Chellas–Segerberg semantics. The proposed semantics has the following advantages over Berto's: (i) we model the deliberate choice of initial input of imaginative episodes (in a multi-agent setting), (ii) we show frame correspondences for axiomatic analogues of Berto's validities, which (iii) allows the possibility to disregard axioms that might be considered not plausible as principles concerning imaginative episodes. We do not take a definite stance on whether these should be disregarded but give reasons for why one might want to disregard them. Finally, we compare our semantics briefly with recent work, which aims to model voluntary imagination, and argue that our semantics models different aspects. [ABSTRACT FROM AUTHOR]

A pneumatic seed metering device is required for the high speed and intelligent variable operation in recent years. However, the existing complicated transmission and pneumatic system and mechanical structure cannot fully meet the largescale production of pneumatic supply with the high stability, due mainly to the pressure loss caused by a curved pipe. In this study, the invention problem problem-solving theory (TRIZ) and axiomatic theory design (AD) methods were applied to carry out the innovative design of a pneumatic seeding device for rapeseed. Firstly, the seeding maturity prediction and evolution were used to clarify the development stage, evolution path, and potential of seed metering using TRIZ technology. The existing seeding technology was in a recession recovery period, while the evolution of the technology system was in line with the Scurve evolutionary law and evolutionary model. The future seed metering device was preferred for the integration in the simple, microscopic, controllable, and automated evolutionary path. Secondly, the design process model was established using the integration of TRIZ and AD. TRIZ tools were introduced in the process of mapping functional to structural domains. Among them, the "conflict resolution principles" was adopted to solve the contradiction and conflicts of the transmission and pneumatic systems in the existing seed metering device. The invention principles were selected to optimize the structural parameters. Finally, the motor was utilized to directly drive the seeding disk and the built-in air chamber of the fan. The original design matrix was developed using independent design axioms and the minimum entropy. An innovative system was designed to integrate the motor- fan with the pneumatic seed metering device for rape. The trial production and processing were performed on two technical implementation schemes. The motor fan was determined to arrange on the same side after optimization, particularly for the better airtightness and structural stability. The integrated motor drive was used to simplify the transmission, whereas, the integrated fan was to eliminate the gas transmission pipe, in order to reduce the wind pressure loss. As such, the improved transmission and pneumatic system were required only a small space without the additional power. The test results show that the integrated seed metering device was fully meetmet the requirements of single seed metering. A better performance was achieved in the qualified index is more than 90%, even reached reaching up to 99.82%, when the absolute value of suction negative pressure was 1.0-2.0 kPa and the working speed was less than 7 km/h. The required pressure for the qualified index of 90% was lower than before. The innovative design of the pneumatic seed metering device was integrated the power and pneumatic sources, which was were in the line with the technological system evolution path, individual start and stop of the seeding unit without any influence on the rows. More importantly, the mechanical structure and transmission were better matched for the development trend of intelligent variables. This finding can provide an innovative design idea and references for the design of a pneumatic seed device. [ABSTRACT FROM AUTHOR]

The Indian Railways is India's biggest employer and undeniably influences the country's transportation network, economy, and social and cultural systems. The network is split into zones for operational reasons. It is vital to evaluate these railway networks to identify their strengths and shortcomings and to improve their performance. Past works often use Data Envelopment Analysis to evaluate railway services. Our contribution lies in the inclusion of several aspects not previously considered, such as (i) both tangible and intangible criteria, (ii) the hierarchical nature of the problem, and (iii) additional useful criteria and data to analyze the performance of the zones, including physical assets, operating ratio, accidents, comfort, travel experience, flexibility, transparency, etc. We use the novel Hierarchical Fuzzy Axiomatic Design method to evaluate the performance of sixteen zones in the Indian Railways since it suits our problem well. We find that the Southern Railway zone performs best, while the Northeast Frontier zone is ranked last. We also identify the strengths and weaknesses of all railway zones. [ABSTRACT FROM AUTHOR]

Interval games are an extension of cooperative coalitional games, in which players are assumed to face payoff uncertainty. Characteristic functions thus assign a closed interval instead of a real number. This study revisits two interval game versions of Shapley values (i.e., the interval Shapley value and the interval Shapley-like value) and characterizes them using an axiomatic approach. For the interval Shapley value, we show that the existing axiomatization can be generalized to a wider subclass of interval games called size monotonic games. For the interval Shapley-like value, we show that a standard axiomatization using Young's strong monotonicity holds on the whole class of interval games. [ABSTRACT FROM AUTHOR]

logistics occupies an important place in production activities and directly affects the duration of production and product quality. Considering the limited number of studies in the literature on production logistics, which is so important, it is seen that the studies are related to the determination of storage strategies, selection of storage vehicles, structuring of material transport movements, selection of material transport vehicle types, cellular layout, structuring of intracellular and intercellular movements. The use of fuzzy and weighted fuzzy information axiom, which is a fuzzy-based selection approach, for transport activities in industrial cells will be a new study in the literature. The information axiom, which is included in the design methodology with axioms, was used to determine the simplest internal logistics transportation method. An application study was carried out in the factory of an automotive supplier company. The most suitable option among alternative transport methods with different criteria was determined by applying fuzzy information axiom and weighted fuzzy information axiom methodologies. With these approaches, it has been tried to find the simplest and most efficient cell feeding method that provides the most customer expectations. The differences between the current internal logistics transportation method and the proposed lean internal logistics transportation method are given. In order to help decision makers, make decisions without hesitation, the study has been strengthened with sensitivity analysis. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to support total productive maintenance implementers by providing a roadmap for autonomous maintenance (AM) preparation phase. Design/methodology/approach: The authors use the axiomatic design (AD) methodology with lean philosophy as a paradigm. Findings: This is an exploratory research to find the most important factors in AM preparation phase. A decoupled AD design ensures an effective usage of training within industry (TWI) and the introduction of standardized work (SW). TWI provides value in importance it assigns to leaders, with its "train the trainers" approach and in preparing a training program. Besides being an effective training method, TWI job instruction (TWI JI) provides needed information infrastructure to front load operators SW and equipment trainings. Research limitations/implications: Although AD, TWI and lean artifacts are generally field proven, the research is limited due to the lack of an industrial application. Practical implications: In many real-life projects, companies do not know where to start and how to proceed, which leads to costly iterations. The proposed roadmap minimizes iterations and increases the chance of project success. Originality/value: The authors apply AD for the first time to AM preparation phase despite it is used in the analysis of lean manufacturing. AD permits to structure holistically the most relevant lean manufacturing solutions to obtain a risk free roadmap. TWI has emerged as a training infrastructure; TWI JI-based operator SW training and the adaptation of JI structure to equipment training are original additions. [ABSTRACT FROM AUTHOR]

Dual type-2 fuzzy cones are defined. Formulae for infimum and supremum of any number of fuzzy grades are derived. These formulae are used to study basic properties of dual type-2 fuzzy cones. It is shown that most properties of type-1 fuzzy cones remain valid. An axiomatic approach to Pareto set reduction is then considered. A method of Pareto set reduction with the use of dual type-2 fuzzy cones is outlined. [ABSTRACT FROM AUTHOR]

'Leave no one behind' has become an important principle of the entire 2030 Sustainable Development Agenda and the Sustainable Development Goals that brings inequality to the centre stage. Although a precise definition of what it is to lag behind is essential to assess sustainable economic growth and social progress a discussion on the desirable properties of such a measure is absent in the literature. This paper fills that gap by proposing and discussing a number of normative and analytical properties a measure of the 'Leave no one behind' principle should satisfy. The axioms proposed are necessary and sufficient to characterize the fuzzy measure by García-Pardo et al. [8] and together with other additional axioms make the structure of this measure more transparent. • Leaving no one behind is the central focus of the Sustainable Development Goals. • The Leaving no one behind principle suggests going beyond the averages. • The ambiguity of the left behind principle makes it convenient to use a fuzzy approach. • We discuss desirable properties of a measure of the extent an individual lags behind. • A subset of axioms characterizes the fuzzy set proposed by García-Pardo et al. [8]. [ABSTRACT FROM AUTHOR]

Institution theory represents the fully axiomatic approach to model theory in which all components of logical systems are treated fully abstractly by reliance on category theory. Here, we survey some developments over the last decade or so concerning the institution theoretic approach to non-classical aspects of model theory. Our focus will be on many-valued truth and on models with states, which are addressed by the two extensions of ordinary institution theory known as L -institutions and stratified institutions, respectively. The discussion will include relevant concepts, techniques, and results from these two areas. [ABSTRACT FROM AUTHOR]

We define a class of subshifts defined by a family of allowed patterns of the same shape where, for any contents of the shape minus a corner, the number of ways to fill in the corner is the same. For such a subshift, a locally legal pattern of convex shape is globally legal, and there is a measure that samples uniformly on convex sets. We show by example that these subshifts need not admit a group structure by shift-commuting continuous operations. Our approach to convexity is axiomatic, and only requires an abstract convex geometry that is "midpointed with respect to the shape". We construct such convex geometries on several groups, in particular strongly polycyclic groups and free groups. We also show some other methods for sampling finite patterns, and show a link to conjectures of Gottshalk and Kaplansky. [ABSTRACT FROM AUTHOR]

Social awareness of the environment has promoted the vigorous development of remanufacturing. Traditional product design does not consider the remanufacturability, which leads to improper disposal at the end of the product's life, resulting in environmental pollution and resource waste. In this paper, a method for the generation and optimization of product design schemes was established, in which remanufacturability was included at the early design stage of the product. Firstly, based on axiomatic design, the Z-shaped mapping was upgraded to the tree topology mapping, which was then incorporated into the scheme generation model, and seven remanufacturability design constraint criteria were used as constraints to obtain a product design set of scenarios. Secondly, the entropy weight method and analytic hierarchy process were combined to calculate the weights of the four evaluation indicators: functionality, economy, stability, and environment; and a differential evolution algorithm was used to optimize the scheme. Finally, a lathe was taken as a case to illustrate the applicability and effectiveness of the proposed methodology. The results showed that the method could successfully generate product design schemes that improved remanufacturability and met the needs of users. [ABSTRACT FROM AUTHOR]

This paper presents a new theoretical approach to the study of robotics manipulators dynamics. It is based on the well-known geometric approach to system dynamics, according to which some axiomatic definitions of geometric structures concerning invariant subspaces are used. In such a framework, certain typical problems in robotics are mathematically formalised and analysed in axiomatic form. The outcomes are sufficiently general that it is possible to discuss the structural properties of robotic manipulation. A generalized theoretical linear model is used, and a thorough analysis is made. The noninteracting nature of this model is also proven through a specific theorem. [ABSTRACT FROM AUTHOR]

Supplier selection is one of the most important steps of supply chain management, and choosing the right supplier is of great importance in achieving the goals of the companies under competitive conditions. In this study, the supplier selection problem in a company operating in the logistics sector is discussed. Firstly, critical spare parts have been selected by FSN (Fast-Slow-Non-Moving) analysis in order to determine the product group from which supplier selection would be made. Axiomatic Design and Dematel (The Decision Making Trial and Evaluation Laboratory) method, which are among the Multi-Criteria Decision Making (MCDM) techniques, have been proposed to solve the problem. The relationships between the criteria influencing the supplier selection have been interpreted via Dematel and the criteria have been divided into two groups as "dispatcher" and "receiver", and selection and ranking among the suppliers have been carried out with Axiomatic Design. In addition, considering the fact that the criteria do not have equal weight, the criteria have been weighted by the Analytical Hierarchy Process (AHP) method and the ranking obtained by Weighted Axiomatic Design have been compared with the previous ranking. Finally, the criteria determined as "receiver" in the Dematel method have been removed from the analysis and the methodology has been repeated. Thus, the effect of determining the cause-effect relationship between the criteria on the results has been interpreted. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to present a method for improving the preliminary design process of an aircraft. Design/methodology/approach: The approach of this paper is using Axiomatic Design (AD) principles in the aircraft preliminary design process. The aircraft design process consists of modules and disciplines, which are loosely coupled that can disrupt designers' ability. Consequently, designers should define suitable functional requirements (FRs) and design parameters for products to avoid or limit coupling between them. As modular architecture is commonly defined as having a one-to-one mapping from the function domain to the physical domain, the independence axiom in AD could support the modularity of the design process. Therefore, these features guide us to use AD principles at the first steps of the aircraft design process. Findings: Reduction coupling between different FRs and consequently less repetitive activities and design iteration in the design process by using AD principles are the finding of this paper. Practical implications: This concept could be used for the design process of every complex product. Originality/value: Looking at the preliminary design of a Blended Wing Body unmanned aerial vehicle with respect to the AD is a new technique to achieve a modular design process. [ABSTRACT FROM AUTHOR]

Purpose: Additive manufacturing (AM) technologies have tremendous applications in industries owing to their unique advantages. Sustainable AM (SAM) is gaining significance because of lightweight structures, lattice geometries and customized parts for industrial applications. To facilitate design for SAM, design guidelines from AM and environment viewpoints are to be analyzed. In this context, this paper aims to present the analysis of SAM guidelines. Design/methodology/approach: This work divides 26 identified SAM guidelines into four categories. Grey axiomatic design was used to calculate the weights of guidelines categories. Further, the grey technique for order preference by similarity to ideal solution was used as a solution methodology to prioritize the SAM guidelines. Findings: The top identified guidelines are "Design for reusability" and "Optimize part orientation for build time and roughness." Implementing proper design guidelines leads to many sustainable benefits such as minimum material consumption, energy consumption and emissions. Originality/value: This study would facilitate Am product designers to deploy prioritized guidelines for enhancing the effectiveness of the additively manufactured product with sustainability benefits. The prioritized guidelines would guide the AM product designers to take maximum advantage of the AM process by deploying design for AM and design for environment guidelines. This study contributed a structured approach for design engineers and practitioners to deploy guidelines during the early stages of product design to ensure AM feasibility with minimal environmental impact. [ABSTRACT FROM AUTHOR]

To control manufacturing processes, integration of flows of manufacturing information is an important starting point. In this regard, an effective Integrated Manufacturing Information System (IMIS) which is capable of monitoring, analyzing, and inspecting manufacturing processes properly is critical. Often, most of difficulties in achieving an effective IMIS stem from a poor design for the system architecture. This study particularly addresses the problem of coupling in architecture of an IMIS and its effect on the system performance. This study employs "Independence Axiom" of the Axiomatic Design (AD) theory to deal with the problem and uses "times in process" and "utilized capacities of available resources" as two important criteria for evaluating the system performance. To verify the proposed methodology, a real IMIS is addressed, its stochastic behavior is simulated in Visual SLAM and AweSim (version 3.o) software environment, and the outcomes are analyzed by using logistic regression method for each level of system decomposition. Results of the analyses indicate that fulfillment of independence axiom of AD theory can significantly enhance performance of the concerned IMIS. [ABSTRACT FROM AUTHOR]

There are several multicriteria decision-making (MCDM) approaches presented in the literature with their characteristics. Although traditional MCDM approaches are considered a proper implementation to select the best alternative from available types, they failed to consider uncertainty which is quite high and desires to be thoughtfully measured in the selection process. This research focuses on extending MCDM in the neutrosophic environment using axiomatic design (AD) as a novel contribution to selecting appropriate Computed Tomography (CT) devices. We present a new linguistic scale for evaluating criteria and alternatives based on single-valued triangular neutrosophic numbers (SVTrN). The proposed approach is superior to other existing approaches due to its simplicity and ability to simulate natural human thinking via considering truth, indeterminacy, and falsity degrees. Then, applying it will increase the value of imaging for medical decision-making and decrease needless costs. So, this study can be valuable to researchers by helping them consider the appropriate medical imaging system selection problem theoretically under uncertainty, and for governments and organizations to design better satisfying medical imaging evaluation systems. [ABSTRACT FROM AUTHOR]

Starting from the notion of a multidistance, we formalize, through a suitable system of axioms, the concept of an inequality measure defined on a nonempty set with no additional structure implemented a priori. Among inequality measures, apart from multidistances we pay special attention to dispersions, and study their main features. Classical concepts will be generalized to this abstract setting. Multidistances are then revisited, and some new methods to generate them are implemented. A wide spectrum of interdisciplinary applications is outlined in the final section. [ABSTRACT FROM AUTHOR]

Products classified as hazardous materials are used extensively in various sectors and can be transported from the location where they are produced to their destinations by different methods. Hazardous materials transportation differs from other transportation types due to the chemicals in the content of the products or flammable and explosive materials. For this reason, the alternative that provides the lowest cost or the fastest delivery may not be the best solution for the transport of hazardous materials. Petrol, which is in the hazardous materials class, is transported in higher amounts than other hazardous materials due to it is widely consumed. In this study, a model is proposed to determine the most suitable transportation mode for petroleum. In the proposed model, seven criteria are determined as transportation cost, accident risk, transportation speed, capacity, flexibility, service area and damage cost. The importance weights of the criteria are calculated by the fuzzy AHP method, and alternative transportation modes are evaluated with the weighted fuzzy axiomatic design method considering the criteria. In addition, sensitivity analysis is performed to evaluate the effect of criterion weights on the results. As a result of the study, maritime transport is determined as the most suitable transportation mode for petroleum. [ABSTRACT FROM AUTHOR]

The blockchain platforms (BPs) have emerged as important tools for improving enterprise data security. However, the selection of a suitable BP for is a challenging issue for enterprises. In this paper, a novel heterogenous multi-criteria decision-making (MCDM) model is proposed to facilitate the BP selection and evaluation process. First, the evaluation criteria for BPs are defined through an analysis of popular BPs. Second, based on the defined evaluation criteria, multiple types of fuzzy numbers are adopted to accurately represent the evaluation criteria. Then, to deal with multiple types of fuzzy numbers, a hybrid distance measure is proposed to determine the negative and positive ideal separation matrices of the evaluation criteria. In addition, using the axiomatic design's information content metric the as basis, an improved method is proposed to unify the evaluation of multiple types into a single number. An improved weight method is then proposed based on the combination of objective and subjective weighting to obtain the comprehensive weights of the criteria. Finally, a closeness degree metric is introduced to obtain the ranking order of all BP alternatives. An example case is analyzed to illustrate how to evaluate and select a suitable BP. The superiority of the proposed heterogeneous model is verified by comparisons with state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Axiomatic fuzzy sets (AFS) theory has seen extensive application in classification tasks in recent years. Yet, efficiently generating precise fuzzy descriptions for each target class from a multitude of complex concepts is challenging. This study aims to bridge this gap by transforming the challenge into a combinatorial optimization problem. We adopt an advanced model-based evolutionary optimization method, Randomized Coordinate Shrinking Classification (RACOS), to create an interpretable classifier within the AFS framework. By refining the definition of the complex concept set in AFS theory, we define a feasible search space for the optimization method. Innovative fitness functions have been developed focusing on semantic discrimination and prediction accuracy. Concurrently, we establish an encoding–decoding mechanism to link the solution vector with the complex concept for each fitness function. Ultimately, the complex concepts, guided by various fitness functions, are integrated into the class's fuzzy description using AFS logical operations. Our method demonstrates competitive classification performance and superior interpretability compared to other evolutionary fuzzy rule-based classifiers. • Develop encoding–decoding mechanism to bridge complex concept and solution vector. • Design various fitness function to balance prediction accuracy and interpretability. • Covert training AFS-based classifier to solving combinatorial optimization problem. • Generate semantic description for prediction result in form of natural language. [ABSTRACT FROM AUTHOR]

According to the concept of physical integration as understood in axiomatic design, design parameters of a product should be integrated into a single physical part or a few parts with the aim of reducing the information content, while still satisfying the independence of functional requirement. However, no specific method is suggested in the literature for determining the optimal degree of physical integration in a given design. This is particularly important with the current advancement in technologies such as additive manufacturing. As new manufacturing technologies allow physical elements to be integrated in new ways, new methods are needed to help designers optimize physical integration given the specific constraints and conflicts of each design. This study proposes an algorithm that uses graph partitioning to allow a designer to optimize the integration of functional requirements into a target number of parts, with the goal of minimizing the co-allocation of incompatible functional requirements in the same part. The operation and viability of the algorithm are demonstrated via two numerical examples and a practical example of designing a pencil. [ABSTRACT FROM AUTHOR]

The Group Identification Problem ("Who is a J?") introduced by Kasher and Rubinstein [14] assumes a finite class of agents, each one with an opinion about the membership to a group J of the members of the society, consisting in a function that indicates for each agent, including herself, the degree of membership to J. The problem is that of aggregating those functions, satisfying different sets of axioms and characterizing different aggregators. The literature has already considered fuzzy versions of this problem. In this paper we consider alternative fuzzy presentations of the axiomatic of the original problem. While some results are analogous to those of the original crisp model, we show that our fuzzy version is able to overcome some of the main impossibility results of Kasher and Rubinstein. [ABSTRACT FROM AUTHOR]

Concept design evaluation is the most critical part of product design, which determines the direction of the subsequent design stage. Due to the various uncertainties inherent in decision-maker (DM)'s linguistic evaluation, such as fuzziness and randomness, how to deal with these uncertainties reasonably is a challenge. Only using a single uncertainty treatment method may not be enough to select an appropriate conceptual design. Therefore, this paper aims to develop an extended information axiom concept design evaluation model combining linguistic Z-numbers (LZNs) and axiomatic design methods to deal with the uncertainty in concept design evaluation. Specifically, the LZNs are used to express DM's subjective evaluation information and the reliability of the evaluation result. In the evaluation process, the uncertainty caused by linguistic variables is represented by the cloud model. Moreover, the compatibility weights of concepts are derived objectively based on the compatibility matrix. Finally, the design combination with the minimum information content is obtained by using the extended information axiom. The feasibility and applicability of this method are verified by an evaluation example of ink pen concept design. Compared with the existing methods, the proposed method considers more uncertainty and is more in line with the actual situation. [ABSTRACT FROM AUTHOR]

In this paper, considering L being a complete residuated lattice, we first introduce the concept of mediate L-fuzzy relations and give its characterizations by L-fuzzy upper and lower rough approximation operators. Then we provide an axiomatic approach to characterize L-fuzzy rough sets by L-fuzzy unions and L-fuzzy intersections. Concretely, we present axiomatic characterizations of L-fuzzy rough sets with respect to serial, reflexive, symmetric, transitive, mediate and Euclidean L-fuzzy relations. Finally, we give characterizations of L-fuzzy upper (lower) rough approximation operators by L-closure (interior) operators from a categorical aspect. [ABSTRACT FROM AUTHOR]

Put forward a kind of association rules mining method based on fuzzy genetic algorithm, this approach by building a mining model, the association rules and fuzzy genetic algorithm fuses in together, and then given to the fitness function of the mining space, and uses threshold to limit the fuzzy genetic algorithm will cross distribution and compile the fitness function, the improved method excavation stability is strong, the mining accuracy is high. The clustering analysis method of multidimensional fuzzy genetic algorithm mapping association network is studied, and the multidimensional module layout target is analyzed by using fuzzy hierarchical analysis technology and improved genetic algorithm combined with the clustering target of each angle, and the module division of each angle is realized. The main structure of the product is constructed with process model as the integration framework, style as the organization form, and feature list as the expression mechanism. The product characteristics based on fuzzy genetic algorithm are studied, the main structure configuration design process model mapping relation analysis, combined with the main structure of the joint model, together to achieve the fuzzy genetic algorithm (GA) variant design of fine-grained axiomatic mode, based on the associated network building and integration of new product design process, product structure of multidimensional optimization problem is solved. [ABSTRACT FROM AUTHOR]

This paper introduces a method to improve the design procedure of axiomatic design theory (AD) with Extenics. A comprehensive review of the AD indicates that the powerful principle of AD has been widely studied and applied to many areas, however, inexperienced practitioners of the AD theory still find it difficult to follow or apply the principles in their design which inadvertently often leads to misunderstanding and skepticism. The lack of definitive descriptions for all the elements and specific approaches to guiding the mapping process restricts the development and application of AD theory. This paper improves the design procedure of AD with Extenics. The elements in AD domain are expressed by basic-elements of Extenics, and the formulations are generated. The mapping process based on AD and Extenics is developed. The improved design procedure provides designers with a theoretical foundation based on the logical and rational thought process, meanwhile the solution space can be expanded and innovative designs are inspired. Based on the proposed design procedure, a computer-aided system is developed, which makes the complex and fuzzy design activity clear and easy to follow by filling in the blanks in a step-by-step manner. An example of a novel corn harvester header design scheme is considered to illustrate the validity of the improved design procedure. [ABSTRACT FROM AUTHOR]

Both national and international encouragements for research and development (R&D) projects have been growing worldwide. Since R&D projects include various uncertainties related to time, technology, finance, and knowledge, risk management studies are highly significant for the success of these projects. In risk management, all of the potential actions that might have negative impacts on the processes or outputs of a project should be determined, and if it is possible, their negative impacts should be reduced before the project starts. In this study, after risks in R&D projects are determined, the alternative projects are prioritized with respect to these risks by using an approach based on interval-valued intuitionistic fuzzy AHP and fuzzy information axiom. Interval-valued Intuitionistic Fuzzy Analytic Hierarchy Process (IVIF AHP) is used to determine the importance degrees of the determined risk factors while fuzzy information axiom is used to evaluate R&D projects considering these risk factors. It is revealed that the most important risk is "Abnormal changes in cost" while the least important one is "Deficiencies in contract articles". [ABSTRACT FROM AUTHOR]

This study addresses the problem of design of systems for recoverability and discusses that a modularisation of the system architecture can effectively facilitate the recovering operations for a damaged system. To modularise the system architecture, Design Structure Matrix (DSM) methodology along with Axiomatic Design (AD) theory are employed. The study discusses that preventing propagation of the failure(s) to the rest of the system architecture can significantly contribute to the recovery of the system and proposes a methodology and utilises the Mean Time to Recovery (MTTR) as a good indicator reflecting the stochastic behaviour of system recoverability. The present study mathematically shows that modularisation of the system architecture can considerably augment the probability of success in recovering and fulfilling the physical components following experiencing a failure in the system, significantly reduce the length of recovery time and improve the system recoverability. To verify the presented method, architecture of information flow in a real contract is addressed. Results from the application of the method indicated that modularisation of the architecture of the information flow in the contract significantly reduces the volume of time and effort required for adjusting content of the clauses and improves the system recoverability considerably. [ABSTRACT FROM AUTHOR]

Summary: Electric power systems try to maximize resilience by various enhancement strategies as preventive and corrective actions against extreme weather events. This paper presents an operational network reconfiguration strategy during a high wind event to strengthen the resiliency of distribution networks. In the proposed resilience enhancement strategy, a bi‐level optimization problem is formulated with two conflicting objectives (i) maximizing grid resilience and (ii) realize the primary objective by a minimum number of out‐of‐service lines (OSLs) switching operations. Furthermore, the algorithm considers the priority of loads, which is an important characteristic of modern distribution grids. The optimization problem is solved by the bi‐level genetic algorithm (BiGA). The IEEE 33‐bus network is utilized to demonstrate the application of the developed algorithm. The simulation results show a significant improvement in the resiliency of the tested network and reveal that switching operations can be used effectively to increase the resiliency of distribution networks against natural disasters. Furthermore, sensitivity analysis is performed to show the effectiveness of the proposed approach for finding the global optimal point. The proposed network reconfiguration strategy helps to prepare for severe weather conditions. [ABSTRACT FROM AUTHOR]

Lorenzo Mascheroni 's 1797 work La geometria del compasso , which develops a geometry based solely on compass constructions, is considered by the author as stepping back behind the "demarcation line" of Euclidean geometry. In this work Mascheroni emphasizes the practical aspects of this geometry over a theoretical approach. A century later, in 1899, David Hilbert and his student Michael Feldblum proposed a totally different approach – algebraic and axiomatic – concerning geometric constructions based on various instruments. Taking into account that, at the end of the 18th century, straightedge geometry was also developed, one may ask what happened to the image of instrument-based geometry during the 19th century? By focusing on Mascheroni's book and its reception, this article aims to examine the various views and conceptions of mathematicians with respect to this geometry. [ABSTRACT FROM AUTHOR]

Surprisingly, despite that fuzzy sets were introduced more than fifty years ago, there is not consensus yet about how to extend the notion of inclusion in such a framework. Recently, alternatively to previous methods in the literature, we introduced an approach in which we make use of the so-called φ -index of inclusion. This approach has a main difference with respect to previous ones: the degree of inclusion is identified with a function instead of with a value in [ 0 , 1 ] , although such a feature makes it difficult to compare the φ -index of inclusion with existing axiomatic approaches concerning measures of inclusion. This is the reason why in this paper we define two different and natural measures of inclusion by means of the φ -index of inclusion and, then, show that both measures satisfy some standard axiomatic approaches about measures of inclusion in the literature. In addition, taking into account the relationship of fuzzy entropy with Young axioms for measures of inclusion, we present also a measure of entropy based on the φ -index of inclusion that is in accordance with the axioms of De Luca and Termini. [ABSTRACT FROM AUTHOR]

Fuzzy relations R : A 2 → [ 0 , 1 ] are widely used in decision-making in order to represent degrees of preference between alternatives in A. Examining fuzzy relations, this paper first reflects on an inherent incompatibility inside the domain of reciprocal fuzzy preference relations and preference structures. Aiming at clarifying the semantics of reciprocal fuzzy relations by means of that of weak fuzzy relations, a general frame is then proposed for studying the transformation between them, based on the notion of reciprocal functions. Next, we show that reciprocal relations can be naturally endowed with a preference structure of their own, containing two relations respectively showing a semantics of strict preference and lack of preference. Finally, we study the compatibility between these reciprocal preference structures and the standard preference structures of weak fuzzy preference relations by means of an axiomatic approach, leading to a system of functional equations that is shown to admit different solutions, allowing to explicitly assign one of the available semantics for reciprocal preference relations. [ABSTRACT FROM AUTHOR]

This paper contributes to the theory of average rate of change (ARC) measurement. We use an axiomatic approach to generalize the conventional ARC measures (such as the difference quotient and the continuously compounded growth rate) in several directions: to outcome variables with arbitrary connected domains, to not necessarily time-shift invariant dependence on time, to more general (than an interval) time sets, to a path-dependent setting, and to a benchmark-based evaluation. We also revisit and generalize the relationship between the ARC measurement and intertemporal choice models. • Average rate of change (ARC) measurement is related to intertemporal choice. • An axiomatic approach to ARC measurement is developed. • Various generalizations of the conventional ARC measures are proposed. [ABSTRACT FROM AUTHOR]