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The Dempster–Shafer theory (DST), also known as Belief function theory (BFT), finds extensive application across various domains involving data fusion. However, it is not uncommon to encounter counterintuitive results when combining highly conflicting pieces of evidence using the Dempster combination rule (DCR). While the literature offers several combination rules, only a few address these shortcomings effectively. To address these limitations and rectify the issue of counterintuitive outcomes, a novel weighted evidence fusion rule has been introduced. This fusion approach comprises four key steps: First, the reliability degree of each evidence set, also known as body of evidence (BOE) is determined based on its compatibility degree and total correlation. This step helps to mitigate conflicts arising from unreliable sources. Second, the degree of credibility of each BOE is computed, taking into account distance of evidence and uncertainty degree, further enhancing the accuracy of the fusion process. Third, the reliability and credibility degrees are combined to derive weights for each BOE, ensuring that more weight is assigned to trustworthy sources of evidence. Finally, these weights for each BOE are used to compute a modified Basic Probability Assignment (BPA) for each proposition, which are then fused using the Dempster combination rule. Numerous numerical examples, as well as artificial and real datasets, have been employed to emphasize the effectiveness and potential of this innovative approach. Furthermore, through comparative analysis, it becomes evident that the proposed rule consistently outruns other existing methods, ensuring more accurate and reliable outcomes.

Starting with this paper, we intend to develop a program aiming at construction of boundary conditions (BCs) for hyperbolic relaxation systems. Physically, such BCs are not always available. The construction is based on the assumption that the relaxation systems and well-posed BCs for the corresponding equilibrium systems are given. This paper focuses on the linearized Suliciu model. We obtain strictly dissipative and compatible BCs for the linearized model with different non-characteristic boundaries. Moreover, the effectiveness of the constructed BCs is shown by resorting to formal asymptotic solutions and energy estimates.

The aim of this work is to develop a new compatibility for the uncertain multiplicative linguistic preference relations and determine the optimal weights of decision makers (DMs), which are very suitable to deal with group decision making (GDM) problems involving uncertain multiplicative linguistic preference relations. First, the concepts of compatibility degree and compatibility index for the two uncertain multiplicative linguistic preference relations are proposed. Then we prove the property that the synthetic uncertain linguistic preference relation is of acceptable compatibility under the condition that uncertain multiplicative linguistic preference relations given by DMs are all of acceptable compatibility with a specific linguistic preference relation, which is the scientific basis of using the uncertain multiplicative linguistic preference relations in the GDM. Next, in order to determine the weights of decision makers, we construct an optimal model based on the criterion of minimizing the compatibility index. Finally, we develop an application of the optimal weights approach compared with the equal weights approach where we analyze a GDM regarding the selection of investment.

We develop some new cases of the induced continuous ordered weighted averaging (ICOWA) operator and study their desirable properties, which are very suitable to deal with group decision making (GDM) with interval fuzzy preference relations. First, we present the consensus indicator ICOWA (CI-ICOWA) operator which uses the consensus indicator of the interval fuzzy preference as the order inducing variable in the ICOWA operator. Then the concept of compatibility degree (CD) for two interval fuzzy preference relations is defined based on the continuous ordered weighted averaging (COWA) operator and the compatibility degree ICOWA (CD-ICOWA) operator is proposed which uses the CD as the order inducing variable in the ICOWA operator. Next, we investigate some desirable properties of the CD-ICOWA operator. Additionally, we construct an optimization model to obtain the weights of experts by minimizing the compatibility degree in the GDM. Finally, an illustrative numerical example is used to verify the developed approaches.

The aim of this paper is to develop a new compatibility, which is very suitable to deal with group decision making (GDM) problems involving interval multiplicative preference relations, based on the continuous ordered weighted geometric averaging (COWGA) operator. First, we define some concepts of the compatibility degree and the compatibility index for the two interval multiplicative preference relations based on the COWGA operator. Then, we study some desirable properties of the compatibility index and investigate the relationship between each expert's interval multiplicative preference relation and the synthetic interval multiplicative preference relation. The prominent characteristic of the compatibility index based on the COWGA operator is that it can deal with the compatibility of all the arguments in two interval arguments considering the risk attitude of decision maker rather than the compatibility of the two simple points in intervals. Second, in order to determine the experts' weights in the GDM with the interval multiplicative preference relations, we propose an optimal model based on the criterion of minimizing the compatibility index. Finally, we give a numerical example to develop the new approach to GDM with interval multiplicative preference relations.

Recently, De Baets et al. have characterized the fuzzy tolerance relations that a given strict order relation is compatible with. In general, the compatibility of a strict order relation with a binary fuzzy relation guarantees also the compatibility of its associated betweenness relation with that binary fuzzy relation. In this paper, we study the compatibility of an arbitrary ternary relation with a binary fuzzy relation. We prove that this compatibility can be expressed in terms of inclusions of the binary fuzzy relation in the traces of the given ternary relation.

Inspired by Borcherds' work on "G-vertex algebras," we formulate and study an axiomatic counterpart of Borcherds' notion of G-vertex algebra for the simplest nontrivial elementary vertex group, which we denote by G₁. Specifically, we formulate a notion of axiomatic G₁-vertex algebra, prove certain basic properties and give certain examples, where the notion of axiomatic G₁-vertex algebra is a nonlocal generalization of the notion of vertex algebra. We also show how to construct axiomatic G₁-vertex algebras from a set of compatible G₁-vertex operators.

Let be the full transformation semigroup on a nonempty set X and E be an equivalence relation on X. Then

In this paper, we study $\sigma$-skew McCoy rings under the $\sigma$-compatible or the $\sigma$-semicompatible conditions. We show that if $R$ is a semicommutative right or left artinian ring which is $\sigma$-semicompatible with an epimorphism $\sigma$, then the Jacobson radical $J(R)$ is $\sigma$-skew McCoy. As a corollary, we get that the Jacobson radical of a semicommutative artinian ring is right McCoy. We also show that every $\sigma$-compatible right duo ring is $\sigma$-skew McCoy and that for $\sigma$-compatible regular rings, the notions of the $\sigma$-skew McCoy and the right McCoy coincide. In addition, we show that every $\sigma$-semicompatible semicommutative ring is linearly $\sigma$-skew Camillo and that every matrix ring over a division ring is linearly $\sigma$-skew Camillo for any endomorphism $\sigma$.

Research shows that data-driven decision making using business analytics can create competitive advantages for organisations. However, this can only happen if the organisations successfully accept and use the business analytics effectively. Many studies reported business analytics implementation in large organisations, and fewer studies focus on Small and Medium Enterprises (SMEs). Furthermore, SMEs are scoring lower scores in technology absorption. Therefore, it is essential to examine the business analytics adoption among SMEs. Previous research has reported that relative advantage and compatibility were the most highlighted factors under the technology dimension in adopting innovative technologies. However, the literature reported inconsistent findings on the significance of relative advantage and compatibility in adopting various technologies. Therefore, this research conducted a quantitative survey-based study to examine the significance of relative advantage and compatibility in predicting business analytics adoption among SMEs. The sample was selected using systematic random sampling from a Malaysian national entrepreneurs database. There were 241 SMEs that responded to the online survey sent by email. The analysis using the partial least squares structural equation modelling (PLS-SEM) informed that relative advantage was significantly related to business analytics adoption; however, compatibility did not influence the business analytics adoption by SMEs in Malaysia. This finding shows that the better the relative advantage of business analytics SMEs know, the higher the possibility of adoption. In addition, less compatibility of the SMEs in Malaysia hindered the business analytics adoption. This study contributes to the theoretical aspect, which statistically informed the finding out of inconsistent gaps in technology adoption. Furthermore, this study also contributes to the practical aspect, in which managers, owners, vendors, and policy-makers can use these findings to spur and facilitate business analytics adoption among SMEs in developing countries.

This paper presents an examinations of the G space theory that was established recently for a unified formulation of compatible and incompatible models for mechanics problems using the finite element and meshfree settings. Using the generalized gradient smoothing technique, we first give a general definition for G spaces with more details on the G¹ space containing both continuous and discontinuous functions. The physical meanings and implications of various numerical treatments used in the G space theory are discussed in detail. Both normed and un-normed G spaces are discussed with emphases on the normed G spaces. Some important properties and a set of useful inequalities for the normed G spaces are proven in theory and analyzed in detail. Because discontinuous functions are allowed in a G space, much more types of function approximation methods and techniques can be used to create shape functions for numerical models. These models can be compatible and incomputable but are all stable and converge to the exact solution to the corresponding strong formulation as long as it is well-posed, based on the normed G space theory. Methods based on normed G space theory does not use the derivatives of the displacement functions in the formulation and is known as the weakened weak (W²) formulation that has a number of attractive properties such as conformability, softness, upper/lower bound, superconvergence, and ultra accuracy.

The network effect is a key factor influencing the development of e-business and technological innovation. At the same time, compatibility decisions can determine the success or failure of businesses and technologies. This study explores the compatibility strategies in the context of network effects using a two-stage game-theoretical model for a duopoly. In the first stage, two firms make their compatibility decisions, and in the second stage, two firms are engaged in Bertrand price competition. Major findings are (1) other things being fixed, two firms are more likely to be compatible with each other when they have similar market shares, (2) the compatibility decisions of firms will not be influenced by consumers' switching costs, (3) the order of their compatibility decisions will not change the resulting equilibrium, and (4) based on firms' compatibility decisions, the Bertrand price competition may still lead to market failure, necessitating governmental intervention or regulations.

The aim of this study is to empirically explore the influences of a set of key technological, organizational, and environmental (TOE) factors on the achievement of a strategic promised benefit of private portals, which is competitive advantage. Such exploration has not received attention in the web-based information systems’ area. To explore these influences, a theoretical model was developed on the basis of the information system adoption’s literature. The model postulates the TOE factors as crucial antecedents to the realization of competitive advantage. To validate the theoretical model, a questionnaire was constructed by focusing on the most precise measurements items for the TOE factors. A total of 241 responses were collected from the private portal’s users in a higher education institution in Saudi Arabia. The structural equation modeling approach was applied for conducting the required assessment. The results demonstrate that among the tested TOE factors, the relative advantage of private portals and the competitive pressure to adopt them have positive impacts on the achievement of competitive advantage. The empirical evidences produced by this study provide more clarifications about the factors that should be managed carefully to gain competitive advantage from the adopted information system innovations.

The effect of compatibility on phase morphology and orientation of isotactic polypropylene (iPP) blends under shear stress was investigated via dynamic packing injection molding (DPIM). The compatibility of iPP blended with other polymers, namely, atactic polypropylene (aPP), octane-ethylene copolymer (POE), ethylene-propylene-diene rubber (EPDM) and poly(ethylene-co-vinyl acetate) (EVA), have first been studied using dynamic mechanical analysis (DMA). These blends were subjected to DPIM, which relies on the application of shear stress fields to the melt/solid interfaces during the packing stage by means of hydraulically actuated pistons. The phase morphology, orientation and mechanical properties of the injection-molded samples were characterized by SEM, 2D WAXS and Instron. For incompatible iPP/EVA blends, a much elongated and deformed EVA particles and a higher degree of iPP chain orientation were observed under the effect of shear. However, for compatible iPP/aPP blends, a less deformed and elongated aPP particles and less oriented iPP chains were deduced. It can be concluded that the compatibility between the components decreases the deformation and orientation in the polymer blends. This is most likely due to the hindering effect, resulting from the molecular entanglement and interaction in the compatible system.

To enhance the impact strength of polyamide 6, hydrolytic polymerization modification by the polyaminoamide-g-poly(ethylene glycol) (PAAEG) derivatives with poly(ethylene glycol) (PEG) molecular weight of 400–10000 was studied. Amide groups of polyaminoamide segments were postulated to form hydrogen bonding with polyamide 6, and hydroxy groups of PAAEG units were expected to react with carboxylic acid groups of polyamide 6 forming copolymers during the polymerization. The improved compatibility in amorphous regions of blends has been confirmed by differential scanning calorimetry (DSC) and scanning electron microscopy (SEM) of fracture surfaces. The effects of PAAEG on the water absorption and notch sensitivity of blends were investigated, using water uptake measurement and mechanical testings, respectively. For comparison, pure polyamide 6 and the blend of PEG/polyamide 6 were also investigated. The addition of PAAEG retarded the crystallization of polyamide 6, but did not make remarkable influences on its crystalline structure. As a consequence of the strong interactions between the dispersed phases and polyamide 6 matrices, PAAEG was a more suitable additive for improving the notched impact strength of polyamide 6 than PEG.

The paper is concerned with the so-called natural order on the semigroup , where is the full transformation semigroup on a set X, E is a non-trivial equivalence on X and R is a cross-section of the partition X/E induced by E. We determine when two elements of T_E(X,R) are related under this order, find elements of T_E(X,R) which are compatible with ≤ on T_E(X,R), and observe the maximal and minimal elements and the covering elements.

In this paper, we investigate overdetermined systems of scalar PDEs on the plane with one common characteristic, whose general solution depends on one function of one variable. We describe linearization of such systems and their integration via Laplace transformation, relating this to Lie's integration theorem and formal theory of PDEs.

In this paper we investigate compatible overdetermined systems of PDEs on the plane with one common characteristic. Lie's theorem states that its integration is equivalent to a system of ODEs, and we give a new proof by relating it to the geometry of rank 2 distributions. We find a criterion for integration in quadratures and in closed form, and discuss nonlinear Laplace transformations and symmetric PDE models.

Let (X, ≤) be a totally ordered finite set, be the full transformation semigroup on X and E be an arbitrary equivalence on X. We consider a subsemigroup of defined by

The view exists that Bell-tests would only be about local incompatibility of quantum observables and that quantum non-locality would be an unnecessary concept in physics. In this note, we emphasize that it is not incompatibility at the local level that is important for the violation of Bell-CHSH inequality, but incompatibility at the non-local level of the joint measurements. Hence, non-locality remains a necessary concept to properly interpret the outcomes of certain joint quantum measurements.