Unification Procedure Research Articles

An innovative probabilistic hesitant fuzzy set MCDM perspective for selecting flexible packaging bags after the prohibition on single-use plastics

The probabilistic hesitant elements (PHFEs) are a beneficial augmentation to the hesitant fuzzy element (HFE), which is intended to give decision-makers more flexibility in expressing their biases while using hesitant fuzzy information. To extrapolate a more accurate interpretation of the decision documentation, it is sufficient to standardize the organization of the elements in PHFEs without introducing fictional elements. Several processes for unifying and arranging components in PHFEs have been proposed so far, but most of them result in various disadvantages that are critically explored in this paper. The primary objective of this research is to recommend a PHFE unification procedure that avoids the deficiencies of operational practices while maintaining the inherent properties of PHFE probabilities. The prevailing study advances the hypothesis of permutation on PHFEs by suggesting a new sort of PHFS division and subtraction compared with the existing unification procedure. Eventually, the proposed PHFE-unification process will be used in this study, an innovative PHFEs based on the Weighted Aggregated Sum Product Assessment Method–Analytic Hierarchy Process (WASPAS–AHP) perspective for selecting flexible packaging bags after the prohibition on single-use plastics. As a result, we have included the PHFEs-WASPAS in our selection of the most effective fuzzy environment for bio-plastic bags. The ranking results for the suggested PHFEs-MCDM techniques surpassed the existing AHP methods in the research study by providing the best solution. Our solutions offer the best bio-plastic bag alternative strategy for mitigating environmental impacts.

Regulating the Undesirable: Statusless Women in Israel

This paper explores how laws and procedures in Israel concerning various forms of legal status deem women foreigners to be “statusless.” In particular, it examines the treatment of three groups: Palestinian women residents of the Occupied Palestinian Territories who are married to Palestinian citizens of Israel; asylum-seeking women from Africa; and women from the former Soviet Union who have been trafficked by the sex industry, or who have lost their legal status after separating from an Israeli-citizen spouse. Drawing on various data sources—such as information and case studies published by aid organizations; legal proceedings; discussions held by parliamentary legislative committees; state officials’ commentaries in the media; and interviews with women and service providers—we map the policies that manage the entry and residence of foreigners, and explore their ideological tenets and specific impact on women. We argue that statuslessness is being justified by an ethnocratic discourse that demarcates foreigners as undesirable, and that it is maintained by hobbling existing infrastructures, such as the Convention on the Status of Refugees, family unification procedure, or the Protocol for the Prevention of Human Trafficking—and draining them of their meaning.

On isospin and flavour of leptons and quarks

Isospin emerges naturally from the Lorentz transformation of spinors, if they are based on the vector representation of the Lorentz group. The resulting extended Dirac equation for a massive spin-one-half fermion has two new additional degrees of freedom associated with the up and down components of isospin. This doublet is interpreted as describing the electron and neutrino. It is adjoined with the SU(2) symmetry group. The extended Dirac equation appears in six versions which are connected by similarity transformations. It is argued that this trait may explain the occurrence of the three families of the leptons and suggested that flavour arises genuinely from the algebraic properties of the extended Dirac equation. Its solutions are discussed and the physical role of isospin is elucidated. Isospin symmetry can be gauged, which leads to a weak-interaction-type theory and is valid for finite initial mass. Breaking the isospin SU(2) symmetry yields the correct electric charges of the particles by means of the electroweak unification procedures of the standard model.

Transparent Digital Twin for Output Control Using Belief Rule Base.

A transparent digital twin (DT) is designed for output control using the belief rule base (BRB), namely, DT-BRB. The goal of the transparent DT-BRB is not only to model the complex relationships between the system inputs and output but also to conduct output control by identifying and optimizing the key parameters in the model inputs. The proposed DT-BRB approach is composed of three major steps. First, BRB is adopted to model the relationships between the inputs and output of the physical system. Second, an analytical procedure is proposed to identify only the key parameters in the system inputs with the highest contribution to the output. Being consistent with the inferencing, integration, and unification procedures of BRB, there are also three parts in the contribution calculation in this step. Finally, the data-driven optimization is performed to control the system output. A practical case study on the Wuhan Metro System is conducted for reducing the building tilt rate (BTR) in tunnel construction. By comparing the results following different standards, the 80% contribution standard is proved to have the highest marginal contribution that identifies only 43.5% parameters as the key parameters but can reduce the BTR by 73.73%. Moreover, it is also observed that the proposed DT-BRB approach is so effective that iterative optimizations are not necessarily needed.

A strategy to build a unified data set of moment magnitude estimates for low-to-moderate seismicity regions based on European–Mediterranean data: application to metropolitan France

SUMMARYSeismic hazard assessment (SHA) requires earthquake events characterized in terms of the moment magnitude (Mw) scale both in the earthquake catalogues and in the ground motion databases (SHA data sets). However, published Mw estimates for the same event may actually differ due to the adoption of different computation methods, input data, or seismic networks. The main objective of this paper is to develop a novel strategy to assign a unique Mw value for each earthquake and unified to an Mw reference data set that can be applied to low-to-moderate seismicity regions (Mw < 4.5) such as Metropolitan France, the target region of our study. The strategy consists of first collecting all Mw estimated directly by spectral or temporal inversion in a large area of the European–Mediterranean zone, including regional and specific studies in our target region. Then, the sources of Mw estimates are ranked in five different categories, from global to specific studies. A GCMT (Global Centroid Moment Tensor project) standard Mw value is recomputed and a quality flag is assigned depending on the level of the information provided by the sources. Mw estimates are then compared at the European–Mediterranean scale with those provided by the CMT services, chosen as reference. Mw estimates are subsequently corrected for their systematic deviations by progressively including lower magnitude estimates as one moves from high ranked categories to lower ones at each step of the unification procedure. In this work, the collected data set contains 6752 Mw estimates of 4454 shallow events (depth < 40 km) that occurred between 1963 and 2019 and computed by 34 sources (bulletins, publications,…, etc). A unified Mw value could be attributed to 185 events (2.36 ≤ Mw ≤ 5.35) in France and neighbouring regions and 3351 events (3.06 ≤ Mw ≤ 7.57) in the European–Mediterranean region. Finally, we showed that this Mw data set is consistent with European SHA data sets but leads to slightly larger Mw values compared to the French SHA data sets. We also noted that some variability still subsist in Mw data set compared to the existing SHA data sets, especially for Mw < 5.0. This new unified Mw data set is a first step toward the building of future catalogues. It will contribute to greatly improve the coherence of Mw definitions in the next generation of SHA data sets for both metropolitan France and Europe.

Efficient Full Higher-Order Unification

We developed a procedure to enumerate complete sets of higher-order unifiers based on work by Jensen and Pietrzykowski. Our procedure removes many redundant unifiers by carefully restricting the search space and tightly integrating decision procedures for fragments that admit a finite complete set of unifiers. We identify a new such fragment and describe a procedure for computing its unifiers. Our unification procedure, together with new higher-order term indexing data structures, is implemented in the Zipperposition theorem prover. Experimental evaluation shows a clear advantage over Jensen and Pietrzykowski's procedure.

Efficient Full Higher-Order Unification

We developed a procedure to enumerate complete sets of higher-order unifiers based on work by Jensen and Pietrzykowski. Our procedure removes many redundant unifiers by carefully restricting the search space and tightly integrating decision procedures for fragments that admit a finite complete set of unifiers. We identify a new such fragment and describe a procedure for computing its unifiers. Our unification procedure, together with new higher-order term indexing data structures, is implemented in the Zipperposition theorem prover. Experimental evaluation shows a clear advantage over Jensen and Pietrzykowski's procedure.

Variant-based Equational Unification under Constructor Symbols

Equational unification of two terms consists of finding a substitution that, when applied to both terms, makes them equal modulo some equational properties. A narrowing-based equational unification algorithm relying on the concept of the variants of a term is available in the most recent version of Maude, version 3.0, which provides quite sophisticated unification features. A variant of a term t is a pair consisting of a substitution sigma and the canonical form of tsigma. Variant-based unification is decidable when the equational theory satisfies the finite variant property. However, this unification procedure does not take into account constructor symbols and, thus, may compute many more unifiers than the necessary or may not be able to stop immediately. In this paper, we integrate the notion of constructor symbol into the variant-based unification algorithm. Our experiments on positive and negative unification problems show an impressive speedup.

Flow over a non-uniform sheet with non-uniform stretching (shrinking) and porous velocities

Viscous flow over a porous and stretching (shrinking) surface of an arbitrary shape is investigated in this article. New dimensions of the modeled problem are explored through the existing mathematical analogies in such a way that it generalizes the classical simulations. The latest principles provide a framework for unification, and the consolidated approach modifies the classical formulations. A realistic model is presented with new features in order to explain variety of previous observations on the said problems. As a result, new and upgraded version of the problem is appeared for all such models. A set of new, unusual, and generalized transformations is formed for the velocity components and similarity variables. The modified transformations are equipped with generalized stretching (shrinking), porous velocities, and surface geometry. The boundary layer governing equations are reduced into a set of ordinary differential equations (ODEs) by using the unification procedure and technique. The set of ODEs has two unknown functions f and g. The modeled equations have five different parameters, which help us to reduce the problem into all previous formulations. The problem is solved analytically and numerically. The current simulation and its solutions are also compared with existing models for specific value of the parameters, and excellent agreement is found between the solutions.

Comparative Analysis of System Dynamics Software Packages

There are various modeling techniques used worldwide. Capturing system dynamics with support of appropriate software packages represents a field of study, which is applied in various domains and real-life situations. This paper first introduces particular applications for modeling and simulation of dynamics based on stock-and-flow diagrams. Afterwards, these applications are compared by means of usability evaluation tools, and lessons learned from the evaluation process and modeling and simulation experience are introduced. Therefore, issues like standardization and unification procedures, necessity to capture historical data timelines, or transformation of common speech to a model during conceptualization stage are discussed.

Unification modulo a 2-sorted Equational theory for Cipher-Decipher Block Chaining

We investigate unification problems related to the Cipher Block Chaining (CBC) mode of encryption. We first model chaining in terms of a simple, convergent, rewrite system over a signature with two disjoint sorts: list and element. By interpreting a particular symbol of this signature suitably, the rewrite system can model several practical situations of interest. An inference procedure is presented for deciding the unification problem modulo this rewrite system. The procedure is modular in the following sense: any given problem is handled by a system of `list-inferences', and the set of equations thus derived between the element-terms of the problem is then handed over to any (`black-box') procedure which is complete for solving these element-equations. An example of application of this unification procedure is given, as attack detection on a Needham-Schroeder like protocol, employing the CBC encryption mode based on the associative-commutative (AC) operator XOR. The 2-sorted convergent rewrite system is then extended into one that fully captures a block chaining encryption-decryption mode at an abstract level, using no AC-symbols; and unification modulo this extended system is also shown to be decidable.

РОЛЬ КОМПЬЮТЕРНО-ИНФОРМАЦИОННЫХ ТЕХНОЛОГИЙ В ПРОЦЕССЕ ПРОФИЛЬНОГО ОБУЧЕНИЯ

The article describes the conditions and forms of special environment for the application of computer and information technology in the informatization of school education, providing effective realization of the didactic principles of computer systems that foster the creation of interactive educational environment for students and teachers, unification and dynamic management procedures educational process. Models of specialization training. Outlines the differences of the content of training in specialized classes using computer and information technology. Given the solution didactic tasks is possible through the profile differentiation of elective courses, reflecting the type of professionalization.

Three Layer Closure of Strassman Metroplasty for Bicornuate Uterus

A 36 years old lady presented with long standing primary infertility of 20 years. Investigations revealed her to have bicornuate uterus. Rest of the infertility work up did not reveal any other abnormality. Reproductive potential following the unification procedure after obtaining a good cavity was discussed and she was taken up for metroplasty. A laparoscopic strassman metroplasty was performed. Longitudinal incisions were given on medial surfaces of both the horns using harmonic shears. Extra care was taken while multi layer suturing keeping in mind the criticism that the procedure has received due to the high incidence of rupture in a gravid uterus. Meticulous three-layered suturing of the uterus was performed. A unified good sized cavity was obtained which was confirmed on transvaginal ultrasound.

On strong normalization and type inference in the intersection type discipline

We introduce a new unification procedure for the type inference problem in the intersection type discipline. It is well known that type inference in this case should succeed exactly for the strongly normalizing expressions. We give a proof for the strong normalization result in the intersection type discipline, which we obtain by putting together some well-known results and proof techniques. Our proof uses a variant of Klop’s extended λ -calculus, for which it is shown that strong normalization is equivalent to weak normalization. This is proved here by means of a finiteness of developments theorem, obtained following de Vrijer’s combinatory technique. The main property of this extended calculus is uniformity, i.e. weak and strong normalizabilities coincide. The strong normalizability result is therefore a consequence of the fact, first established by Coppo and Dezani (for the λ -calculus) that typability implies weak normalizability. We then show that the unification process which is the basis for type inference exactly corresponds to reduction in the extended λ -calculus. Finally we show that our notion of unification allows us to compute a principal typing for any typable λ -expression.

Solving equations with sequence variables and sequence functions

Term equations involving individual and sequence variables and sequence function symbols are studied. Function symbols can have either fixed or flexible arity. A sequence variable can be instantiated by any finite sequence of terms. A sequence function abbreviates a finite sequence of functions all having the same argument lists. It is proved that solvability of systems of equations of this form is decidable. A new unification procedure that enumerates a complete almost minimal set of solutions is presented, together with variations for special cases. The procedure terminates if the solution set is finite. Applications in various areas of artificial intelligence, symbolic computation, and programming are discussed.

On Type Inference in the Intersection Type Discipline

We introduce a new unification procedure for the type inference problem in the intersection type discipline. We show that unification exactly corresponds to reduction in an extended λ-calculus, where one never erases arguments that would be discarded by ordinary β-reduction. We show that our notion of unification allows us to compute a principal typing for any strongly normalizing λ-expression.

GENERATING HIERARCHICAL FUZZY SYSTEMS

The proposed type of hierarchical fuzzy systems is based on the rule base hierarchy. A quite new algorithm for designing a hierarchical fuzzy system from a conventional fuzzy system is developed and implemented. The important part is the unification procedure. Redundant intermediate labels are found and subsequently unified. Basic requirements are fulfilled – subsystems of a hierarchical system are simple and transparent. A single high-dimensional and large rule base is replaced by a collection of low-dimensional rule bases with small number of rules. The input-output relation remains unchanged and all properties and propositions of the original fuzzy system are preserved by the hierarchical fuzzy system.

A Unification Procedure to the Analysis and Synthesis of Antenna Arrays

The far field pattern synthesis of arrays involves the calculation of an antenna array excitation factor, and this is performed in different ways depending on the adopted method. On the other hand, the determination of the array factor, when the excitation coefficients are known, is usually performed by a direct summation. This paper proposes a generalized procedure that can be applied to the analysis and to the synthesis of continuous and discrete arrays to evaluate the far field pattern. The proposed method employs the Fourier Relation, to derive the relationship between the array factor and the excitation distribution of a discrete array, and it is based on the Fourier Transform. Due to the finite nature of arrays, it is possible to use the Fast Fourier Transform, which permits an efficient and rapid way to perform the calculations using a computer. The method is applied to some typical synthesis problems and compared with published results. It can be seen that this new theory simplifies the usual synthesis procedure and that the processing time is dramatically reduced. Then, the method is applied to obtain synthesis techniques that control the radiation pattern through the use of the Fourier Transform properties.

Semantic bootstrapping of type-logical grammar

A two-stage procedure is described which induces type-logical grammar lexicons from sentences annotated with skeletal terms of the simply typed lambda calculus. First, a generalized formulae-as-types correspondence is exploited to obtain all the type-logical proofs of the sample sentences from their lambda terms. The resulting lexicons are then optimally unified. The first stage constitutes the semantic bootstrapping (Pinker, Language Learnability and Language Development, Harvard University Press, 1984), while the unification procedure of Buszkowski and Penn represents a first attempt at structure-dependent distributional learning of the syntactic and semantic categories. This effort extends earlier induction procedures (Buszkowski and Penn, 1990, Studia Logica 49, 431--454; Kanazawa, 1998, CSLI Publications and the European Association for Logic, Language and Information) for classical categorial grammar to at first the non-associative Lambek calculus, and then to a large class of type logics enriched by modal operators and structural rules.

Numerical simulation of spilled oil by fictitious domain method

Pollution due to spilled oil presents serious natural environment issues. In order to take effective measures against such accidents, the knowledge of behavior of oil in such accidents is urgently required. Although its behavior both offshore and in the surfzone is important, this paper concentrates on the latter problem. A flow field of seawater and spilled oil above and under the beach is simulated numerically in this study. This research effort adopts the Cross model as a constitutive equation for spilled oil. Oil adhesion properties are taken into consideration through a friction type boundary condition prescribed on the surface of spilled oil. Flow equations for respective fluids and boundary conditions between them are unified into a single flow equation to construct a numerical model. The fictitious domain method plays an important role in the unification procedure. Computation becomes rather simple due to unification of equations.