Properties In Order Research Articles

A Novel Construction Method of (OP) Polynomial and Rational Fuzzy Implications

Abstract: In this article, we develop new constructed methods with specific conditions. The first method is a generalization of convex combination using n fuzzy implications. The second method is a parameterization of Lukasiewicz implication in an Ordering Property (OP) fuzzy implication form. The innovation in this work is the presentation of three new constructed methods of (OP) polynomial and (OP) rational fuzzy implications. We investigate some families of Ordering Property (OP) and Ordering Property (OP) Rational fuzzy implications. To these methods, we give some coefficient conditions in order to satisfy basic properties like ordering property (OP), identity property (IP) and contrapositive symmetry (CP). Background: Fuzzy implication functions are one of the main operations in fuzzy logic. They generalize the classical implication, which takes values in the set {0, 1}, to fuzzy logic, where the truth values belong to the unit interval [0, 1]. The study of this class of operations has been extensively developed in the literature in the last 30 years from both theoretical and applicational points of view. Introduction: In this paper, we develop five new methods for constructing fuzzy implications with specific properties. The paper starts by presenting the first fuzzy implication construction machine that uses n fuzzy implications with specific conditions. Next, we parameterize Lukasiewicz implication and create new families of (OP) polynomial and (OP) rational implications. For each method we investigate which conditions are satisfied and we give some examples. Methods: The first constructed method uses n fuzzy implications in a linear product representation. The second method is an (OP) polynomial implication a parameterized Lukasiewicz implication. The third method is a rational implication with five parameters. In the fourth method we give a general form in the previous method by changing variables x and y with increasing functions. Finally, the last method is another (OP) rational implication with three parameters. Results: In each method we present the properties that are satisfied. We generalize the (OP) polynomial and rational by replacing the variables with monotonic functions or add powers on them. Finally, we generalize and we give examples of new produced fuzzy implications. Conclusion: As a future work, we can create new families of rational implications by changing the polynomials of the numerator and denominator so that they satisfy more properties. Finally, the new methods we presented can contribute in the construction of uninorms and copulas under certain conditions.

ABOLITION OF THE JESUIT ORDER (THE SOCIETY OF JESUS) AND ITS CONSEQUENCES FOR THE UZHHOROD JESUIT COLLEGIUM

The Jesuit Order is one of the most high-powered religious orders in early modern history. From the Order's foundation until its liquidation, the whole of Europe had a network of monasteries, collegiums, and universities. The liquidation of the Order arose the questions of spiritual and educational succession and the fate of movable and immovable property of the Society of Jesus. The abolition of the Order had significant consequences both for the whole organization and for individual components, namely educational institutions (collegiums, universities), for all Order members from the head (general) to the paters, fathers in individual missions. The author considers the reasons for the liquidation of the Society of Jesus. The author also tries to find out how it affected the situation of the Uzhhorod Jesuit Collegium, what happened with the Order's property, and what was the fate of the paters and masters who were providing the functioning of the institution in Uzhhorod. Based on available sources, the author states that after the announcement of the dismissal of the Society of Jesus (1773), the Uzhhorod Collegium continued to work as usual for two years. At first, the property was transferred to the newly created Educational Fund. Later, Empress Maria Theresa donated a part of it to the canonized shortly before (1771) Greek Catholic Eparchy of Mukachevo. The official transfer of the Jesuit buildings, castle, and library funds to the Greek Catholic Eparchy of Mukachevo took place on August 1, 1775. For almost two centuries, from donations or ransoms from local nobles, Uzhhorod Jesuits received land estates, forests, vineyards, meadows, various buildings, mills, etc. After the dissolution of the Order, the majority of lands were given to the educational fund, then sold. Its proceeds were used for the needs of the educational fund.

The “Second Egypt”: Cretan Refugees, Agricultural Development, and Frontier Expansion in Ottoman Cyrenaica, 1897–1904

AbstractThis article investigates the Ottoman state's endeavor to create the “second Egypt” by consolidating its imperial authority along the coastline and hinterland of Cyrenaica from 1897 to 1904. It examines the strategic settlement of Cretan Muslim refugees in territories situated between Benghazi and Derna and in al-Jabal al-Akhdar following the Cretan insurrection of 1897–98. I argue that Cretan Muslim refugees-turned-settlers served as skilled agriculturalists and experienced armed sentries who were integral to the Ottoman state's plans for economic development and expansionism in Cyrenaica. Focusing particularly on ‘Ayn al-Shahhat and Marsa Susa, this article contends that the establishment of Cretan Muslim agricultural colonies served to undermine the political and economic position of the Sanusi order by appropriating the order's properties and access to resources. This work offers a new perspective on how the Ottoman state reasserted its sovereignty in its frontier territory in Cyrenaica by harnessing the power of migration.

A Method of Generating Fuzzy Implications from n Increasing Functions and n + 1 Negations

In this paper, we introduce a new construction method of a fuzzy implication from n increasing functions g i : [ 0 , 1 ] → [ 0 , ∞ ) , ( g ( 0 ) = 0 ) ( i = 1 , 2 , … , n , n ∈ ℕ ) and n + 1 fuzzy negations N i ( i = 1 , 2 , … , n + 1 , n ∈ ℕ ). Imagine that there are plenty of combinations between n increasing functions g i and n + 1 fuzzy negations N i in order to produce new fuzzy implications. This method allows us to use at least two fuzzy negations N i and one increasing function g in order to generate a new fuzzy implication. Choosing the appropriate negations, we can prove that some basic properties such as the exchange principle (EP), the ordering property (OP), and the law of contraposition with respect to N are satisfied. The worth of generating new implications is valuable in the sciences such as artificial intelligence and robotics. In this paper, we have found a novel method of generating families of implications. Therefore, we would like to believe that we have added to the literature one more source from which we could choose the most appropriate implication concerning a specific application. It should be emphasized that this production is based on a generalization of an important form of Yager’s implications.

Data-Driven Optimization of Order Admission Policies in a Digital Print Factory

On-demand digital print service is an example of a real-time embedded enterprise system. It offers mass customization and exemplifies personalized manufacturing services. Once a print order is submitted to the print factory by a client, the print service provider (PSP) needs to make a real-time decision on whether to accept or refuse this order. Based on the print factory's current capacity and the order's properties and requirements, an order is refused if its acceptance is not profitable for the PSP. The order is accepted with the most appropriate due date in order to maximize the profit that can result from this order. We have developed an automated learning-based order admission framework that can be embedded into an enterprise environment to provide real-time admission decisions for new orders. The framework consists of three classifiers: Support Vector Machine (SVM), Decision Tree (DT), and Bayesian Probabilistic Model (BPM). The classifiers are trained by history orders and used to predict completion status for new orders. A decision integration technique is implemented to combine the results of the classifiers and predict due dates. Experimental results derived using real factory data from a leading print service provider and Weka open-source software show that the order completion status prediction accuracy is significantly improved by the decision integration strategy. The proposed multiclassifier model also outperforms a standalone regression model.

Expected Utility and Equilibrium with Subjective Choice Sets and Strategic Reporting

This paper studies an economy where agents trade using a shared language, so that they do not need to meet in person with goods physically present. Agents provide vague descriptions of proposed net trades, which we interpret as arising either from inherent limitations in what the agents can describe or from strategic presentations of information. We construct a family of orders over terms in the language, arising from an individual's preferences over consumption as subjectively perceived, illustrate the induced order's properties, and show the constructive existence of competitive equilibrium. Finally, we illustrate the relationship between the existence of a competitive equilibrium obtained in the language and the one that would result from an interaction involving perceived consumption sets.

On the Ordering Property and Law of Importation in Fuzzy Logic

In this paper, the authors investigate the ordering property (OP), , together with the general form of the law of importation(LI), i.e., , whereis a t-norm andis a fuzzy implication for the four main classes of fuzzy implications. The authors give necessary and sufficient conditions under which both (OP) and (LI) holds for S-, R-implications and some specific families of QL-, D-implications. Following this, the paper proposes the sufficient condition under which the equivalence between CRI and triple I method for FMP can be established. Moreover, this conclusion can be viewed as a unified triple I method, a generalized form of the known results proposed by Wang and Pei.