Designing Software Architectures As a Composition of Specializations of Knowledge Domains

This paper summarizes our experimental research and software development activities in designing robust, adaptable and reusable software architectures. Several years ago, based on our previous experiences in object-oriented software development, we made the following assumption: ‘A software architecture should be a composition of specializations of knowledge domains’. To verify this assumption we carried out three pilot projects. In addition to the application of some popular domain analysis techniques such as use cases, we identified the invariant compositional structures of the software architectures and the related knowledge domains. Knowledge domains define the boundaries of the adaptability and reusability capabilities of software systems. Next, knowledge domains were mapped to object-oriented concepts. We experienced that some aspects of knowledge could not be directly modeled in terms of object-oriented concepts. In this paper we describe our approach, the pilot projects, the experienced problems and the adopted solutions for realizing the software architectures. We conclude the paper with the lessons that we learned from this experience

Some characterizations of T-power based implications

Recently, the so-called family of T-power based implications was introduced. These operators involve the use of Zadeh’s quantifiers based on powers of t-norms in its definition. Due to the fact that Zadeh’s quantifiers constitute the usual method to modify fuzzy propositions, this family of fuzzy implication functions satisfies an important property in approximate reasoning such as the invariance of the truth value of the fuzzy conditional when both the antecedent and the consequent are modified using the same quantifier. In this paper, an in-depth analysis of this property is performed by characterizing all binary functions satisfying it. From this general result, a fully characterization of the family of T-power based implications is presented. Furthermore, a second characterization is also proved in which surprisingly the invariance property is not explicitly used.Peer ReviewedPostprint (author's final draft

Immediate consequences operator on generalized quantifiers

The semantics of a multi-adjoint logic program is usually defined through the immediate consequences operator TP. However, the definition of the immediate consequences operator as the supremum of a set of values can provide some problem when imprecise datasets are considered, due to the strict feature of the supremum operator. Hence, based on the flexibility of generalized quantifiers to weaken the existential feature of the supremum operator, this paper presents a generalization of the immediate consequences operator with interesting properties for solving the aforementioned problem. © 2022 The Author(s

Representations through a monoid on the set of fuzzy implications

Fuzzy implications are one of the most important fuzzy logic connectives. In this work, we conduct a systematic algebraic study on the set II of all fuzzy implications. To this end, we propose a binary operation, denoted by ⊛, which makes (I,⊛I,⊛) a non-idempotent monoid. While this operation does not give a group structure, we determine the largest subgroup SS of this monoid and using its representation define a group action of SS that partitions II into equivalence classes. Based on these equivalence classes, we obtain a hitherto unknown representations of the two main families of fuzzy implications, viz., the f- and g-implications

The ⊛-composition of fuzzy implications: Closures with respect to properties, powers and families

Recently, Vemuri and Jayaram proposed a novel method of generating fuzzy implications from a given pair of fuzzy implications. Viewing this as a binary operation ⊛ on the set II of fuzzy implications they obtained, for the first time, a monoid structure (I,⊛)(I,⊛) on the set II. Some algebraic aspects of (I,⊛)(I,⊛) had already been explored and hitherto unknown representation results for the Yager's families of fuzzy implications were obtained in [53] (N.R. Vemuri and B. Jayaram, Representations through a monoid on the set of fuzzy implications, fuzzy sets and systems, 247 (2014) 51–67). However, the properties of fuzzy implications generated or obtained using the ⊛-composition have not been explored. In this work, the preservation of the basic properties like neutrality, ordering and exchange principles , the functional equations that the obtained fuzzy implications satisfy, the powers w.r.t. ⊛ and their convergence, and the closures of some families of fuzzy implications w.r.t. the operation ⊛, specifically the families of (S,N)(S,N)-, R-, f- and g-implications, are studied. This study shows that the ⊛-composition carries over many of the desirable properties of the original fuzzy implications to the generated fuzzy implications and further, due to the associativity of the ⊛-composition one can obtain, often, infinitely many new fuzzy implications from a single fuzzy implication through self-composition w.r.t. the ⊛-composition

The Gini index,the dual decomposition of aggregation functions, and the consistent measurement of inequality

In several economic fields, such as those related to health, education or poverty, the individuals’ characteristics are measured by bounded variables. Accordingly, these characteristics may be indistinctly represented by achievements or shortfalls. A difficulty arises when inequality needs to be assessed. One may focus either on achievements or on shortfalls but the respective inequality rankings may lead to contradictory results. Specifically, this paper concentrates on the poverty measure proposed by Sen. According to this measure the inequality among the poor is captured by the Gini index. However, the rankings obtained by the Gini index applied to either the achievements or the shortfalls do not coincide in general. To overcome this drawback, we show that an OWA operator is underlying in the definition of the Sen measure. The dual decomposition of the OWA operators into a self-dual core and anti-self-dual remainder allows us to propose an inequality component which measures consistently the achievement and shortfall inequality among the poor.Aggregation functions, dual decomposition, OWA operators, Gini index, consistent measures of achievement/shortfall inequality, Sen index, poverty measures.

Inter-Piece Sampling and Convolution: Portfolio of 5.1 Acousmatic and Electronica Compositions, Interactive Diagrams and Text

This practice-based PhD – ‘Inter-piece Sampling and Convolution’ – evolved against the background of composers such as Amon Tobin and Monty Adkins, who use techniques and workflows common to both acousmatic and electronica music. The pieces in this thesis are linked through a sustained commitment to working across these two musical contexts and through their relationships to source materials and pulses. Sound materials have been sampled from within the pieces themselves, and materials from older pieces have been convolved with newer sounds, furthering the connections between pieces. The continual feeding-forward of source material promoted the synchronous development of the conceptual tool: Input, Sculpt, Output, which brought about the evolution of intricate diagrams. All of the pieces are for fixed media, and nine of the ten are in 5.1-format surround sound. The complex web of interrelationships created by the process of sampling and convolving material from previous pieces demanded an innovative means of representation. This representation took on a diagrammatic form in order to facilitate the analysis of a sound’s continuous (re)appropriation, explicated within supporting text. The diagrams indicate the extensive use of sampling and convolution to connect pieces, and include embedded hyperlinks to audio at various stages. As a result, textual analysis of techniques and their implications takes place across multiple pieces, and results in a wider scope for individual commentaries. The hyperlinked nature of the diagrams provides a foundation for further research, and a number of conclusions are posited about the use of sampling and convolution across multiple pieces