Fuzzy cardinality based evaluation of quanti®ed sentences

Quantified statements are used in the resolution of a great variety of problems. Several methods have been proposed to evaluate statements of types I and II. The objective of this paper is to study these methods, by comparing and generalizing them. In order to do so, we propose a set of properties that must be fulfilled by any method of evaluation of quantified statements, we discuss some existing methods from this point of view and we describe a general approach for the evaluation of quantified statements based on the fuzzy cardinality and fuzzy relative cardinality of fuzzy sets. In addition, we discuss some concrete methods derived from the mentioned approach. These new methods fulfill all the properties proposed and, in some cases, they provide an interpretation or generalization of existing methods

Application of decision trees and multivariate regression trees in design and optimization

Induction of decision trees and regression trees is a powerful technique not only for performing ordinary classification and regression analysis but also for discovering the often complex knowledge which describes the input-output behavior of a learning system in qualitative forms;In the area of classification (discrimination analysis), a new technique called IDea is presented for performing incremental learning with decision trees. It is demonstrated that IDea\u27s incremental learning can greatly reduce the spatial complexity of a given set of training examples. Furthermore, it is shown that this reduction in complexity can also be used as an effective tool for improving the learning efficiency of other types of inductive learners such as standard backpropagation neural networks;In the area of regression analysis, a new methodology for performing multiobjective optimization has been developed. Specifically, we demonstrate that muitiple-objective optimization through induction of multivariate regression trees is a powerful alternative to the conventional vector optimization techniques. Furthermore, in an attempt to investigate the effect of various types of splitting rules on the overall performance of the optimizing system, we present a tree partitioning algorithm which utilizes a number of techniques derived from diverse fields of statistics and fuzzy logic. These include: two multivariate statistical approaches based on dispersion matrices, an information-theoretic measure of covariance complexity which is typically used for obtaining multivariate linear models, two newly-formulated fuzzy splitting rules based on Pearson\u27s parametric and Kendall\u27s nonparametric measures of association, Bellman and Zadeh\u27s fuzzy decision-maximizing approach within an inductive framework, and finally, the multidimensional extension of a widely-used fuzzy entropy measure. The advantages of this new approach to optimization are highlighted by presenting three examples which respectively deal with design of a three-bar truss, a beam, and an electric discharge machining (EDM) process

Intersections between some families of (U,N)- and RU-implications

(U,N)-implications and RU-implications are the generalizations of (S,N)- and R-implications to the framework of uninorms, where the t-norms and t-conorms are replaced by appropriate uninorms. In this work, we present the intersections that exist between (U,N)-implications and the different families of RU-implications obtainable from the well-established families of uninorms

Design decisions: concordance of designers and effects of the Arrow’s theorem on the collective preference ranking

The problem of collective decision by design teams has received considerable attention in the scientific literature of engineering design. A much debated problem is that in which multiple designers formulate their individual preference rankings of different design alternatives and these rankings should be aggregated into a collective one. This paper focuses the attention on three basic research questions: (i) “How can the degree of concordance of designer rankings be measured?”, (ii) “For a given set of designer rankings, which aggregation model provides the most coherent solution?”, and (iii) “To what extent is the collective ranking influenced by the aggregation model in use?”. The aim of this paper is to present a novel approach that addresses the above questions in a relatively simple and agile way. A detailed description of the methodology is supported by a practical application to a real-life case study

Fuzzy logic: An analysis of logical connectives and their characterizations

The focus of this thesis is to determine exactly which functions serve as appropriate fuzzy negation, conjunction and disjunction functions. To this end, the first chapter serves as motivation for why fuzzy logic is needed, and includes an original demonstration of the inadequacy of many valued logics to resolve the sorites paradox. Chapter 2 serves as an introduction to fuzzy sets and logic. The canonical fuzzy set of tall men is examined as a motivating example, and the chapter concludes with a discussion of membership functions. Four desirable conditions of the negation function are given in Chapter 3, but it is shown that they are not independent. It suffices to take two of these conditions, monotonicity and involutiveness, as negation axioms. Two characterization proofs are given, one with an increasing generator and the other with a decreasing generator. An example of a general class of negation functions is studied, along with their corresponding increasing and decreasing generators. Chapters 4 and 5 provide an analysis of fuzzy conjunction and disjunction functions, respectively. Five axioms for each are given: boundary conditions, commutativity, associativity, monotone non-decreasing, and continuity. Yager\u27s class of conjunction and disjunction functions are each shown to satisfy all five of these axioms. The additional assumption of strict monotonicity is added to obtain pseudo-characterizations analogous to the characterizations of the negation function. Finally, it is shown that although the min function is a conjunction function, it does not have a decreasing or an increasing generator. Similar results are obtained in Chapter 5 for disjunction functions, with a concluding theorem that the max function has no generators. The interactions of these three connectives is the content of Chapter 6. In this chapter, negation, conjunction, and disjunction triples are considered that satisfy both of DeMorgan\u27s laws. Distributivity of conjunction and disjunction over each other is examined. It is then shown that the only conjunction and disjunction pair that satisfies the distributivity axiom is the min, max pair. In conclusion, Chapter 7 discusses why having unique functions serve as conjunction and disjunction is desirable. It also contains a brief discussion of the implication connective and some areas for further investigation

Development and evaluation of multiple criteria decision-making approaches to watershed management

Decision-making in environmental management is complex due to the multiplicity arid diversity of management objectives and technological choices. This suggests that modelers and experts could utilize (I) multiple-criteria decision-making (MCDM) approaches to assist stakeholder groups in integrating and synthesizing relevant data and information to address ecological and socio-economic concerns and (2) uncertainty approaches to quantify the risks related to the impact of decision alternatives. Since decisions made under uncertainty and MCDM methods have been studied almost independently, most of the MCDM approaches do not address the uncertainties of real world decision situations. This dissertation presents the use of a MCDM methodology and its related decision-making tool, RESTORE. RESTORE is an integrative geographical information system-based decision-making tool that was developed to help watershed councils prioritize and evaluate restoration activities at the watershed level. RESTORE's deterministic performance evaluation module is developed from experts' knowledge and experiences. However, to filly address the complexity of the various landscape processes and human subjectivity, RESTORE should involve uncertainties inherent to experts' knowledge. No single method is able to model all types of uncertainty, therefore the examination of various uncertainty theories is critical before selecting one best suited to a specific decision context. This work explores three uncertainty theories: certainty factor model, Dempster-Shafer theory, and fuzzy set theory. To evaluate these methods in a MCDM watershed restoration context, we (1) identified criteria to assess the suitability of a method for a specific MCDM context, (2) characterized each theory in terms of the identified criteria using RESTORE, and (3) applied each theory using RESTORE. Special emphasis was given to the development of a comprehensive fuzzy MCDM methodology. Uncertainty-based MCDM approaches provide a valuable tool in analyzing complex watershed management issues. When used properly, the proposed MCDM methodology allows decision-makers (DMs) to explore a broader range of drivers and consequences. The inclusion of uncertainty analysis provides DMs with meaningful information on the quality of the evidence supporting the impact of a decision alternative, allowing them to make more informed decisions

Neutrosophic SuperHyperAlgebra and New Types of Topologies

In general, a system S (that may be a company, association, institution, society, country, etc.) is formed by sub-systems Si { or P(S), the powerset of S }, and each sub-system Si is formed by sub-sub-systems Sij { or P(P(S)) = P2(S) } and so on. That’s why the n-th PowerSet of a Set S { defined recursively and denoted by Pn(S) = P(Pn-1(S) } was introduced, to better describes the organization of people, beings, objects etc. in our real world. The n-th PowerSet was used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order to build the SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one in fact encounters SuperHyperStructures. Also, six new types of topologies have been introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology

Constructing Probability Boxes and Dempster-Shafer Structures

This report summarizes a variety of the most useful and commonly applied methods for obtaining Dempster-Shafer structures, and their mathematical kin probability boxes, from empirical information or theoretical knowledge. The report includes a review of the aggregation methods for handling agreement and conflict when multiple such objects are obtained from different sources

The development of a typology of science teachers' views on the nature of science and science practical work: an evaluative pilot study

Many theories on the nature of science and the nature of learning have been proposed. In particular, two theoretical orientations have been identified as having a decisive impact on activities in the school science classroom, namely "Inductivism" and "Constructivism". Inductivism views observations as objective, facts as constants and knowledge as being obtained from a fixed external reality. The constructivist view sees all knowledge as "reality" reconstructed in the mind of the learner. Each view predisposes certain orientations towards the science curriculum and within it particularly to assessment. It is postulated that teachers' views on science will influence how they teach and assess it. An "inductivist" teacher is more likely to reward certain approved responses from learners whereas a "constructivist" teacher is more likely to attend to learners' unique observations as evidence of their thinking. In this study a questionnaire was developed in an attempt classify science teachers according to their views on the nature of science and learning, and during this process encourage them to reflect on these views. It is hoped that the instrument could measure any changes in teacher's views as a result of the teachers becoming more reflective practitioners over time. Research indicates that the majority of teachers have a predominantly inductivist view of science. The study confirmed the results of other researchers by showing that a majority of non-tertiary science educators could be classified as being strongly inductivist. However, the overall proportion of these teachers was not as high as expected. Of possible concern was the indication that the strongly constructivist group showed very strong inductivist tendencies when assessing written tests which involved pupils' responses to laboratory observations