Multiple Criteria Ranking and Choice with All Compatible Minimal Cover Sets of Decision Rules

We introduce a new multiple criteria ranking/choice method that applies Dominance-based Rough Set Approach (DRSA) and represents the Decision Maker's (DM's) preferences with decision rules. The DM provides a set of pairwise comparisons indicating whether an outranking (weak preference) relation should hold for some pairs of reference alternatives. This preference information is structured using the lower and upper approximations of outranking (S) and non-outranking (S c ) relations. Then, all minimal-cover (MC) sets of decision rules being compatible with this preference information are induced. Each of these sets is supported by some positive examples (pairs of reference alternatives from the lower approximation of a preference relation) and it does not cover any negative example (pair of alternatives from the upper approximation of an opposite preference relation). The recommendations obtained by all MC sets of rules are analyzed to describe pairwise outranking and non-outranking relations, using probabilistic indices (estimates of probabilities that one alternative outranks or does not outrank the other). Furthermore, given the preference relations obtained in result of application of each MC set of rules on a considered set of alternatives, we exploit them using some scoring procedures. From this, we derive the distribution of ranks attained by the alternatives. We also extend the basic approach in several ways. The practical usefulness of the method is demonstrated on a problem of ranking Polish cities according to their innovativeness

Uncertain Multi-Criteria Optimization Problems

Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relationships used when modeling optimization problems. Moreover, the notion of symmetry has appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better solution with respect to one objective may compromise other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories such as probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems have not yet been explored in depth, and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed in various uncertain frameworks with special emphasis on optimization problems

Citizen Science: Reducing Risk and Building Resilience to Natural Hazards

Natural hazards are becoming increasingly frequent within the context of climate change—making reducing risk and building resilience against these hazards more crucial than ever. An emerging shift has been noted from broad-scale, top-down risk and resilience assessments toward more participatory, community-based, bottom-up approaches. Arguably, non-scientist local stakeholders have always played an important role in risk knowledge management and resilience building. Rapidly developing information and communication technologies such as the Internet, smartphones, and social media have already demonstrated their sizeable potential to make knowledge creation more multidirectional, decentralized, diverse, and inclusive (Paul et al., 2018). Combined with technologies for robust and low-cost sensor networks, various citizen science approaches have emerged recently (e.g., Haklay, 2012; Paul et al., 2018) as a promising direction in the provision of extensive, real-time information for risk management (as well as improving data provision in data-scarce regions). It can serve as a means of educating and empowering communities and stakeholders that are bypassed by more traditional knowledge generation processes. This Research Topic compiles 13 contributions that interrogate the manifold ways in which citizen science has been interpreted to reduce risk against hazards that are (i) water-related (i.e., floods, hurricanes, drought, landslides); (ii) deep-earth-related (i.e., earthquakes and volcanoes); and (iii) responding to global environmental change such as sea-level rise. We have sought to analyse the particular failures and successes of natural hazards-related citizen science projects: the objective is to obtain a clearer understanding of “best practice” in a citizen science context

Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences

Mathematical fuzzy logic (MFL) specifically targets many-valued logic and has significantly contributed to the logical foundations of fuzzy set theory (FST). It explores the computational and philosophical rationale behind the uncertainty due to imprecision in the backdrop of traditional mathematical logic. Since uncertainty is present in almost every real-world application, it is essential to develop novel approaches and tools for efficient processing. This book is the collection of the publications in the Special Issue “Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences”, which aims to cover theoretical and practical aspects of MFL and FST. Specifically, this book addresses several problems, such as:- Industrial optimization problems- Multi-criteria decision-making- Financial forecasting problems- Image processing- Educational data mining- Explainable artificial intelligence, etc

Discrete Mathematics and Symmetry

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book