Special Issue for the 10th Anniversary of Axioms: Logic

Published for the first time in 2012, Axioms is celebrating its 10th anniversary. To mark this significant milestone and celebrate the achievements made throughout the years, we organized a Special Issue entitled “10th Anniversary of Axioms-Logic” for Axioms‘ “Logic” section.

Logic has a wide range of applications in the field of mathematics. This Special Issue presents high-quality papers with original research on logic, mathematical logic and their applications, with a primary (but not sole) focus on algebraic logic; fuzzy logic; descriptive set theory; decision-making; computability, or recursion, theory; and algorithmic and combinatorial optimization.

We created this Special Issue to honor the collective efforts of those who have contributed to the success of the journal and to the gathering of scientific aspects in mathematical logic related to current challenges and future innovation.

We are honored to announce that the top experts in this field have contributed papers to this Special Issue. In total, the Special Issue consists of 10 papers that were selected from more than 20 submissions. The papers were written by scholars renowned for their work on fuzzy logic from different countries around the world, including Canada, Poland, China, Slovakia, Lithuania, Turkey, Pakistan, Germany, Serbia, Portugal, Taiwan, Norway, India, Saudi Arabia, Thailand and Mexico. We first note Imran Ali et al.’s paper on a Granular Computing Approach to Evaluate Spatio-Temporal Events in Intuitionistic Fuzzy Sets Data through Formal Concept Analysis, which is an interesting contribution to granular computing and intuitionistic fuzzy logic. Subsequently, we have the paper on the Application of the Methodology of Multi-Valued Logic Trees with Weighting Factors in the Optimization of a Proportional Valve by Adam Deptula et al., which describes an application of multiple-valued logic. Next, Saba Ayub et al. offer a new approach for combining fuzzy and rough sets for decision analysis in Linear Diophantine Fuzzy Rough Sets on Paired Universes with Multi Stage Decision Analysis. In the succeeding entry, we have a paper titled Proving, Refuting, Improving by Branislav Boricic, which offers a novel perspective on these concepts. Shianghau Wu then presents an interesting application of fuzzy clustering for the COVID-19 pandemic in Spatial Fuzzy C-Means Clustering Analysis of U.S. Presidential Election and COVID-19 Related Factors in the Rustbelt States in 2020. Following Wu, Alfredo Roque Freire discusses if set theory really grounds arithmetic truth in his article of the same name. Next, we have Trond Steihaug’s article on Colonel Titus’ Problem from the 17th Century, followed by a paper on Interval Type-3 Fuzzy Control for Automated Tuning of Image Quality in Televisions by Oscar Castillo et al., which considers a new area in fuzzy logic based on type-3 fuzzy sets and their application in a manufacturing problem. Tapan Senapati et al. then provide an Analysis of Interval-Valued Intuitionistic Fuzzy Aczel–Alsina Geometric Aggregation Operators and Their Application to Multiple Attribute Decision-Making in the penultimate article. Finally, we conclude with a paper by Gia Sirbiladze et al., which covers New Fuzzy Extensions on Binomial Distribution.

We are grateful to all the authors that have contributed to this Special Issue and the reviewers who have offered their comments on the contributions. In addition, we are grateful to the editors of the journal for their support in making this Special Issue a success. We expect that the collected papers will advance the current state of both logic and fuzzy logic.