Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence
Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence
Quasi-metrics and the semantics of logic programs
Fundamenta Informaticae
The Complexity of Tree Automata and Logics of Programs
SIAM Journal on Computing
Definition of general aggregation operators through similarity relations
Fuzzy Sets and Systems
Fuzzy Mathematics in Medicine
On the aggregation of some classes of fuzzy relations
Technologies for constructing intelligent systems
Representation theorems for fuzzy orders and quasi-metrics
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Difference Equations: From Rabbits to Chaos (Undergraduate Texts in Mathematics)
Difference Equations: From Rabbits to Chaos (Undergraduate Texts in Mathematics)
Distance and similarity measures for fuzzy operators
Information Sciences: an International Journal
Fuzzy Optimization and Decision Making
A fuzzy closeness approach to fuzzy multi-attribute decision making
Fuzzy Optimization and Decision Making
Denotational semantics for programming languages, balanced quasi-metrics and fixed points
International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
Fuzzy Sets and Systems
Midpoints for fuzzy sets and their application in medicine
Artificial Intelligence in Medicine
Sequence spaces and asymmetric norms in the theory of computational complexity
Mathematical and Computer Modelling: An International Journal
Aggregation of asymmetric distances in Computer Science
Information Sciences: an International Journal
On aggregation of normed structures
Mathematical and Computer Modelling: An International Journal
On quasi-metric aggregation functions and fixed point theorems
Fuzzy Sets and Systems
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In 2003, Nieto and Torres introduced the notions of segment and midpoint between fuzzy sets with the aim of giving applications to medicine [J.J. Nieto, A. Torres, Midpoints for fuzzy sets and their application in medicine, Artif. Intell. Med. 27 (2003) 81-101]. Since then the interest in the study of such concepts have grown significantly because of their applicability to model real problems where the solution can be associated with a range of ''middle ways'' between two given positions. Recently, J. Casasnovas and F. Rosello have generalized the previous work of Nieto and Torres, giving an explicit description of segments and midpoints between fuzzy sets for, among others, the well-known weighted maximum distance [J. Casasnovas, F. Rosello, Averaging fuzzy biopolymers, Fuzzy Sets Syst. 152 (2005) 139-158]. On the other hand, in 1999 Romaguera and Schellekens introduced the theory of dual complexity spaces as a part of the development of a topological foundation for the complexity analysis of programs and algorithms [S. Romaguera, M. Schellekens, Quasi-metric properties of complexity spaces, Topology Appl. 98 (1999) 311-322]. Later on, this complexity structure was extended by Garcia-Raffi, Romaguera and Sanchez-Perez in order to obtain a suitable framework for the complexity analysis of exponential time algorithms [L.M Garcia-Raffi, S. Romaguera, E.A. Sanchez-Perez, The supremum asymmetric norm on sequence algebras: A general framework to measure complexity spaces, Electronic Notes in Theoret. Comput. Sci. 74 (2003) 12]. Inspired by the fact that in this theory the role of complexity measure is carried out by an asymmetric distance, in this paper we propose an asymmetric version of the weighted maximum distance to apply the midset theory to complexity analysis. So concise descriptions of segments and midsets between fuzzy sets for the mentioned asymmetric distance are provided. As an application of the obtained results, we prove formally that the average running time, for the Largetwo algorithm, is a midpoint between the running time of computing of the best case and the worst case by means of several connections between our new weighted maximum distance and the complexity measure introduced by Garcia-Raffi, Romaguera and Sanchez-Perez.