Quantitative modeling in biology can be difficult due to parameter value scarcity. An alternative is qualitative modeling since it requires few to no parameters. This article presents a qualitative modeling derived from boolean networks where fuzzy logic is used and where edges can be tuned. Fuzzy logic being continuous, its variables can be finely valued while remaining qualitative. To conside...

In Boolean logic, a Karnaugh map may be regarded either as a pictorial form of a trugh table, or as an extension of the Venn diagram. However, when fuzzy logic is concerned another minimization method is required, and therefore an extension of a Karnaugh map is investigated. In this paper a new minimization algorithm is developed in order to remove the existing disadvantage of simplifying fuzzy...

Calculation of the viewshed from a digital elevation model (OEM) is a common capability of a GIS packages. Two mistaken assumptions are made, however: first, that the OEM is accurate, and second that the viewshed is a Boolean phenomenon. The inaccuracy of the OEM data is acknowledged in reporting of the root-mean-squared error. The mistake of the Boolean viewshed is recognizable in the real-wor...

Fuzzy inference systems (FIS) enable automated assessment and reasoning in a logically consistent manner akin to the way in which humans reason. However, since no conventional fuzzy set theory is in the Boolean frame, it is proposed that Boolean consistent fuzzy logic should be used in the evaluation of rules. The main distinction of this approach is that it requires the execution of a set of s...

The aim of this thesis is to develop the fuzzy relational calculus. To develop this calculus, we study four algebraic formalisations of fuzzy relations which are called fuzzy relation algebras, Zadeh categories, relation algebras and Dedekind categories, and we strive to arrive at their representation theorems. The calculus of relations has been investigated since the middle of the nineteenth c...

Recent research on fuzzy quantification for information retrieval has proposed the application of semi-fuzzy quantifiers for improving query languages. Fuzzy quantified sentences are useful as they allow additional restrictions to be imposed on the retrieval process unlike more popular retrieval approaches, which lack the facility to accurately express information needs. For instance, fuzzy qua...

In recent years, geometric-mean averaging operators (GMA operators) have been proposed to overcome the drawbacks of the existing T-operators and averaging operators for handling the Boolean “AND” and “OR” operations in fuzzy information retrieval. However, the GMA operators can not deal with queries represented by generalized fuzzy numbers. In this paper, we present generalized fuzzy number geo...

This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Lukasiewicz n-valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the n-valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the al...

Multi-criteria evaluation (MCE) is perhaps the most fundamental of decision support operations in geographical information systems (GIS). This paper reviews two main MCE approaches employed in GIS, namely Boolean and Weighted Linear Combination (WLC), and discusses issues and problems associated with both. To resolve the conceptual di€ erences between the two approaches, this paper proposes the...