Fuzzy quantifiers

All of these linguistic terms except fuzzy modifiers are represented in each context by appropriate fuzzy sets. Fuzzy predicates are represented by fuzzy sets defined on universal sets of elements to which the predicates apply. Fuzzy truth values and fuzzy probabilities are represented by fuzzy sets defined on the unit interval [0,1]. Fuzzy quantifiers are either absolute or relative they are represented by appropriate fuzzy numbers defined either on the set of natural numbers or on the interval [0,1]. Fuzzy modifiers are operations by which fuzzy sets representing the various other linguistic terms are appropriately modified to capture the meaning of the modified linguistic terms. 

In a crude way, it is useful to distinguish the following four types of fuzzy propositions, each of which may, in addition, be quantified by an appropriate fuzzy quantifier. 

Reasoning based on fuzzy propositions of the four types, possibly quantified by various fuzzy quantifiers, is usually referred to as approximate reasoning. Although approximate reasoning is currently a subject of intensive research, its basic principles are already well established. For example, the most common inference rules of classical logic, such as modus ponens,... 

In general, fuzzy quantifiers are fuzzy numbers that take part in fuzzy propositions. They are of two kinds. Fuzzy quantifiers of the first kind are defined onR and characterize linguistic terms such as about 10, much more than 100, and at least about 5. Fuzzy quantifiers of the second kind are defined on [0,1] and characterize linguistic terms such as almost all, about half, and most. 

Malczewski J. Ordered weighted averaging with fuzzy quantifiers GIS-based multicriteria evaluation for land-use suitability analysis. International Journal of Applied Earth Observation and Geoinformation 8, 270-277, 2006... 

Zadeh, L. A., "A computational approach to fuzzy quantifiers in natural languages," Computers and Mathematics with Applications, 9, pp. 149-184,1983. 

The fourth section concerns the question of quantification of shape complementarity. Fuzzy measures, which can be used to quantify the fitting of molecular surface patches, are employed. Some conclusions are drawn in the final section. 

Fuzzy logic systems grew out of a desire to quantify rule-based expert systems. Fuzzy set theory had provided us with an effective framework for dealing with fuzzy information and for translating control strategies based on an expert knowledge into an automatic control strategy. 

This new method for quantifying chip breakabiiity was derived based on the fundamentals of fuzzy reasoning. It is assumed that the following three factors and the associated... 

Braglia, M. Bevilacqua, M. 2000. Fuzzy modelling and analytical hierarchy processing as a means of quantifying risk levels associated with failure modes in production systems. Technology, Law and Insurance 5 125-134... 

An important question of the LOWA operator is the determination of W. A possible solution consists of representing the concept ot fuzzy majority by means of the weights of W, using a nondecreasing proportional/wzzi/ linguistic quantifier [69] Q in its computation ... 

Some examples of a nondecreasing proportional fuzzy linguistic quantifier are "most" (0.3,0.8), "at least half" (0, 0.5) and "as many as possible" (0.5,1). When a fuzzy linguistic quantifier Q is used to compute the weights of LOWA operator (b, it is symbolized by Og. 

In the methodology developed by Watano et al. (50,51), four fuzzy variables were used, namely ZR (zero), PS (positive small), PM (positive medium) and PL (positive large). The values of D t), AD t) and V(t) were all classified into these four categories. Ten rules were proposed to relate measured D(t) and AD(t) with V((). Consequently, V(t) can be quantified using the if-then statement. An example is given as follows ... 

The latter case assumes the standard intersection of two fuzzy sets. Relative quantifiers are defined on [0, 1] (almost all, about half, most) and may be used in propositions of the form ... 

---