The Theory of Fuzzy Logic and its Application to Real Estate Valuation

Fuzzy logic is based on the central idea that in fuzzy sets each element in the set can assume a value from 0 to 1, not just 0 or 1, as in classic set theory. Thus, qualitative characteristics and numerically scaled measures can exhibit gradations in the extent to which they belong to the relevant sets for evaluation. This degree of membership of each element is a measure of the element’s "belonging" to the set, and thus of the precision with which it explains the phenomenon being evaluated. Fuzzy sets can be combined to produce meaningful conclusions, and inferences can be made, given a specified fuzzy input function. The article demonstrates the application of fuzzy logic to an income-producing property, with a resulting fuzzy set output.

The likelihood interpretation as the foundation of fuzzy set theory

In order to use fuzzy sets in real-world applications, an interpretation for the values of membership functions is needed. The history of fuzzy set theory shows that the interpretation in terms of statistical likelihood is very natural, although the connection between likelihood and probability can be misleading. In this paper, the likelihood interpretation of fuzzy sets is reviewed: it makes fuzzy data and fuzzy inferences perfectly compatible with standard statistical analyses, and sheds some light on the central role played by extension principle and α-cuts in fuzzy set theory. Furthermore, the likelihood interpretation justifies some of the combination rules of fuzzy set theory, including the product and minimum rules for the conjunction of fuzzy sets, as well as the probabilistic-sum and bounded-sum rules for the disjunction of fuzzy sets

The Theory of Fuzzy Logic and its application to Real Estate Valuation

Fuzzy logic is based on the central idea that in fuzzy sets each element in the set can assume a value from 0 to 1, not just 0 or 1, as in classic set theory. Thus, qualitative characteristics and numerically scaled measures can exhibit gradations in the extent to which they belong to the relevant sets for evaluation. This degree of membership of each element is a measure of the element’s "belonging" to the set, and thus of the precision with which it explains the phenomenon being evaluated. Fuzzy sets can be combined to produce meaningful conclusions, and inferences can be made, given a specified fuzzy input function. The article demonstrates the application of fuzzy logic to an income-producing property, with a resulting fuzzy set output

“Fuzzy time”, a Solution of Unexpected Hanging Paradox (a Fuzzy interpretation of Quantum Mechanics)

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and show why it is helpful to consider the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time

Fuzzy measures and integrals in MCDA

This chapter aims at a unified presentation of various methods of MCDA based onfuzzy measures (capacity) and fuzzy integrals, essentially the Choquet andSugeno integral. A first section sets the position of the problem ofmulticriteria decision making, and describes the various possible scales ofmeasurement (difference, ratio, and ordinal). Then a whole section is devotedto each case in detail: after introducing necessary concepts, the methodologyis described, and the problem of the practical identification of fuzzy measuresis given. The important concept of interaction between criteria, central inthis chapter, is explained in details. It is shown how it leads to k-additivefuzzy measures. The case of bipolar scales leads to thegeneral model based on bi-capacities, encompassing usual models based oncapacities. A general definition of interaction for bipolar scales isintroduced. The case of ordinal scales leads to the use of Sugeno integral, andits symmetrized version when one considers symmetric ordinal scales. Apractical methodology for the identification of fuzzy measures in this contextis given. Lastly, we give a short description of some practical applications.Choquet integral; fuzzy measure; interaction; bi-capacities

“Fuzzy time”, from paradox to paradox (Does it solve the contradiction between Quantum Mechanics & General Relativity?)

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and show why it is helpful to consider the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. These, provides a new interpretation of Quantum Mechanics.More exactly what we see here is "Particle-Fuzzy time" interpretation of quantum Mechanics, in contrast to some other interpretations of Quantum Mechanics like " Wave-Particle" interpretation. At the end, we propound a question about the possible solution of a paradox in Physics, the contradiction between General Relativity and Quantum Mechanics

Lattice Type Fuzzy Order and Closure Operators in Fuzzy Ordered Sets

Complete lattices and closure operators in ordered sets are considered from the point of view of fuzzy logic. A typical example of a fuzzy order is the graded subsethood of fuzzy sets. Graded subsethood makes the set of all fuzzy sets in a given universe into a completely lattice fuzzy ordered set (i.e. a complete lattice in fuzzy setting). Another example of a completely lattice fuzzy ordered set is the set of all so-called fuzzy concepts in a given fuzzy context; the respective fuzzy order is the graded subconcept/superconcept relation. Conversely, each completely lattice fuzzy ordered set is isomorphic to some fuzzy ordered set of fuzzy concepts of a given fuzzy context. These natural examples motivate us to investigate some general properties of complete lattice-type fuzzy order. Particularly, in this paper we focus mainly on closure operators in fuzzy ordered sets. Preliminaries The notion of a (partial) order plays a central role in mathematics and its applications. It goes back to 19-th century investigations in logi

The Theory of Fuzzy Logic and its application to Real Estate Valuation

Fuzzy logic is based on the central idea that in fuzzy sets each element in the set can assume a value from 0 to 1, not just 0 or 1, as in classic set theory. Thus, qualitative characteristics and numerically scaled measures can exhibit gradations in the extent to which they belong to the relevant sets for evaluation. This degree of membership of each element is a measure of the element’s "belonging" to the set, and thus of the precision with which it explains the phenomenon being evaluated. Fuzzy sets can be combined to produce meaningful conclusions, and inferences can be made, given a specified fuzzy input function. The article demonstrates the application of fuzzy logic to an income-producing property, with a resulting fuzzy set output