scholarly journals Formalization of Human Categorization Process Using Interpolative Boolean Algebra

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Vladimir Dobrić ◽  
Darko Kovačević ◽  
Bratislav Petrović ◽  
Dragan Radojević ◽  
Pavle Milošević
Keyword(s):  
Fuzzy Logic ◽  
Boolean Algebra ◽  
Order Relation ◽  
Prototype Theory ◽  
Fuzzy Relations ◽  
Basic Form ◽  
Cognitive Economy ◽  
Ancient Times ◽  
Human Categorization ◽  
Boolean Implication

Since the ancient times, it has been assumed that categorization has the basic form of classical sets. This implies that the categorization process rests on the Boolean laws. In the second half of the twentieth century, the classical theory has been challenged in cognitive science. According to the prototype theory, objects belong to categories with intensities, while humans categorize objects by comparing them to prototypes of relevant categories. Such categorization process is governed by the principles of perceived world structure and cognitive economy. Approaching the prototype theory by using truth-functional fuzzy logic has been harshly criticized due to not satisfying the complementation laws. In this paper, the prototype theory is approached by using structure-functional fuzzy logic, the interpolative Boolean algebra. The proposed formalism is within the Boolean frame. Categories are represented as fuzzy sets of objects, while comparisons between objects and prototypes are formalized by using Boolean consistent fuzzy relations. Such relations are directly constructed from a Boolean consistent fuzzy partial order relation, which is treated by Boolean implication. The introduced formalism secures the principles of categorization showing that Boolean laws are fundamental in the categorization process. For illustration purposes, the artificial cognitive system which mimics human categorization activity is proposed.

MEDUSA: A Fuzzy Expert System for Medical Diagnosis of Acute Abdominal Pain

1994 ◽  
Vol 33 (05) ◽  
pp. 522-529 ◽  
Author(s):  
M. Fathi-Torbaghan ◽  
D. Meyer
Keyword(s):  
Fuzzy Logic ◽  
Abdominal Pain ◽  
Expert System ◽  
Acute Abdominal Pain ◽  
Medical Knowledge ◽  
Clinical Problem ◽  
Fuzzy Relations ◽  
Diagnostic Decision ◽  
Special Cases ◽  
Hybrid Concept

Abstract:Even today, the diagnosis of acute abdominal pain represents a serious clinical problem. The medical knowledge in this field is characterized by uncertainty, imprecision and vagueness. This situation lends itself especially to be solved by the application of fuzzy logic. A fuzzy logic-based expert system for diagnostic decision support is presented (MEDUSA). The representation and application of uncertain and imprecise knowledge is realized by fuzzy sets and fuzzy relations. The hybrid concept of the system enables the integration of rulebased, heuristic and casebased reasoning on the basis of imprecise information. The central idea of the integration is to use casebased reasoning for the management of special cases, and rulebased reasoning for the representation of normal cases. The heuristic principle is ideally suited for making uncertain, hypothetical inferences on the basis of fuzzy data and fuzzy relations.

The relation of A to Prov ˹A˺ in the Lindenbaum sentence algebra

1973 ◽  
Vol 38 (2) ◽  
pp. 295-298 ◽  
Author(s):  
C. F. Kent
Keyword(s):  
Boolean Algebra ◽  
Normal Forms ◽  
Order Relation ◽  
Mathematical Induction ◽  
Axiomatic Theory ◽  
Recursive Functions ◽  
Primitive Recursive

Let U be a consistent axiomatic theory containing Robinson's Q [TMRUT, p. 51]. In order for the results below to be of interest, U must be powerful enough to carry out certain arguments involving versions of the “derivability conditions,” DC(i) to DC(iii) below, of [HBGM, p. 285], [F60, Theorem 4.7], or [L55]. Thus it must contain, at least, mathematical induction for formulas whose prenex normal forms contain at most existential quantifiers. For convenience, U is assumed also to contain symbols for primitive recursive functions and relations, and their defining equations. One of these is used to form the standard provability predicate, Prov ˹A˺, “there exists a number which is the Gödel number of a proof of A.” Upper corners denote numerals for Gödel numbers for the enclosed sentences, and parentheses are often omitted in their presence.This paper contains some results concerning the relation between the sentence A, and the sentence Prov ˹A˺ in the Lindenbaum Sentence Algebra (LSA) for U, the Boolean algebra induced by the pre-order relation A ≤ B ⇔ ⊦A → B. Half of the answer is provided by a theorem of Löb [L55], which states that ⊦Prov ˹A˺ → A ⇔ ⊦A. Hence, in the presence of DC(iii), below, it is never true that Prov ˹A˺ < A in the LSA. However, there is a large and interesting set of sentences, denoted here by Γ, for which A < Prov ⌜A⌝.

scholarly journals A study on orderings based on fuzzy quasi- order relations

2021 ◽  
Author(s):  
Zhonglin Chai
Keyword(s):  
Partial Order ◽  
Order Relation ◽  
Fuzzy Relation ◽  
Partial Order Relation ◽  
Fuzzy Relations ◽  
Fuzzy Graph ◽  
Feasible Method ◽  
Order Relations ◽  
Finite Set ◽  
Quasi Order

Abstract This paper further studies orderings based on fuzzy quasi-order relations using fuzzy graph. Firstly, a fuzzy relation on a finite set is represented equivalently by a fuzzy graph. Using the graph, some new results on fuzzy relations are derived. In ranking those alternatives, we usually obtain a quasi-order relation, which often has inconsistencies, so it cannot be used for orderings directly. We need to remake it into a reasonable partial order relation for orderings. This paper studies these inconsistencies, and divides them into two types: framework inconsistencies and degree inconsistencies. For the former, a reasonable and feasible method is presented to eliminate them. To eliminate the latter, the concept of complete partial order relation is presented, which is more suitable than partial order relation to rank the alternatives. A method to obtain a reasonable complete partial order relation for a quasi-order relation is given also. An example is given as well to illustrate these discussions. Lastly, the paper discusses the connection between quasi-order relations and preference relations for orderings and some other related problems.

scholarly journals Types of Complex Fuzzy Relations with Applications in Future Commission Market

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Madad Khan ◽  
Muhammad Zeeshan ◽  
Seok-Zun Song ◽  
Sohail Iqbal
Keyword(s):  
Fuzzy Sets ◽  
Equivalence Relation ◽  
Order Relation ◽  
Fuzzy Relations ◽  
Inverse Relation ◽  
Transitive Relation ◽  
Temporal Dependence ◽  
Symmetric Relation ◽  
Asymmetric Relation ◽  
Fuzzy Order

In this paper, we introduce types of relations on complex fuzzy sets such as the complex fuzzy (CF) inverse relation, complex fuzzy reflexive relation, complex fuzzy symmetric relation, complex fuzzy antisymmetric relation, complex fuzzy transitive relation, complex fuzzy irreflexive relation, complex fuzzy asymmetric relation, complex fuzzy equivalence relation, and complex fuzzy-order relation. We study some basic results and particular examples of these relations. Moreover, we discuss the applications of complex fuzzy relations in Future Commission Market (FCM). We show that the introduction of CF relations to applications of FCMs can give a significant method for describing the temporal dependence between parameters of a Future Commission Market.

scholarly journals The Construction of Type-2 Fuzzy Reasoning Relations for Type-2 Fuzzy Logic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Shan Zhao ◽  
Hongxing Li
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Reasoning ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Fuzzy Logic Systems ◽  
Fuzzy Relation Equations ◽  
Logic Systems ◽  
Special Case

Type-2 fuzzy reasoning relations are the type-2 fuzzy relations obtained from a group of type-2 fuzzy reasonings by using extended t-(co)norm, which are essential for implementing type-2 fuzzy logic systems. In this paper an algorithm is provided for constructing type-2 fuzzy reasoning relations of SISO type-2 fuzzy logic systems. First, we give some properties of extended t-(co)norm and simplify the expression of type-2 fuzzy reasoning relations in accordance with different input subdomains under certain conditions. And then different techniques are discussed to solve the simplified expressions on the input subdomains by using the related methods on solving fuzzy relation equations. Besides, it is pointed out that the computation amount level of the proposed algorithm is the same as that of polynomials and the possibility of applying the proposed algorithm in the construction of type-2 fuzzy reasoning relations is illustrated on several examples. Finally, the calculation of an arbitrary extended continuous t-norm can be obtained as the special case of the proposed algorithm.

scholarly journals APPLICATION OF HEDGE ALGEBRAS FOR CONTROLLING MECHANISMS OF RELATIVE MANIPULATION

2017 ◽  
Vol 55 (5) ◽  
pp. 572
Author(s):  
Phan Bui Khoi ◽  
Nguyen Van Toan
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Controller ◽  
Complex Structure ◽  
Algebraic Approach ◽  
Linguistic Variables ◽  
Fuzzy Relations ◽  
Dynamical Equations ◽  
Linguistic Hedges ◽  
Linguistic Labels ◽  
Computed Torque

This paper presents a method for controlling mechanism of relative manipulation (MRM robot), that based on an algebraic approach to linguistic hedges in fuzzy logic. The proposed model of MRM robot is introduced as two component mechanisms, collaborating to realize technological manipulations. MRM robot has complex structure [1, [2]; therefore, robot system's  mathematical equations describing dynamical behaviors are complicated and voluminous [3,[4, 5]. Furthermore, the components affect MRM robot's dynamics that are difficult to determine adequately and exactly. Applying the well-known methods (based on dynamical equations) such as PD/PID, computed torque algorithm...for robot control is difficult, especially with MRM robot. By dint of the human-like inference mechanism, designing controller thanks to fuzzy logic can overcome the mentioned drawbacks [6]. However, the linguistic variables in fuzzy logic are not represented by any physical values; and hence, the comparison between the linguistic variables is unable. Moreover, composition of fuzzy relations, defuzzification use approximation function which can trigger error in data process. Hedge Algebras(HA) gives favorable conditions to restrict fuzzy logic's drawbacks because the linguistic labels in Hedge Algebras are represented by semantic values; and, composition of fuzzy relations and defuzzification are processed by simple interpolation and mapping functions. The obtained results from HA controller are compared to the obtained results from two methods which are presented in [6] (fuzzy controller and computed torque controller). Keywords: mechanism of relative manipulation (MRM robot), hedge algebras.

Fuzzy logic models in a category of fuzzy relations

2008 ◽  
Vol 13 (6) ◽  
pp. 591-596 ◽  
Author(s):  
Jiří Močkoř
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Relations ◽  
Logic Models
Sign in / Sign up

Export Citation Format

Share Document