This paper indicates that most of fuzzy translating rules for a fuzzy conditional proposition “If x is A then y is B” with A and B being fuzzy concepts can lead to very reasonable…
Abstract
This paper indicates that most of fuzzy translating rules for a fuzzy conditional proposition “If x is A then y is B” with A and B being fuzzy concepts can lead to very reasonable consequences which fit our intuition with respect to several criteria such as modus ponens and modus tollens. Moreover, it is shown that a syllogism holds for most of the methods under the new compositions, though they do not always satisfy the syllogism under the max‐min composition.
M. MIZUMOTO and K. TANAKA
Based on the concept of fuzzy sets of type 2 (or fuzzy‐fuzzy sets) defined by L. A. Zadeh, fuzzy‐fuzzy automata ate newly formulated and some properties of these automata are…
Abstract
Based on the concept of fuzzy sets of type 2 (or fuzzy‐fuzzy sets) defined by L. A. Zadeh, fuzzy‐fuzzy automata ate newly formulated and some properties of these automata are investigated. It is shown that fuzzy‐fuzzy languages characterized by fuzzy‐fuzzy automata are closed under the operations of union, intersection, concatenation, and Kleene closure in the sense of fuzzy sets of type 2, but are not closed under complement. The power of fuzzy‐fuzzy automata as an acceptor is the same as that of ordinary fuzzy automata and finite automata, though fuzzy‐fuzzy automata include fuzzy automata and finite automata as special cases. Finally, fuzzy‐fuzzy grammars are illustrated and it is shown that fuzzy‐fuzzy grammars with context‐free rules can generate context‐sensitive languages.
Triangular norms have been around since the early 1940s and have been used in the context of statistical metric space. A number of examples of existing t‐norms are given which are…
Abstract
Triangular norms have been around since the early 1940s and have been used in the context of statistical metric space. A number of examples of existing t‐norms are given which are known to provide good models of fuzzy set‐theoretic intersections. Pictorial representations of t‐norms that have been made with the aid of a computer are presented and the relationship between t‐norms and parametrised t‐norms is discussed in this context. Several new examples of t‐norms are proposed using triangular functions.
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The problem of selecting the highest grade of membership of fuzzy subsets of type 2 and of choosing the most truthful of a group of fuzzy propositions involve making a choice…
Abstract
The problem of selecting the highest grade of membership of fuzzy subsets of type 2 and of choosing the most truthful of a group of fuzzy propositions involve making a choice among fuzzy subsets on the unit interval. A procedure is proposed for the selection of fuzzy subsets on the unit interval. This procedure involves selecting the subset closest to a linear membership function on the unit interval.
This paper is a continuation of our paper10,11 and formulates a fuzzy team decision problem of type 2. The concept of fuzzy sets of type 2 is introduced to formulate the team…
Abstract
This paper is a continuation of our paper10,11 and formulates a fuzzy team decision problem of type 2. The concept of fuzzy sets of type 2 is introduced to formulate the team decision processes which contain fuzzy‐fuzzy states, fuzzy‐fuzzy information functions, fuzzy‐fuzzy information signals, fuzzy‐fuzzy decision functions and fuzzy‐fuzzy actions. After some definitions of fuzzy‐fuzzy relations and fuzzy‐fuzzy mappings, a model of fuzzy team decision of type 2 is proposed.
ANTONIO DI NOLA, WITOLD PEDRYCZ and SALVATORE SESSA
A problem of handling fuzzy quantities in a process of knowledge acquisition and deriving an inference mechanism by means of fuzzy relation equations is studied in extensive way…
Abstract
A problem of handling fuzzy quantities in a process of knowledge acquisition and deriving an inference mechanism by means of fuzzy relation equations is studied in extensive way. It is clearly pointed out that both of them are closely related and correspond to various types of fuzzy relation equations that are considered. Their relevance to the form of knowledge collected is also indicated. A problem of dimension reduction of a knowledge base is considered as well. Two modes of the use of the knowledge base (goal‐, and data‐driven) are also studied.
Allan Discua Cruz, Leonardo Centeno Caffarena and Marcos Vega Solano
There is a growing interest in understanding the strategic behaviour of family firms producing international commodities such as coffee, particularly in contexts where decisions…
Abstract
Purpose
There is a growing interest in understanding the strategic behaviour of family firms producing international commodities such as coffee, particularly in contexts where decisions about what products to sell, where to commercialise them and how to promote them appear to be highly based on both business and family aspects. The purpose of this paper is to explore product differentiation strategies in family firms in the specialty coffee industry across Latin American countries. Whilst the socioeconomic relevance of coffee production in Central America is unequivocal, the approach and rationale of families that engage in specialty coffee production remain underexplored.
Design/methodology/approach
This study examines product differentiation in specialty coffee family farms across countries in Central America: Guatemala, Honduras and Nicaragua. The study relies on in-depth interviews, case studies and an interpretative approach to unpick the dynamics of product differentiation by families in business dedicated to producing specialty coffee.
Findings
The findings show that product differentiation in specialty coffee family farms is influenced by both business and family aspects and driven by entrepreneurial stewards. Coffee-farming families can engage in product differentiation through a shared vision, a combination of traditional and specialised knowledge, and through the continuous development of an exchange network. The findings reveal a connection between families in business balancing family and business interests, and the strategic intention to build up their assets entrepreneurially over time.
Originality/value
This study contributes to the literature on stewardship and strategic behaviour in family firms when families in business engage in differentiating their products in a highly competitive industry. More specifically, this study focuses on companies across countries where coffee is of crucial socioeconomic importance, and where the said companies are owned and managed by families. The study expands understanding of product differentiation in family-enterprise-first businesses and suggests that the family elements in differentiation can be explained through an entrepreneurial stewardship perspective.
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Yuriy Panteliyovych Kondratenko, Leonid Pavlovych Klymenko and Eyad Yasin Mustafa Al Zu'bi
The purpose of this paper is to propose a general method to simplify the structure of fuzzy controllers' rule base using integrated methodology for reducing the number of fuzzy…
Abstract
Purpose
The purpose of this paper is to propose a general method to simplify the structure of fuzzy controllers' rule base using integrated methodology for reducing the number of fuzzy rules based on modelling and simulation.
Design/methodology/approach
The paper considers the problem of developing effective methods and algorithms for optimization of fuzzy rules bases of Sugeno‐type fuzzy controllers that can be applied to control of dynamic objects, including objects with non‐stationary parameters. The proposed approach based on calculating the impact of each of the rule on the formation of control signals for different types of input signals provides optimization of a linguistic rules database by using exclusion mechanism for rules with negligible influence. The effectiveness of the proposed approach is investigated using a fuzzy PID controller for control of a non‐stationary object of second order.
Findings
In this paper, the authors argued that different aggregation models can be used for structural optimization of fuzzy controllers and not all the rules are actually required in the fuzzy controllers' rule base. Eliminating some of the rules does not necessarily lead to a significant change in the fuzzy controller's output. The proposed integrated approach based on combination of different kinds of reference input signals for fuzzy controllers modelling and simulation is able to provide guidelines to the users which rules are required and which can be eliminated. The results obtained from the case studies demonstrate that the proposed integrated approach is able to reduce the number of rules required and, at the same time, to have the desired values of quality control indices.
Research limitations/implications
In order to demonstrate the feasibility of the proposed approach, only control object of second order with PID fuzzy controller of Sugeno‐type is chosen. Future studies can advance this research by applying the proposed approach in different types of fuzzy systems.
Practical implications
The proposed integrated approach is able to simplify the structural optimization methodology and make it possible to be implemented in real processes of the fuzzy controllers' design.
Originality/value
The value of the current paper is on the proposal of an integrated approach for rule reduction to enhance the practical use of modelling and simulation in a design of fuzzy controllers.
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This paper seeks to identify and propose a standard approach for the selection and optimization of fuzzy sets used in fuzzy decision‐making systems.
Abstract
Purpose
This paper seeks to identify and propose a standard approach for the selection and optimization of fuzzy sets used in fuzzy decision‐making systems.
Design/methodology/approach
The design was based on two principles: selection and optimization. The selection methodology was based on the “Fuzzimetric Arcs” principle, which is an analogy of the trigonometric circle principle. This would allow an initial sinusoidal fuzzy set shape. Other shapes may also be selected using the described formula (trapezoidal, triangular, … , etc.). As the proposal methodology is based on the trigonometric circle, other trigonometric formulae can be applied. For example, linguistic hedges can be defined using standard trigonometric formulae. Regarding optimization, the initial fuzzy set selection was assumed to be of regular shape (sinusoidal, trapezoidal or triangular). An irregular shape may be required by some systems. Hence, a genetic algorithm was proposed as a methodology to optimize the performance of fuzzy systems by mutating different regular shapes.
Findings
A simplified business decision‐making application was described and the proposed selection methodology was explained in the form of an example. Currently, there is no standard for the selection of fuzzy sets as this is dependent on knowledge engineering and the type of application chosen. The proposed methodology offers an easy‐to‐use possible standard which all developers/researchers may adopt irrespective of their application field. Moreover, the proposed methodology may integrate well with object‐oriented technology.
Originality/value
The paper presents standardization of the fuzzy sets selection and optimization technique used in any type of management information systems. This will aid all developers and researchers to enhance their technical communication. It would also enhance the simplicity and effectiveness of optimizing the performance of such systems.
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ANTONIO DI NOLA, WITOLD PEDRYCZ and SALVATORE SESSA
In this paper we deal with fuzzy numbers that modelize uncertain quantities present in many fields of applications, such as man‐machine systems. Main attention is paid to inverse…
Abstract
In this paper we deal with fuzzy numbers that modelize uncertain quantities present in many fields of applications, such as man‐machine systems. Main attention is paid to inverse operations for fuzzy numbers which allow one to solve equations or systems of equations with fuzzy numbers. The relevance of the method proposed for the determination of parameters of fuzzy models is also stressed.