Zadeh's Centenary

This is the introductory paper in a special issue on fuzzy logic dedicated to the centenary of the birth of Lotfi A. Zadeh published by International Journal of Computers Communications & Control (IJCCC). In 1965, Lotfi A. Zadeh published in the journal „Information and Control” the article titled „Fuzzy sets”, which today reaches over 117 thousand citations. The total sum of citations for all his papers is above 253 thousand. Based on the notion of fuzzy sets, fuzzy logic and the concept of soft computing emerged, bringing extremely important implications to the field of Artificial Intelligence (AI). In 2017, I published, whith F.G. Filip and M.J. Manolescu, a 42-page long paper in the IJCCC about the life and masterwork of Lotfi A. Zadeh, from which I will use some information in this material [15]

Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology

Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted. The concept of L-fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov’s intuitionistic fuzzy set. In addition, the class of L-fuzzy sets forms a complete lattice whenever the underlying set L constitutes a complete lattice. Based on these observations, we develop a general approach towards L-fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of L-fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction techniques in terms of interval-valued fuzzy image processing

Simulasi Analisis Kualitas Daya Menggunakan Logika Fuzzy Untuk Meningkatkan Efisiensi Sistem Tenaga Listrik

This study aims to simulate power quality analysis using fuzzy logic to increase the efficiency of the power system. Poor power quality can cause disturbances in the electric power system and reduce the efficiency of the energy used. Therefore, improving power quality is one of the main focuses in the electric power industry.The fuzzy logic method is used in this study to evaluate power quality based on relevant parameters, such as voltage, current, frequency and harmonics. Fuzzy logic is able to overcome the uncertainty and complexity of data related to electric power systems, and provide more adaptive and intelligent solutions. In this study, simulations were carried out using special software that implements fuzzy logic to analyze power quality. The input data obtained from the electric power system is used to build a fuzzy logic model. Then, the simulation results are used to identify existing power quality problems and propose appropriate improvement strategies.The simulation results show that the use of fuzzy logic can significantly increase the efficiency of the power system by minimizing disturbances and optimizing power quality. In addition, fuzzy logic also provides the ability to predict the future conditions of the electric power system and take the necessary precautions. This research has important practical implications in the field of power systems. By using fuzzy logic in power quality analysis, power companies and grid operators can optimize power system operations, reduce power losses, improve energy efficiency, and ensure reliable electricity supply to consumers

Multiconditional Approximate Reasoning with Continuous Piecewise Linear Membership Functions

It is shown that, for some intersection and implication functions, an exact and efficient algorithm exists for the computation of inference results in multiconditional approximate reasoning on domains which are finite intervals of the real numbers, when membership functions are restricted to functions which are continuous and piecewise linear. An implementation of the algorithm is given in the functional programming language Miranda

Implication functions in interval-valued fuzzy set theory

Interval-valued fuzzy set theory is an extension of fuzzy set theory in which the real, but unknown, membership degree is approximated by a closed interval of possible membership degrees. Since implications on the unit interval play an important role in fuzzy set theory, several authors have extended this notion to interval-valued fuzzy set theory. This chapter gives an overview of the results pertaining to implications in interval-valued fuzzy set theory. In particular, we describe several possibilities to represent such implications using implications on the unit interval, we give a characterization of the implications in interval-valued fuzzy set theory which satisfy the Smets-Magrez axioms, we discuss the solutions of a particular distributivity equation involving strict t-norms, we extend monoidal logic to the interval-valued fuzzy case and we give a soundness and completeness theorem which is similar to the one existing for monoidal logic, and finally we discuss some other constructions of implications in interval-valued fuzzy set theory

Homomorphisms on the Monoid of Fuzzy Implications (II, *) - A Complete Characterization

In [4], we had proposed a novel generating methods of fuzzy implications and investigated algebraic structures on the set of all fuzzy implications, which is denoted by II. Again in [5], we had defined a particular function gK on the monoid (II, *) (See Def. 16) and characterised the function K for which gK is a semigroup homomorphism (s.g.h) in two special cases, i.e., K is with trivial range and K (1, y ) = y for all y ∈ [0, 1](neutrality property). In this work we characterise the nontrivial range non neutral implications K such that gK is an s.g.h. and also present their representation

Fuzzy Galois connections on fuzzy sets

In fairly elementary terms this paper presents how the theory of preordered fuzzy sets, more precisely quantale-valued preorders on quantale-valued fuzzy sets, is established under the guidance of enriched category theory. Motivated by several key results from the theory of quantaloid-enriched categories, this paper develops all needed ingredients purely in order-theoretic languages for the readership of fuzzy set theorists, with particular attention paid to fuzzy Galois connections between preordered fuzzy sets.Comment: 30 pages, final versio