Interval Fuzzy Logic Research Articles

A Novel Approach to Type-Reduction and Design of Interval Type-2 Fuzzy Logic Systems

Abstract Fuzzy logic systems, unlike black-box models, are known as transparent artificial intelligence systems that have explainable rules of reasoning. Type 2 fuzzy systems extend the field of application to tasks that require the introduction of uncertainty in the rules, e.g. for handling corrupted data. Most practical implementations use interval type-2 sets and process interval membership grades. The key role in the design of type-2 interval fuzzy logic systems is played by the type-2 inference defuzzification method. In type-2 systems this generally takes place in two steps: type-reduction first, then standard defuzzification. The only precise type-reduction method is the iterative method known as Karnik-Mendel (KM) algorithm with its enhancement modifications. The known non-iterative methods deliver only an approximation of the boundaries of a type-reduced set and, in special cases, they diminish the profits that result from the use of type-2 fuzzy logic systems. In this paper, we propose a novel type-reduction method based on a smooth approximation of maximum/minimum, and we call this method a smooth type-reduction. Replacing the iterative KM algorithm by the smooth type-reduction, we obtain a structure of an adaptive interval type-2 fuzzy logic which is non-iterative and as close to an approximation of the KM algorithm as we like.

Application of Interval Fuzzy Logic in Selecting a Sustainable Supplier on the Example of Agricultural Production

The selection of sustainable suppliers (SSS) is the first step in applying a sustainable supply chain and sustainable production. Therefore, it is necessary to select the supplier that best meets the set sustainability criteria. However, the selection of suppliers cannot be done by applying symmetric information, because the company does not have complete information, so asymmetric information should be used when selecting suppliers. Since the SSS applies three main sustainability criteria, environmental, social, and economic criteria, this decision-making problem is solved by applying multi-criteria decision-making (MCDM). In order to solve the SSS for the needs of agricultural production, interval fuzzy logic was applied in this research, and six suppliers with whom agricultural pharmacies in Semberija work were taken into consideration. The application of interval fuzzy logic was performed using the methods PIPRECIA (Pivot pairwise relative criteria importance assessment) and MABAC (Multi-Attributive Border Approximation Area Comparison). Using the PIPRECIA method, the weights of criteria and sub-criteria were determined. Results of this method showed that the most significant are economic criteria, followed by the social criteria. The ecological criteria are the least important. The supplier ranking was performed using the MABAC method. The results showed that supplier A4 best meets the sustainability criteria, while supplier A6 is the worst. These results were confirmed using other MCDM methods, followed by the sensitivity analysis. According to the attained results, agricultural producers from Semberija should buy the most products from suppliers A4, in order to better apply sustainability in production. This paper showed how to decision make when there is asymmetric information about suppliers.

Methods of Using Fuzzy Interval Logic During Processing of Space States of Complex Biophysical Objects

Methods of Using Fuzzy Interval Logic During Processing of Space States of Complex Biophysical Objects

Performansi Navigasi Robot Leader-Follower menggunakan Algoritma Logika Fuzzy Interval Tipe 2

A leader-follower robot is used to perform different tasks without continuous human assistance. The movement of robot leader-follower to environment who do not structure, avoid persecution and achieving goals is very difficult. Related to the problem, the robot leader-follower requires navigating robots independently using Interval Fuzzy Logic Type-2 (IFLT) 2 Algorithm. The IFLT 2 algorithm performance is successfully applied to this leader-follower robot, with 8 base rules less than the Fuzzy Logic Type 1 Algorithm. This simulation, the robot successfully moves to avoid obstacles and go hand in hand with the position of the follower robot always following the position of the robot leader.

On BL-Algebras and its Interval Counterpart

Interval Fuzzy Logic and Interval-valued Fuzzy Sets have been widely investigated. Some Fuzzy Logics were algebraically modelled by Peter Hájek as BL-algebras. What is the algebraic counterpart for the interval setting? It is known from literature that there is a incompatibility between some algebraic structures and its interval counterpart. This paper shows that such incompatibility is also present in the level of BL-algebras. Here we show both: (1) the impossiblity of match imprecision and the correctness of the underlying BLimplication and (2) some facts about the intervalization of BL-algebras.

A New Way of Applying Interval Fuzzy Logic in Group Decision Making For Supplier Selection

A New Way of Applying Interval Fuzzy Logic in Group Decision Making For Supplier Selection

Robust adaptive mixed H2/H∞ interval type-2 fuzzy control of nonlinear uncertain systems with minimal control effort

A realistic control paradigm should concurrently account for different sources of uncertainty such as those in modeling parameters, external disturbances and noise, as well as operational cost. Yet, this is a daunting task for which many current control approaches lack in one aspect or the other. In particular, the consumed control energy is an important aspect of controller design that is often ignored. In this paper, we propose a stable robust adaptive interval type-2 fuzzy H2/H∞ controller (RAIT2FH2H∞C) for a class of uncertain nonlinear systems that aims to address the above concerns through its hybrid robust/adaptive structure. In particular, the H2 energy and tracking cost function is minimized with respect to a H∞ disturbance attenuation constraint, while the adaptive interval fuzzy logic system (IT2FLS) handles the uncertainties in approximating the unknown nonlinear dynamics of the system. In principle, the interval fuzzy logic approach aims to manage portions of uncertainty that could not be precisiated, leading to improved error performance. Several simulation studies, with or without disturbance and noisy measurements, as well as actual experimental implementation on a 3-PSP (prismatic-spherical-prismatic) parallel robot confirm this assessment. More specifically, in comparison with a competing methodology as well as its type-1 counterpart, the proposed interval type-2 strategy expends better or comparative control effort while reaching considerably better tracking performance.

An interval-valued fuzzy controller for complex dynamical systems with application to a 3-PSP parallel robot

In this paper, we present a novel interval-valued fuzzy model-based controller for handling the effects of uncertainty in controlling a complex dynamical system. Theoretically, model-based controllers may be the ideal control mechanisms; however, they are highly sensitive to model uncertainties and lack robustness. These controllers are also computationally intensive, rendering them unusable for many real-world applications. In this work, we incorporate an interval fuzzy logic paradigm into a computed-torque controller for a 3-PSP parallel robot. This paradigm aims to handle the uncertainties in the robot model. The proposed approach benefits from algebraic operations on type-I fuzzy numbers to enhance its capability in dealing with uncertainty. The simulations prove the superiority of the proposed controller in the presence of uncertainty. Furthermore, comparisons with a competing type-I reduced controller as well as a PD controller show this superiority to be more pronounced especially when noise level is remarkably high. Moreover, the designed controller satisfies the computational complexity constraints for real-time implementation.

S-Implications on Complete Lattices and the Interval Constructor

The aim of this work is to present an approach of interval fuzzy logic based on complete lattices. In particular, we study the extensions of the notions of t-conorms, fuzzy negations and S-implication, from the unit interval to arbitrary complete lattices. Some general properties of S-implications on complete lattices are analyzed. We show that the interval extensions of t-conorms, fuzzy negations and S-implications on complete lattices preserve the optimality property, being the best interval representations of these fuzzy connectives.

Hand Gesture Recognition in an Interval Fuzzy Approach

This paper introduces an interval fuzzy rule-based method for the recognition of hand gestures acquired from a data glove, with an application to the recognition of hand gestures of the Brazilian Sign Language. To deal with the uncertainties in the data provided by the data glove, an approach based on interval fuzzy logic is used. The method uses the set of angles of finger joints for the classification of hand configurations, and classifications of segments of hand gestures for recognizing gestures. The segmentation of gestures is based on the concept of monotonic gesture segment. Each gesture is characterized by its list of monotonic segments. The set of all lists of segments of a given set of gestures determine a set of finite automata able to recognize such gestures.

Characterization of Interval Fuzzy Logic Systems of Connectives by Group Transformations

The global structure of various systems of logic connectives is investigated by looking at abstract group properties of the group of transformations of these. Such characterizations of fuzzy interval logics are examined in Sections 4–9. The paper starts by introducing readers to the Checklist Paradigm semantics of fuzzy interval logics (Sections 2 and 3). In the Appendix we present some basic notions of fuzzy logics, sets and many-valued logics in order to make the paper accessible to readers not familiar with fuzzy sets.

Fuzzy Logic: Misconceptions and Clarifications

Some commonly accepted statements concerning the basic fuzzy logic proposed by Lotfi Zadeh in 1965, have led to suggestions that fuzzy logic is not a logic in the same sense as classical bivalent logic. Those considered herein are: fuzzy logic generates results that contradict classical logic, fuzzy logic collapses to classical logic, there can be no proof theory for fuzzy logic, fuzzy logic is inconsistent, fuzzy logic produces results that no human can accept, fuzzy logic is not proof-theoretic complete, fuzzy logic is too complex for practical use, and, finally, fuzzy logic is not needed. It is either proved or argued herein that all of the these statements are false and are, hence, misconceptions. A fuzzy logic with truth values specified as subintervals of the real unit interval [0.0, 1.0] is introduced. Proofs of the correctness, consistency, and proof theoretic completeness of the truth interval fuzzy logic are either summarized or cited. It is concluded that fuzzy logics deserve the accolade of logic to the same degree that the term applies to classical logics.

A fuzzy logic with interval truth values

The Kenevan Truth Interval Fuzzy Logic, in which truth values of propositions are represented as subintervals of the real unit interval that contain the single truth value rather than the truth value itself, is described herein. Inference rules are presented and proven to be correct, consistent, and as strong as possible. The classical propositional logic is shown to be a special case of the truth interval fuzzy logic in which the truth intervals are restricted to [0.0,0.0] and [1.0,1.0]. If the logic is restricted to propositions and formulas whose truth intervals are contained in the interval [x 0,x 1], 0.5<x 0⩽x 1⩽1.0 , or its negated equivalent, the full logic is reduced to the Zadeh's dispositional logic. A truth interval refinement proof method is described along with proof methods based on a fuzzy analog of the classical concept of logical equivalence for the dispositional logic. The latter are proven to be complete and sound. The computational complexity of the truth interval refinement proof method is shown to be Θ(2 3∗N) ; that of the proof methods based on fuzzy logical consequence, Θ(2 4∗N) ; and all of the proof methods are shown to be decidable and fair. A predicate truth interval fuzzy logic is also introduced.

ファジィ・インターバル論理の提案

真, 偽の他に未知や矛盾の情報を表現するために, 無限多値論理としてのファジィ論理を拡張した「ファジィインターバル論理」を提案する.そこでは, いかなる命題も区間真理値[n, p]を取ることが許されており, そして, その区間真理値は言語真理値の特殊な場合として, また数値真理値の一般化として定義されている.ここで, n及びpは区間[0,1]の間の任意の値である.本論文では, あいまいさと真偽それぞれについて2つの半順序関係を導入して, 基本論理演算が定義されている.それによって構成されるファジィインターバル論理関数のいくつかの性質が明らかにされる.ファジィ論理で成立していたクリーネ律は, ここでは必ずしも成立しない.新しく証明される量子化定理を用いることで, 二つのファジィインターバル論理関数が等しいための必要十分条件は, 4つの区間真理値{[0,0] , [1,1] , [0,1] , [1,0]}についてのみそれらが互いに等しいこと, すなわちファジィインターバル論理は本質的に4値論理であることが証明される.