High speed flexible fuzzy hardware for fuzzy information processing

Supplement to “An interpretation of membership functions and the properties of general probabilistic operators as fuzzy set operators m Part I”

Emerging trends in soft set theory and related topics.

Limitations on the representation of knowledge, and hence the inference methods, naturally limit the domains of the first-generation expert systems. In response to these limitations, fuzzy expert systems or the second-generation of expert systems provide two essential and unique advantages in the design, development, and implementation of expert systems: (1) fuzzy knowledge representation and (2) fuzzy inference methods. It is suggested that second-generation expert systems be designed and implemented with the expressive powers of representation and improved inference methods based on fuzzy logic. A number of research topics and application areas are identified. >

In this chapter, basic definitions, notations, and terminologies of interval analysis and fuzzy set theory have been incorporated. This chapter starts with interval and some of its terminologies. Then, the interval set operations and their arithmetic with algebraic properties with various examples are introduced. Furthermore, fuzzy set with its terminologies, fuzzy set operations, fuzzy arithmetic, and different types of fuzzy numbers are discussed.

In this article, after explaining Zadeh's computing with words (CWW) paradigm, I argue that for this paradigm to be embraced, it must be validated using a Turinglike test, use a scientifically correct fuzzy set model for words, namely interval type-2 fuzzy sets (IT2 FSs), and be simple, meaning that fuzzy set operations should be as simple as possible. These conclusions are drawn using the ideas of Turing, Popper and Occam. Short descriptions are provided for a Perceptual Computer (Per-C), which is an architecture for CWW for making subjective judgments, IT2 FSs, IT2 FS models for words, and why an IT2 FS model captures first-order uncertainties about a word. Short biographies of Zadeh, Turing, Popper and Occam are also provided.

This paper presents the design of a High Speed Multistage Fuzzy Hardware (HSMFH) architecture for fuzzy logic control. In multistage fuzzy rules, there are input, intermediate, and output variables. The intermediate variable is found in the then-part of the current inference stage and in the if-part of the next stage. Traditionally, the then-part evaluation takes more inferring time. Our approach to resolve the problem is to pre-compute the fuzzy set operations of the intermediate variables without information loss. In addition, to accelerate the inference speed, only the active fuzzy set operations are inferred in If-module and Then-module by using the access control (like DMA). By using the simulation example with 294 fuzzy rules (245 rules in the first stage and 49 rules in the second stage,) the HSMFH takes 128 clocks with the pre-computation technique for an inference cycle. In other words, in one clock, the HSMFH can infer 2.30 fuzzy rules with the precomputation technique.

A satisfaction-driven game theoretic approach is developed with application to team-based concurrent product and process design (CPPD). This team approach for CPPD is based upon optimization formalism in which the design team is responsible to optimize overall product functionality (or performance) and the manufacture team pursues to minimize total manufacturing cost. This dual-team model characterizes the respective aspects of product design and process design. In particular, the preference of each team against a design configuration is characterized through the application of fuzzy set theory, whereby the method of Design for Satisfaction (DfS) can be applied to seek the most favorite design that best fulfills the team goal. Based on the strategic team paradigms derived from game theory, fuzzy set operators are used to aggregate satisfaction metrics of two teams. As a result, three team design models plus related algorithms are developed to reveal typical team interactions in the context of design computations. An illustrative example is worked out to demonstrate the satisfaction-driven team design models.

A fuzzy rough set is a pair of fuzzy sets resulting from the approximation of a fuzzy/crist set in a fuzzy approximation space. A fuzzy rough set algebra is a fuzzy set algebra with added dual pair of fuzzy rough approximation operators. In this paper, we study the mathematical structures of fuzzy rough set algebras in infinite universes of discourse. We first define the concept of fuzzy rough set algebras by the axiomatic approach. We then examine the properties of fuzzy rough approximation operators in different types of fuzzy rough set algebras. We also prove that if a system \(({\cal F}(U), \cap, \cup, \sim, L, H)\) is a (respectively, a serial, a reflexive, a symmetric, a transitive, a topological, a similarity) fuzzy rough set algebra then the derived system \(({\cal F}(U), \cap, \cup, \sim, LL, HH)\) is also a (respectively, a serial, a reflexive, a symmetric, a transitive, a topological, a similarity) fuzzy rough set algebra.KeywordsApproximation operatorsFuzzy rough setsFuzzy setsFuzzy rough set algebrasRough sets

The main purpose of this work is to construct a basic concept of fuzzy topology. In this article, we will try to give definition of fuzzy topology, fuzzy open set, fuzzy closed set, fuzzy interior of a fuzzy set, fuzzy closure of a fuzzy set in fuzzy topology and also, we will try to prove some theorems on fuzzy interior and fuzzy closure of a fuzzy topology with the help of extended definition of fuzzy sets and complement of a fuzzy sets.

Irrepressible growth of complex interconnectedness of information systems besides its obvious benefits unfortunately brought up the questions of their vulnerability. Practically universal access to computers has enabled hackers and would-be terrorists to attack information systems and critical infrastructures worldwide. A fuzzy preference relation, based on a fuzzy satisfaction function is applied to a comparison of attack signatures. Fuzzy signatures (their gamma resolution sets) are combined by fuzzy operators. Therefore, a qualitative, fuzzy decision system is achieved. The proposed method provided smoother results that obtained by traditional methods. Experiments demonstrated that the final outcome depended on correct determination of fuzzy values out of signature attacks, also on adequate choice of fuzzy set operator.

Abstract: Landslides cause extensive loss of life and property in the Nepal Himalaya. Since the late 1980s, different mathematical models have been developed and applied for landslide susceptibility mapping and hazard assessment in Nepal. The main goal of this paper is to apply fuzzy logic to landslide susceptibility mapping in the Ghurmi-Dhad Khola area, Eastern Nepal. Seven causative factors are considered: slope angle, slope aspect, distance from drainage, land use, geology, distance from faults and folds, soil and rock type. Likelihood ratios are obtained for each class of causative factors by comparison with past landslide occurrences. The ratios are normalized between zero and one to obtain fuzzy membership values. Further, different fuzzy operators are applied to generate landslide susceptibility maps. Comparison with the landslide inventory map reveals that the fuzzy gamma operator with a γ-value of 0.60 yields the best prediction accuracy. Consequently, this operator is used to produce the final landslide susceptibility zonation map.

The objective of the work is to present some series of the aggregation operators for the picture fuzzy sets (PFSs). As PFSs have been an extended version of the intuitionistic fuzzy set theory which not only considers the degree of acceptance or rejection but also taken into the account the degree of refusal during the analysis. Thus, by considering all these degrees, some aggregation operators, namely picture fuzzy weighted average, picture fuzzy ordered weighted average, and picture fuzzy hybrid average aggregation operators, have been proposed along with their desirable properties. A decision-making approach based on these operators has also been presented. Finally, an illustrative example has been given for demonstrating the approach.

In this paper we will present two theorems for the\njoin and meet operations for general type-2 fuzzy sets with\narbitrary secondary memberships, which can be non-convex\nand/or non-normal type-1 fuzzy sets. These results will be used\nto derive the join and meet operations of the more general\ndescriptions of interval type-2 fuzzy sets presented in [1], where\nthe secondary grades can be non-convex. Hence, this work will\nhelp to explore the potential of type-2 fuzzy logic systems which\nuse the general forms of interval type-2 fuzzy sets which are\nnot equivalent to interval valued fuzzy sets. Several examples\nfor both general type-2 and the more general forms of interval\ntype-2 fuzzy sets are presented.

The paper presents a novel, transistor level, implementation of selected fuzzy set operators suitable for fuzzy control systems realized in low-power hardware. We propose a fully digital, asynchronous realization of basic fuzzy logic (FL) functions, such as the bounded sum, bounded difference, bounded product, bounded complement, fuzzy logic union (MAX) and fuzzy logic intersection (MIN). All of the proposed operators has been implemented in the CMOS TSMC 180nm Technology and verified by means of transistor level simulations in Hspice environment. The proposed structures of the FL functions can easily be scaled to any signal resolutions.

This paper presents the way of implementation of fuzzy set operators at the transistor level. We propose a novel realization of basic fuzzy logic (FL) functions, such as bounded sum, bounded difference, bounded product, bounded complement, fuzzy logic union (MAX) and fuzzy logic intersection (MIN). The proposed structures of the operators may be easily connected in chains, creating larger FL systems.