Introducing rough sets in hesitant fuzzy set domain and using it for the various applications would open up new possibilities in rough set theory. For this purpose the notion of hesitant fuzzy relations is introduced. The foundation of equivalence hesitant fuzzy relation is laid. Definition of anti-reflexive kernel, symmetric kernel etc. is proposed and the formulae to evaluate them are derived...

This paper studies fuzzy filtering design for a class of nonlinear discrete-time uncertain stochastic systems. First, the Takagi and Sugeno fuzzy model is proposed to approximate a nonlinear discrete-time uncertain stochastic system. Next, based on the fuzzy model, the fuzzy estimation for nonlinear discrete-time uncertain stochastic systems is studied. Using a suboptimal approach, the fuzzy es...

The management of uncertainty and imprecision is becoming more and more important in knowledge-based systems. Fuzzy logic provides a systematic basis for representing and inferring with this kind of knowledge. This paper describes an approach for fuzzy inference based on an uncertainty forward propagation method and a change in the granularity of the elements involved. The proposed model is abl...

In this paper, the concept of fuzzy graph is extended to a complex fuzzy graph. Complex fuzzy graphs are encountered in complex fuzzy set theory. The novelty of the complex fuzzy set lies in the range of values its membership function may attain. In contrast to a traditional fuzzy membership function, this range is not limited to [0, 1], but extended to the unit circle in the complex plane. Thu...

Similarity of intuitionistic fuzzy sets is an important measure to indicate the similarity degree between intuitionistic fuzzy sets. Based on the information carried by transforming intuitionistic fuzzy sets into their lower, upper and middle fuzzy sets, we propose a new construction for similarity measures between intuitionistic fuzzy sets. The proposed construction method on similarity measur...

This paper discusses a variation of the Fuzzy ART algorithm referred to as the Fuzzy ART Variant. The Fuzzy ART Variant is a Fuzzy ART algorithm that uses a very large choice parameter value. Based on the geometrical interpretation of the weights in Fuzzy ART, useful properties of learning associated with the Fuzzy ART Variant are presented and proven. One of these properties establishes an upp...

Let S be an ordered semigroup. In this paper we first introduce the concepts of (∈,∈ ∨q)-fuzzy ideals, (∈,∈ ∨q)-fuzzy bi-ideals and (∈,∈ ∨q)-fuzzy generalized bi-ideals of an ordered semigroup S, and investigate their related properties. Furthermore, we also define the upper and lower parts of fuzzy subsets of an ordered semigroup S, and investigate the properties of (∈,∈ ∨q)-fuzzy ideals of S....

Evaluation of efficiency of each of the DMUs (Decision Making Units) in a company is a very important task. Thus, the studies of evaluation of efficiency are being actively carried out, based on production function. Until quite recently, the loglinear production function (the Cobb-Douglas function) has been used for evaluation purposes. The loglinear model evaluates the DMUs by measuring the av...

The upper limb is represented by a simplified link-segment model composed of three rigid segments with ten degrees of freedom. To define appropriate coordinate systems, the upper limb is instrumented by six markers. Using the motion data, the inverse dynamic problem is solved and force and moments generated in joints are found. Then using a new approach in this area, fuzzy logic, total force is...

A concise commentary on observing and modeling complexity within the framework of dynamical systems, information, and computation theories. Deterministic chaos, randomness, order, predictability, uncertainty, and complexity are contrasted. The descriptive abstraction of state is seen to be a natural extension of the symbolization necessary for language and of the number concept. Philosophical c...