Fuzzy subgroups and T -vague groups are interesting fuzzy algebraic structures that have been widely studied. While fuzzy subgroups fuzzify the concept of crisp subgroup, T -vague groups can be identified with quotient groups of a group by a normal fuzzy subgroup and there is a close relation between both structures and T -indistinguishability operators (fuzzy equivalence relations). In this pa...

Choquet integral with respect to fuzzy measure is a generalization of weighted arithmetic mean aggregation operator. It allows taking into account the phenomenon of dependence between criteria. Due to this it is possible to reflect the expert knowledge more accurately without making the model simplification which is the assumption of independence of the aggregation criteria. The problems of Cho...

The paper presents a number of unclear, unsolved or partly solved problems of fuzzy logic, which hinder precise transformation of expert knowledge about proper control of a plant in a fuzzy controller. These vague problems comprise the realization of logical and arithmetic operations and another basic problem, i.e., the construction of membership functions. The paper also indicates how some of ...

Interval arithmetic as part of interval mathematics and Granular Computing is unusually important for development of science and engineering in connection with necessity of taking into account uncertainty and approximativeness of data occurring in almost all calculations. Interval arithmetic also conditions development of Artificial Intelligence and especially of automatic thinking, Computing w...

Multiplicative operations for fuzzy numbers raise several problems both from the theoretical and practical point of view in fuzzy arithmetic. The multiplication based on Zadeh's extension principle and its triangular and trapezoidal approximation is used in several recent works in applications in geology. Recently, new product-type operation are introduced and studied, as e.g. the cross product...

This paper extends the author’s earlier work on the Law of Large Numbers for fuzzy numbers [2] to the case where the fuzzy numbers are of type L-R. Namely, we shall define a class of Archimedean triangular norms in which the equality lim n→∞ Nes(mn − ≤ ηn ≤ mn + = 1, for any > 0, holds for all sequences of fuzzy numbers, ξi = (Mi, α, β)LR, i ∈ N, with twice differentiable and concave shape func...

The Nikon Coolpix885® conventional digital camera is utilized to reform three-dimensional (3-D) turbulent pattern on lake that is situated in University Technology Malaysia (UTM). The main objective of this study is to use fuzzy arithmetic to reduce the errors arising from noise in digital camera data when constructing turbulent pattern flow. In doing so, the fuzzy B-spline algorithm, which ass...

The COCOMO Model is well known as the currently predominate model for software cost estimation. It allows one to work from linguistic variables to estimate software project effort and schedule. This basis in linguistic variables encourages research of the COCOMO Model as a fuzzy system. As is known in fuzzy circles and is shown here, fuzzy arithmetic based on the popular fuzzy extension princip...

This thesis develops the idea of probabilistic arithmetic. The aim is to replace arithmetic operations on numbers with arithmetic operations on random variables. Specifically, we are interested in numerical methods of calculating convolutions of probability distributions. The long-term goal is to be able to handle random prob­ lems (such as the determination of the distribution of the roots of ...

Chiclana et al. [Chiclana, F., Herrera-Viedma, E., Herrera, F., Alonso, S. (2007). European Journal of Operational Research 182, 383–399] provided some IOWA operators for aggregating the individual fuzzy preference elations. The aim of this work is further to study their desired properties under group decision making problem with fuzzy preference relations. First, it is proved that the collecti...