The notion of ∈-soft set and q-soft set based on a fuzzy set is introduced, and characterizations for an ∈-soft set and a q-soft set to be (idealistic) soft BCK/BCIalgebras are provided. Using the notion of (∈,∈∨ q)-fuzzy BCK/BCI subalgebras/ideals, characterizations for an ∈-soft set and a q-soft set to be (idealistic) soft BCK/BCI-algebras are established. AMS subject classifications: 06D72, ...

Two classes of fuzzy mappings, called pseudolinear and g-pseudolinear fuzzy mappings are introduced by relaxing the definitions of pseudo-convex and pseudo-invex fuzzy mappings. First, some characterizations of pseudolinear and g-pseudolinear fuzzy mappings are obtained. Then, characterizations of the solution sets of pseudolinear and g-pseudolinear fuzzy programs are derived.

Fuzzy logic is a mathematical approach towards the human way of thinking and learning. Based on if-then rules, we can design fuzzy controllers with the intuitive experience of human beings. However, it is not practical for a designer to find necessary number of rules and determine appropriate parameters by hand. Hence, we incorporate a reinforcement learning method with basic fuzzy rules so tha...

Q-learning is one of the most popular reinforcement learning methods that allows an agent to learn the relationship between interval-valued state and action spaces, through a direct interaction with the environment. Fuzzy Q-learning is an extension to this algorithm to enable it to evolve Fuzzy Inference Systems (FIS) which range on continuous state and action spaces. In a FIS, the interaction ...

We discuss the second quantization of scalar field theory on the q–deformed fuzzy sphere S2 q,N for q ∈ IR, using a path–integral approach. We find quantum field theories which are manifestly covariant under Uq(su(2)), have a smooth limit q → 1, and satisfy positivity and twisted bosonic symmetry properties. Using a Drinfeld twist, they are equivalent to ordinary but slightly “nonlocal” QFT’s o...

This paper addresses the problem of tuning the input and the output parameters of a fuzzy logic controller. The system learns autonomously without supervision or a priori training data. Two novel techniques are proposed. The first technique combines Q(λ)-learning with function approximation (fuzzy inference system) to tune the parameters of a fuzzy logic controller operating in continuous state...

In crisp production inventory problem, let q, a, b, d, R and r be the quantity produced per cycle, the holding cost, production cost, production quantity per day, the total demand quantity and the demand quantity per day, respectively. We consider three fuzzification methods. Firstly, we fuzzify q, a, b, d, R and r to triangular fuzzy numbers. Secondly, we fuzzify d and r to triangular fuzzy nu...

Maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets and presented an application of fuzzy soft sets in a decision making problem. The aim of this paper is to apply the concept of fuzzy soft sets to n-ary hypergroup theory. The concepts of (∈(γ), ∈(γ) ∨ q(δ))-fuzzy soft (invertible) n-ary subhypergroups over a commutative n-ary hypergroup are intro...

d Department of Mathematics and Statistics, University of Swat, Swat, Khyber Pakhtoonkhwa, Pakistan ABSTRACT The concept of interval-valued fuzzy set is one of the most important and useful generalisation of Zadeh's fuzzy sets which is successfully applied by engineers and scientists in the field of Robotics, Control Theory and Computer Engineering. In this paper, we introduce new and useful ge...