Implication functions in interval-valued fuzzy set theory

Interval-valued fuzzy set theory is an extension of fuzzy set theory in which the real, but unknown, membership degree is approximated by a closed interval of possible membership degrees. Since implications on the unit interval play an important role in fuzzy set theory, several authors have extended this notion to interval-valued fuzzy set theory. This chapter gives an overview of the results pertaining to implications in interval-valued fuzzy set theory. In particular, we describe several possibilities to represent such implications using implications on the unit interval, we give a characterization of the implications in interval-valued fuzzy set theory which satisfy the Smets-Magrez axioms, we discuss the solutions of a particular distributivity equation involving strict t-norms, we extend monoidal logic to the interval-valued fuzzy case and we give a soundness and completeness theorem which is similar to the one existing for monoidal logic, and finally we discuss some other constructions of implications in interval-valued fuzzy set theory

Assessment of Sustainable Development

The objective of this paper is to introduce fuzzy set theory and develop fuzzy mathematical models to assess sustainable development based on context-dependent economic, ecological, and societal sustainability indicators. Membership functions are at the core of fuzzy models, and define the degree to which indicators contribute to development. Although a decision-making process regarding sustainable development is subjective, fuzzy set theory links human expectations about development, expressed in linguistic propositions, to numerical data, expressed in measurements of sustainability indicators. In the future, practical implementation of such models will be based on elicitation of expert knowledge to construct a membership function. The fuzzy models developed in this paper provide a novel approach to support decisions regarding sustainable development.agriculture;assessment;fuzzy set theory;sustainable development

Short Term Load Forecasting New Year Celebration Holiday Using Interval Type-2 Fuzzy Inference System (Case Study: Java – Bali Electrical System)

Celebration of New Year In the Indonesian is constituted the one of the visit Indonesian’s tourism. This event course changes the load of electrical energy. The electrical energy providers that control and operation of electrical in Java and Bali (Java, Bali Electrical System) is required to be able to ensure continuity of load demand at this time, and forecast for the future. Short-term load forecasting very need to be supported by computational methods for simulation and validation. The one of computation’s methods is Interval Type – 2 Fuzzy Inference System (IT-2 FIS). Interval Type-2 Fuzzy Inference System (IT-2 FIS) as the development of methods of Interval Type-1 Fuzzy Inference System (IT-1 FIS), it is appropriate to be used in load forecasting because it has the advantages that very flexible on the change of the footprint of uncertainty (FOU), so it supports to establish an initial processing of the time series, computing, simulation and validation of system models. Forecasting methods used in this research are IT-2 FIS. The process for to know and analyzing the peak load a day is the specially day and 4 days before New year Celebration in the previous year continued analysis by using IT-2 FIS will be obtained at the peak load forecasting New Year Celebration in the coming year. This research shown the average of error value in 2012, 2013 and 2014 is 0,642%. This value is better than using the IT-1 FIS which has a value of error to 0.649%. This research concluded that IT-2 FIS can be used in Short Term Load Forecasting

Construction of aggregation operators with noble reinforcement

This paper examines disjunctive aggregation operators used in various recommender systems. A specific requirement in these systems is the property of noble reinforcement: allowing a collection of high-valued arguments to reinforce each other while avoiding reinforcement of low-valued arguments. We present a new construction of Lipschitz-continuous aggregation operators with noble reinforcement property and its refinements. <br /

How to control if even experts are not sure: Robust fuzzy control

In real life, the degrees of certainty that correspond to one of the same expert can differ drastically, and fuzzy control algorithms translate these different degrees of uncertainty into different control strategies. In such situations, it is reasonable to choose a fuzzy control methodology that is the least vulnerable to this kind of uncertainty. It is shown that this 'robustness' demand leads to min and max for &- and V-operations, to 1-x for negation, and to centroid as a defuzzification procedure