In this study, Fuzzy Cognitive Maps (FCMs), which are powerful tools for graphical representation of knowledge, are analyzed from an ambiguity and fuzziness perspective. In conventional FCMs the causal strengths are represented with singleton (crisp) fuzzy numbers, but recently, other researchers proposed different FCM structures where uniform (interval) or triangular fuzzy numbers are used in causal strength representation. Here, FCMs are analyzed by means of fuzziness and ambiguity measures that are proposed in literature to investigate the capability of models to represent uncertainties. In addition, two new measures, called the average ambiguity measure (AAM) and the average fuzziness measure (AFM), are proposed to indicate uncertainty representation of an FCM. A well-known FCM model of a public health system is used as a case study to show how the fuzzy weights determine the uncertainty representation of FCMs, and then the outcomes are discussed.
Scientists want to comprehend and control complex systems. Their success depends on the ability to face also the challenges of the corresponding computational complexity. A promising research line is artificial intelligence (AI). In AI, fuzzy logic plays a significant role because it is a suitable model of the human capability to compute with words, which is relevant when we make decisions in complex situations. The concept of fuzzy set pervades the natural information systems (NISs), such as living cells, the immune and the nervous systems. This paper describes the fuzziness of the NISs, in particular of the human nervous system. Moreover, it traces three pathways to process fuzzy logic by molecules and their assemblies. The fuzziness of the molecular world is useful for the development of the chemical artificial intelligence (CAI). CAI will help to face the challenges that regard both the natural and the computational complexity.
Fuzzy rule interpolation is one of the tools for reducing computational complexity of fuzzy systems, and can be used when there are gaps in the knowledge base. These gaps can be natural, due to cost, or due to rule base reduction. The fuzzy interpolation methods are all descendent techniques of Kóczy and Hirota's linear interpolation. In this paper we provide a retrospective on the development of these techniques, and then focus on an early technique of conservation of fuzziness which has advantages in interpolation in hierarchical fuzzy systems as only near flank information is meant to be used and this allows the interpolation between different levels in the fuzzy rule base hierarchy. We point out an error and rectify it using a triangular extension which restores the intuitive, philosophical and practical nature of the approach.
This paper proposes a parametric programming approach to address the notion of the time value of delays in the presence of mixed (random and fuzzy) uncertainties that result from unreliable systems. To consider different types of delay time values, the system states are appropriately and carefully identified and defined, and a cost-based fuzzy decision model that incorporates several unreliability factors is constructed. Then, the proposed model is transformed into a pair of nonlinear programs parameterized by the possibility level to identify the lower and upper bounds on the minimal total cost per unit time at and thus construct the membership function. To provide analytical expressions, a special case with analytical results is also presented. In contrast to existing studies, the results derived from the proposed solution procedure conserve the fuzziness of the input information, representing a significant difference from the crisp results obtained using approaches based on probability theory. The results indicate that the proposed approach can provide more precise information to managers and improve decision-making in practical system design.
We deal with multi-objective optimization problems in various fields and in some of them, the objectives are found to be conflicting in nature. We obtain multiple optimal or near-optimal solutions of the problem using a multi-objective evolutionary algorithm (MOEA). In this study, an approach is proposed for enhancing the use of MOEA to establish important input–output relationships of some manufacturing processes. In the proposed approach, after getting an initial set of Pareto-front data points through MOEA, the trade-off solutions are used to train a neuro-fuzzy system (NFS) utilizing an EOA. This trained NFS is then used to get a modified Pareto-front and the modified trade-off solutions are clustered using different clustering algorithms. These clustered solutions are then analyzed to establish the relationships among decision variables and objectives. These principles will surely enrich the knowledge of designers and inspire them to apply this approach for a broad range of practical problems. The data related to two different engineering problems are used to show the applicability of the proposed approach.
This paper presents a continuous review inventory model with backorders and lost sales with fuzzy demand and learning considerations. The imprecision in demand is characterized by triangular fuzzy numbers. The triangular fuzzy numbers, counts upon lead time, are used to construct fuzzy lead time demand. It is assumed that the imprecision captured by these fuzzy numbers reduce with time because of learning effect. This implies that the decision maker gathers information about the inventory system and builds up knowledge from the previous shipments. Learning process occurs in setting and estimating the fuzzy parameters to reduce errors and costs. Under these considerations, the proposed model offers a policy and a solution algorithm to calculate the number of orders and reorder level such that the total annual cost attains a minimum value. The results of the proposed model are compared with the continuous review inventory system with fuzzy demand with or without learning effect. It is shown that learning effect in fuzziness reduces the ambiguity associated with the decision making process. Finally, numerical examples are provided to illustrate the importance of using learning in fuzzy model. The convexity of the total cost function is also proved.
The core of soft computing consists of fuzzy sets and systems (FSS) computing with words (CW) and the computational theory of perceptions (CTP). In the introduction of this paper we give a brief presentation of that subject. The second section of the paper focuses on a general view on fuzziness in evolutionary biology. The view on evolutionary biology is a meta-scientific reflection: The theory of FSS complemented by CW and CTP builds a stack of methodologies to help bridge the gap between systems and phenomena in the real world and scientific theories. Lotfi A. Zadeh established the theory of FSS to bridging this gap in the 1960s when he compared living systems that are very complex and man-made systems e.g. in electrical engineering. We use Zadeh's stack of soft computing methodologies in this tradition to reflect the field of evolutionary biology in the view of the evolutionary biologist, historian and philosopher of biology Ernst Mayr who emphasized that most theories in biology are based not on laws but on concepts.
Uncertainty is a central part of many data analysis methodologies. Although quantifying the uncertainty has long been discussed, the research on it is still in progress. The level of fuzziness in fuzzy system modeling is a source of uncertainty which can be classified as a parameter uncertainty. Upper and lower values of the level of fuzziness for Fuzzy C-Mean (FCM) clustering methodology have been found as 2.6 and 1.4 respectively in our previous studies. In this paper, we concentrate on the usage of uncertainty associated with the level of fuzziness in determination of the number of clusters in FCM in any data. We propose MiniMax ε-stable cluster validity index based on the uncertainty associated with the level of fuzziness within the framework of Interval Valued Type 2 fuzziness. If the data have a clustered structure, the optimum number of clusters may be assumed to have minimum uncertainty under upper and lower levels of fuzziness. Our investigation shows that the half range of upper and lower levels of fuzziness would be enough to determine the optimum number of clusters.
Load profiling has become an important issue in power industry and has gain more attention from utility company worldwide due to deregulation and liberalization. A lot of work had been done to obtain a method to determine typical load profiles (TLPs) of electricity consumers. Load profiles represents consumers electricity consumption pattern and provide useful data to both consumer and electricity provider. This paper presents the TLPs determination through clustering technique by using Fuzzy C-Means (FCM) algorithm. Two of the most important parameters in FCM are fuzziness parameter, m and optimal number of cluster, c. This paper shows the determination of the suitable fuzziness parameter through observation of experimental result of the cluster validity indexes value. Cluster validity indexes were used to determine c. Three cluster validity indexes were discussed in this paper. They are Xie-Beni index, Non-fuzzy index and Davies-Bouldin index. Objectives of this paper are to obtain groups of TLPs by using FCM clustering and to determine the suitable value of the fuzziness parameter, m. The data used in this project are obtained from Tenaga Nasional Berhad (TNB).