Evolution of fuzzy logic: from intelligent systems and computation to human mind

Inspired by human’s remarkable capability to perform a wide variety of physical and mental tasks without any measurements and computations and dissatisfied with classical logic as a tool for modeling human reasoning in an imprecise environment, Lotfi A. Zadeh developed the theory and foundation of fuzzy logic with his 1965 paper “Fuzzy sets” (Zadeh in Inf Control 8:378–53, 1965) and extended his work with his 2005 paper “Toward a generalized theory of uncertainty (GTU)—an outline” (Zadeh in Inf Control, 2005). Fuzzy logic has at least two main sources over the past century. The first of these sources was initiated by Peirce in the form what he called a logic of vagueness in 1900s, and the second source is Lotfi’s A. Zadeh work, fuzzy sets and fuzzy Logic in the 1960s and 1970s.     

A hesitant fuzzy model of computational trust considering hesitancy,vagueness and uncertainty

The aim of this work is to introduce a trust model, which is highly consistent with the social nature of trust in computational domains. To this end, we propose a hesitant fuzzy multi-criteria decision making based computational trust model capable of taking into account the fundamental building blocks corresponding to the concept of trust. The proposed model is capable of considering the contextuality property of trust and the subjective priorities of the trustor regarding the chosen goal. This is due to viewing trust not as a single label or an integrated concept, but as a collection of trustworthiness facets that may form the trust decision in various contexts and toward different goals. The main benefit of the proposed model is the consideration of the hesitancy of recommenders and the trustor in the process of trust decision making which can create a more flexible mapping between the social and computational requirements of trust. This type of formulation also allows for taking into account the vagueness of the provided opinions. In addition to the vagueness of the provided opinions, the model is capable of considering the certainty of recommendations and its effect on the aggregation process of gathered opinions. In the proposed model, the taste of the recommenders and the similarity of opinions are also considered. This will allow the model to assign more weight to recommendations that have a similar taste compared to the trustor. Finally, taking into consideration the attitudes of the trustors toward change of personality that may occur for various entities in the environment is another advantage of the proposed model. A step-by-step illustrative example and the results of several experimental evaluations, which demonstrate the benefits of the proposed model, are also presented in this paper.     

On the absence of strict boundaries—Vagueness, haziness, and fuzziness in philosophy, science, and medicine

This contribution deals with developments in the history of philosophy, logic, and mathematics during the time before and up to the beginning of fuzzy logic. Even though the term “fuzzy” was introduced by Lotfi A. Zadeh in 1964/1965, it should be noted that older concepts of “vagueness” and “haziness” had previously been discussed in philosophy, logic, mathematics, applied sciences, and medicine. This paper delineates some specific paths through the history of the use of these “loose concepts”. Vagueness was avidly discussed in the fields of logic and philosophy during the first decades of the 20th century—particularly in Vienna, at Cambridge and in Warsaw and Lvov. An interesting sequel to these developments can be seen in the work of the Polish physician and medical philosopher Ludwik Fleck.Haziness and fuzziness were concepts of interest in mathematics and engineering during the second half of the 1900s. The logico-philosophical history presented here covers the work of Bertrand Russell, Max Black, and others. The mathematical–technical history deals with the theories founded by Karl Menger and Lotfi Zadeh. Menger's concepts of probabilistic metrics, hazy sets (ensembles flous) and micro-geometry as well as Zadeh's theory of fuzzy sets paved the way for the establishment of soft computing methods using vague concepts that connote the nonexistence of sharp boundaries.     

On not being rational

Summary A Bayesian decision-theoretic approach appears to me as a sensible idealization of a guide to behaviour. At the same time I would like to understand why my behaviour is not always of this form: I sometimes use randomization and I sometimes find confidence intervals acceptable. Not all of my problems have an explicit cost function. Am I lazy or irrational? Do I use non-Bayesian conventions to help communicate? Is the cost of rationality-computation missing from the Bayesian model?     

An integrated AHP and VIKOR for design concept evaluation based on rough number

Design concept evaluation at the early stage of product design has been widely recognized as one of the most critical phases in new product development as it determines the direction of the downstream design activities. However, the information at this stage is mainly subjective and imprecise which only depends on experts’ judgments. How to handle the vagueness and subjectivity in design concept evaluation becomes a critical issue. This paper presents a systematic evaluation method by integrating rough number based analytic hierarchy process (AHP) and rough number based compromise ranking method (also known as VIKOR) to evaluate design concepts under subjective environment. In this study, rough number is introduced to aggregate individual judgments and preferences and deal with the vagueness in decision-making. A novel AHP based on rough number is presented to determine the weight of each evaluation criterion. Then an improved rough number based VIKOR is proposed to evaluate the design concept alternatives. Sensitivity analysis is conducted to measure the impact of the decision makers’ risk to the final evaluation results. Finally, a practical example is put forward to validate the performance of the proposed method. The result shows that the proposed decision-making method can effectively enhance the objectivity in design concept evaluation under subjective environment.     

论服饰品装饰人体部位的模糊性

服饰品作为装饰人体的配饰,品种多范围大艺术形式多样化,特性也各异。本文从服饰品对人体装饰部位的角度,探析＂模糊性＂哲学理念在创新设计中的体现,寻觅服饰品新式样模糊性的成因,进而为服饰品的创新设计点燃绽放的礼花。     

外贸函电中的礼貌策略

外贸函电是世界各国从事国际贸易活动的人们相互交流、传递信息的一种重要手段,而信函是否礼貌得体则对国际贸易活动的成功起着至关重要的作用。本文从委婉语、模糊语两个方面就如何在信函中使语言更加礼貌进行了探讨。     

城市解读--试论城市意象的模糊性及对策

文章就现代城市特色缺乏、意象衰微而提出城市意象模糊性问题,追溯了其理论与３两方面的原因。作者探讨了相关的对策理论及其非决策 之后,就所截取的城市的四个片断进行了对策性的研究,以期对提高城市意象力作出有益的探索与尝度。     

装饰画认识的模糊性

装饰画是一个笼统含糊的概念，绘画及图形的装饰性都不同程度地存在于美术创作和设计领域中。装饰画可以体现出绘画性，也可表现为图形，还也可应用为设计。     

A fuzzy group data envelopment analysis model for high-technology project selection: A case study at NASA

The assessment and selection of high-technology projects is a difficult decision making process at the National Aeronautic and Space Administration (NASA). This difficulty is due to the multiple and often conflicting objectives in addition to the inherent technical complexities and valuation uncertainties involved in the assessment process. As such, a systematic and transparent decision making process is needed to guide the assessment process, shape the decision outcomes and enable confident choices to be made. Various methods have been proposed to assess and select high-technology projects. However, applying these methods has become increasingly difficult in the space industry because there are many emerging risks implying that decisions are subject to significant uncertainty. The source of uncertainty can be vagueness or ambiguity. While vague data are uncertain because they lack detail or precision, ambiguous data are uncertain because they are subject to multiple interpretations. We propose a data envelopment analysis (DEA) model with ambiguity and vagueness. The vagueness of the objective functions is modeled by means of multi-objective fuzzy linear programming. The ambiguity of the input and output data is modeled with fuzzy sets and a new α-cut based method. The proposed models are linear, independent of α-cut variables, and capable of maximizing the satisfaction level of the fuzzy objectives and efficiency scores, simultaneously. Moreover, these models are capable of generating a common set of multipliers for all projects in a single run. A case study involving high-technology project selection at NASA is used to demonstrate the applicability of the proposed models and the efficacy of the procedures and algorithms.