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1 – 10 of over 17000The problem of expanding a meaningful entropic theory for fuzzy information cannot be thought of as being a mere (more or less formal) extension of Shannon theory. By using the…
Abstract
The problem of expanding a meaningful entropic theory for fuzzy information cannot be thought of as being a mere (more or less formal) extension of Shannon theory. By using the information theory of deterministic functions, the present author had already obtained some results in this way, and he herein continues this approach. After a short background on the different entropies of deterministic functions and on membership entropy of fuzzy sets, successively mixed entropy of fuzzy sets, joint membership functions of independent fuzzy sets, and conditional entropy of fuzzy sets with respect to other fuzzy sets are considered; the problem of defining transinformation between fuzzy sets, as a generalisation of the well known Shannon concept, is then examined. One of the conclusions of the article is that it is possible to build up a meaningful information theory of fuzzy sets by using the entropy of deterministic functions.
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This paper is a continuation of our paper10,11 and formulates a fuzzy team decision problem of type 2. The concept of fuzzy sets of type 2 is introduced to formulate the team…
Abstract
This paper is a continuation of our paper10,11 and formulates a fuzzy team decision problem of type 2. The concept of fuzzy sets of type 2 is introduced to formulate the team decision processes which contain fuzzy‐fuzzy states, fuzzy‐fuzzy information functions, fuzzy‐fuzzy information signals, fuzzy‐fuzzy decision functions and fuzzy‐fuzzy actions. After some definitions of fuzzy‐fuzzy relations and fuzzy‐fuzzy mappings, a model of fuzzy team decision of type 2 is proposed.
Addresses the problem of matching two fuzzy sets. Proposes a matching method that considers the extent to which both fuzzy sets have the same meaning. For a given degree of…
Abstract
Addresses the problem of matching two fuzzy sets. Proposes a matching method that considers the extent to which both fuzzy sets have the same meaning. For a given degree of similarity between two sets, the same meaning decreases as the fuzziness increases and, in particular, for equal fuzzy sets the degree of matching is a function of the fuzziness only. A complete matching of two sets is obtained only when they are equal and crisp. Finally, the inverse problem is studied, of characterizing one of the sets used in the match when knowing the other set and the result of the matching.
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Jian‐Gang Tang, Mao‐Kang Luo and Miao Liu
The purpose of this paper is to study free L‐fuzzy left R‐module, using the language of categories and functors for the general description of L‐fuzzy left R‐modules generated by L…
Abstract
Purpose
The purpose of this paper is to study free L‐fuzzy left R‐module, using the language of categories and functors for the general description of L‐fuzzy left R‐modules generated by L‐fuzzy set. In the language of categories and functors, an L‐fuzzy left R‐modules generated by L‐fuzzy set is called a free object in the category of L‐fuzzy left R‐modules determined by L‐fuzzy set.
Design/methodology/approach
Category theory is used to study the existent quality, unique quality and material structure of L‐fuzzy left R‐modules generated by L‐fuzzy set.
Findings
The paper gives the uniqueness, structure and existence theorems of free object in the category of L‐fuzzy left R‐modules determined by L‐fuzzy set, and the authors prove that the fuzzy free functor is left adjoint to the fuzzy underlying functor.
Research limitations/implications
Some property of free L‐fuzzy left R‐modules will need to be further researched.
Originality/value
The paper defines a new class of L‐fuzzy left R‐modules, i.e. free L‐fuzzy left R‐modules, research and explore free L‐fuzzy left R‐modules in theory.
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P. Baguley, T. Page, V. Koliza and P. Maropoulos
Time to market is the essential aim of any new product introduction process. Performance measures are simple quantities that indicate the state of manufacturing organisations and…
Abstract
Purpose
Time to market is the essential aim of any new product introduction process. Performance measures are simple quantities that indicate the state of manufacturing organisations and are used as the basis of decision‐making at this crucial early stage of the process. Fuzzy set theory is a method for using qualitative data and subjective opinion. Fuzzy sets have been used extensively in manufacturing for applications including control, decision‐making, and estimation. Type‐2 fuzzy sets are a novel extension of type‐1 fuzzy sets. Aims to examine this subject.
Design/methodology/approach
This research explores the increased use of type‐2 fuzzy sets in manufacturing. In particular, type‐2 fuzzy sets are used to model “the words that mean different things to different people”.
Findings
A model that can leverage design process knowledge and predict time to market from performance measures is a potentially valuable tool for decision making and continuous improvement. A number of data sources, such as process maps, from previous research into time to market in a high technology products company, are used to structure and build a type‐2 fuzzy logic model for the prediction of time to market.
Originality/value
This paper presents a demonstration of how the type‐2 fuzzy logic model works and provides directions for further research into the design process for time to market.
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Amit Kumar, Shiv Prasad Yadav and Surendra Kumar
The purpose of this research is to develop a new approach for analyzing the fuzzy reliability of a series and parallel system. Also to introduce definition of L‐R type interval…
Abstract
Purpose
The purpose of this research is to develop a new approach for analyzing the fuzzy reliability of a series and parallel system. Also to introduce definition of L‐R type interval valued triangular vague set and certain Tω‐based arithmetic operations between two L‐R type interval valued triangular vague sets.
Design/methodology/approach
In the proposed approach using a fault tree an interval valued vague fault tree is developed for the system in which the fuzzy reliability of each component of the system is represented by a L‐R type interval valued triangular vague set. Then with the help of a developed interval valued vague fault tree an algorithm is developed to analyze the fuzzy system reliability.
Findings
For numerical verification of the proposed approach the fuzzy reliability of the basement flooding has been analyzed using the existing approaches and the proposed approach. Comparing the results of existing approaches and the proposed approach, it has been shown that the uncertainty about the reliability is minimized using the proposed approach and the results are exact. While using the existing approaches the results are approximate due to approximate product of triangular vague sets and interval valued triangular vague sets.
Originality/value
The paper introduces a new approach for analyzing the fuzzy system reliability using Tω‐based arithmetic operations over L‐R type interval valued triangular vague sets.
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Two solution concepts for a FMP problem are suggested. The first one makes use of level sets of the fuzzy set of feasible alternatives. The second solution is based on the concept…
Abstract
Two solution concepts for a FMP problem are suggested. The first one makes use of level sets of the fuzzy set of feasible alternatives. The second solution is based on the concept of Pareto maximum in vector optimization. It is shown that both solutions are equivalent in a sense that they give the same fuzzy value of a function maximized. It is suggested that if a decision‐maker is to choose a single element, then his choice must be based not only on the membership value of this element in the solution fuzzy set but also on the corresponding value of the function maximized. In this respect the situation is similar to that typical for vector optimization. The approach suggested in this paper is further used for analysing games with fuzzy sets of strategies of the players. A fuzzy equilibrium solution is introduced, which can provide a base for an agreement between the players.
R. Kleyle, A. de Korvin and T. McLaughlin
In this paper we discuss a mechanism for making business decisions on the basis of an expected penalty function associated with cost variance. We assume that the decision maker is…
Abstract
In this paper we discuss a mechanism for making business decisions on the basis of an expected penalty function associated with cost variance. We assume that the decision maker is knowledgeable of the economic environment in which the decision will be made, but that he has no hard data” such as a market research report. In this setting fuzzy logic is more applicable than ordinary statistical decision theory. We develop a method of computing a fuzzy expected penalty based on a fuzzy distribution of cost variance and a fuzzy penalty function. These fuzzy expected penalties are then defuzzified” so that a non‐fuzzy decision can be made.
D. Dutta Majumder and Kausik Kumar Majumdar
In this paper, we present a brief study on various paradigms to tackle complexity or in other words manage uncertainty in the context of understanding science, society and nature…
Abstract
In this paper, we present a brief study on various paradigms to tackle complexity or in other words manage uncertainty in the context of understanding science, society and nature. Fuzzy real numbers, fuzzy logic, possibility theory, probability theory, Dempster‐Shafer theory, artificial neural nets, neuro‐fuzzy, fractals and multifractals, etc. are some of the paradigms to help us to understand complex systems. We present a very detailed discussion on the mathematical theory of fuzzy dynamical system (FDS), which is the most fundamental theory from the point of view of evolution of any fuzzy system. We have made considerable extension of FDS in this paper, which has great practical value in studying some of the very complex systems in society and nature. The theories of fuzzy controllers, fuzzy pattern recognition and fuzzy computer vision are but some of the most prominent subclasses of FDS. We enunciate the concept of fuzzy differential inclusion (not equation) and fuzzy attractor. We attempt to present this theoretical framework to give an interpretation of cyclogenesis in atmospheric cybernetics as a case study. We also have presented a Dempster‐Shafer's evidence theoretic analysis and a classical probability theoretic analysis (from general system theoretic outlook) of carcinogenesis as other interesting case studies of bio‐cybernetics.
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In the present literature on fuzzy sets and fuzzy information, there is much confusion between entropies of fuzzy sets and fuzzy sets of entropies. After a thorough critical…
Abstract
In the present literature on fuzzy sets and fuzzy information, there is much confusion between entropies of fuzzy sets and fuzzy sets of entropies. After a thorough critical review of this question, proposes a unified approach based on the theory of deterministic functions. One must carefully distinguish between index of fuzziness, uncertainty of fuzziness and uncertainty of randomness on the one hand; and uncertainty of fuzzy sets and uncertainty of possibility on the other hand. This new framework could provide new approaches to management of uncertainty originating from both probability and possibility distributions.
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