Iranian journal of fuzzy systems
Volume:19 Issue: 3, May-Jun 2022

This paper presents two approaches for testing quality to make adecision based on the extended process capability indices. Common methodsin measuring quality of the manufactured product have widely focused on theprecise specification limits, but in this study the lower and upper specificationlimits are considered as non-precise/fuzzy sets. Based on  a general statistical approach using an extended process capability index, the purpose of this study is  estimating a critical value  to determine whether the process meets the customer requirements. Moreover, a simulation approach to analyze the manufacturing process capability has been suggested for testing quality based on fuzzy specifications by normal data. Meanwhile, this paper discusses howwell the Monte Carlo simulation approach can be used for non-normal data.Finally, the real application of the proposed methods is investigated in a realcase study.

This paper proposes a novel method for the construction of a fuzzy metrics and demonstrates application in image segmentation. Some new properties of t-norms, t-conorms, aggregation functions, and fuzzy metrics are proved, which provides the procedures for constructing a new fuzzy metric. We prove that by applying some types of t-norms, t-conorms and aggregation functions on the sequence of fuzzy metrics, a new fuzzy metric could be obtained. The application of the fuzzy metric constructed in this way is illustrated in image segmentation by using the textsf{FCM} algorithm. For the purpose of constructing a new fuzzy metric, an extended aggregation function called generalized quasi-arithmetic mean is considered.

The notion of betweenness spaces is very important in  convex structure theory. In this paper,  it is generalized to continuous lattices. Then  its some characterizations and properties are investigated.Finally  the categorical relationship between fuzzy generalized convex spacesand fuzzy betweenness spaces is discussed by using a special antitone Galois connection.

One of the nice properties of the first-order logic is the compactness of satisfiability. It states that a finitely satisfiable theory is satisfiable. However, different degrees of satisfiability in fuzzy logics will pose various kinds of compactness in these logics.In this article, after an overview on the results around the compactness of satisfiability and compactness of $K$-satisfiability in H'{a}jek Basic logic, some new results are given around this issue.It will be shown that there are topologies on $[0,1]$ and $[0,1]^2$ for which the interpretation of all logical connectives of the Basic logic is continuous. Furthermore, a topology on first-order structures will be introduced for any similarity relation as well. Then by the same ideas as in continuous logic, the results around the compactness of satisfiability will be extended for Basic logic.

Fuzzy logic systems (FLSs) are proper tools for learning and predicting of real-world problems. Type-2 fuzzy sets are developments of the conventional type-1 fuzzy sets which are applied for prediction problems with uncertainty. Interval type-2 fuzzy logic system (IT2 FLSs) is the most wildly used type-2 FLS due to its efficiency and simplicity. Passenger demand prediction has a crucial role in the public transportation sector. Because of the nonlinearity and instability of the passenger arrivals prediction, IT2 FLS can be an appropriate method for solving this problem. In this paper, we develop a fuzzy logic system named KIT2 TSK for passenger arrivals prediction in subway stations. In our proposed model, we utilize the Kumaraswamy distribution in the construction of an IT2 TSK FLS. Furthermore, we develop a new input selection measure that applies the Schweizer–Sklar t-conorm operator in the variable selection process. The flexibility of the Kumaraswamy distribution leads to the ability to approximate several distributions using the same equation by different values for its shape parameters. Utilizing this property, we adopt our proposed model for passenger arrivals prediction of one line of the Tehran subway system as a case study. Moreover, to see the results on unusual days, passenger demand on public holidays, weekends, and special events are also taken into account. The results demonstrate that our proposed methodology has better performance in the hourly prediction of passenger arrivals compared to the benchmarks. The results for the chaotic Mackey-Glass problem also show the superiority of our proposed model.

In this paper, notions of LM fuzzy topological derived internal relation space and LMfuzzy topological derived interior space are introduced.It is proved that they are categorically isomorphic to LM fuzzy topological internalrelation space and LM fuzzy topological space. Also, notions of LM fuzzy topologicalderived enclosed relation space and LM fuzzy topological derived closure space are introduced. It is proved that they are categorically isomorphic to LM fuzzy topological enclosed relation space and LM fuzzy topological space.

The current study aimed to describe the notion of the L-graph, which is constructed on a residuated lattice, presenting the idea of the maximal product of two L-graphs.    Moreover, the applied algorithm demonstrated its efficiency to a great extent to improve the educational system.    The results showed that the maximal product of both G and H and reversely, H    and  G are isomorphic L-graphs.    The maximal product of two L-graph automata was represented as a new notion,    followed by investigating their self-sufficiency conditions in two different modes.    In addition,  A(Z(G))star~A(Z(H)) and A(Z(H))star~A(Z(G))  were proved as two isomorphic-related L-graph automata considering the residuated lattice properties.    Then, correlations among A(Z(G))star A(Z(H)),  A(Z(G)),  and A(Z(H)) behaviors were explained.    As a result, some theorems of the relationship between L-graph automata and their maximal product were introduced.    Subsequently, some related theorems were proved, and several examples were provided to illustrate these new notions. Further, an application of the maximal product of two related L-graph automata was expressed in the factors affecting the spared of the coronavirus,  and accordingly,    some solutions were suggested to reduce the spread of the virus.

In this article, we propose a new distance measure between intuitionistic fuzzy sets(IFSs), which takes into account the membership degree, non-membership degree, and their difference between membership and non-membership degree of intuitionistic fuzzy sets, as well as the exponential distance measure to avoid information loss. Meanwhile we prove that it satisfies the axiomatic definition of distance measure, and do comparison analysis with some widely used distance measures. Finally, we apply our distance measure in pattern recognition, these results show that our distance measure can significantly overcome the drawback of information loss and have more widely application scope.

Connectivity is an inevitable part of fuzzy graph theory. This article discusses about a parameter in  fuzzy graph theory termed as   neighborhood connectivity index. Several bounds and index values of structures like trees, cycles and complete fuzzy graphs are obtained. Generalized formula for neighborhood connectivity index of fuzzy graphs obtained by operations like union, join, composition, Cartesian product and tensor product are also developed. An algorithm for finding neighborhood connectivity index is also proposed. On practical grounds, a human trafficking problem is discussed as a real-life application.

Different extensions of fuzzy sets like intuitionistic, picture, Pythagorean, and spherical have been proposed to model uncertainty. Although these extensions are able to increase the level of accuracy, imposing rigid restrictions on the grades are the main problem of them. In these types of fuzzy sets, the value of grades and also the sum of them must be in the closed unit interval of [0, 1]. The sum condition seriously restricts the eligible values for grades. q-rung orthopair and T-spherical fuzzy sets have been introduced to establish a framework to tackle the mentioned problem for two-grade and three-grade fuzzy sets, respectively. Reducing the value of grades by means of power operator is the backbone idea of the both sets. However, these fuzzy sets are suffering from two drawbacks. The first one arises from the fact that there is no automatic structure to identify a proper power. Also, information loss is the other one which affects the accuracy of the decision-making process. This problem is a damaging consequence of changing the values of the grades. This paper introduces a novel reducing strategy to improve q-rung orthopair and T-spherical fuzzy sets by tackling the mentioned drawbacks. The proposed strategy solves out the former problem by establishing an automatic framework for finding a proper power which guarantee enough reduction of the values. The automatic framework is used for reducing the value of the maximum grade. Besides, the novel strategy reduces the rest of the grades according to their distance with the the maximum grade and it’s reduction rate. This paper proves mathematically that the ratio between the grades before and after of the reduction process will be intact, which results in solving information loss problem. Moreover, the higher accuracy level of the novel reduction strategy in comparison with the preceding methods, q-rung orthopair and T-sipherical fuzzy sets, is shown via different examples.

In real life, occurrences of a series of things are supposed to come in an order. Therefore, it is necessary to regard sequence as a crucial factor in managing different kinds of things in fuzzy environment. However, few related researches have been made to provide a reasonable solution to this demand. Therefore, how to measure degree of uncertainty of ordinal fuzzy sets is still an open issue. To address this issue, a novel ordinal fuzzy entropy is proposed in this paper taking orders of propositions into consideration in measuring level of uncertainty in fuzzy environment. Compared with previously proposed entropies, effects on degrees of fuzzy uncertainty brought by sequences of sequential propositions are embodied in values of measurement using proposed method in this article. Moreover, some numerical examples are offered to verify the correctness and validity of the proposed entropy.

The main goal of this paper is to study universal and existential quantifiers on involutive monoidal t-norm based algebras, which are algebraic semantics for the logic of involutive left-continuous t-norms and their residua, and the resulting class of algebras will be called monadic IMTL-algebras. First we study some of their related algebraic properties and prove that the variety of monadic IMTL-algebras is the equivalent algebraic semantics of monadic predicate fuzzy logic $mathbf{mMTL_{forall}}$, which is equivalent to the modal fuzzy logic $mathbf{S5(IMTL)}$, and show the completeness for $mathbf{IMTL_{forall}}$ via functional monadic IMTL-algebras. Moreover we start a systematic study of monadic algebraic structures that related to the monadic IMTL-algebras, some of which constitute the monadic MTL-algebras, monadic WNM-algebras, monadic NM-algebras, monadic BL-algebras, monadic MV-algebras and monadic Boolean algebras.Finally we give some representations of monadic IMTL-algebras. In particular, we character representable and directly indecomposable monadic IMTL-algebras by monadic filters.